The Universe in a Toy 1.Speed, velocity, acceleration 2.Acceleration due to gravity 3.Kinetic Energy 4.Thermal Energy 5.Gravitational potential energy 6.Electric potential energy 7.Momentum 8.Conservation of energy and momentum 9.Conservation of angular momentum 10.Inertia (Newton's First Law) 11.Newton's Second Law 12.Newton's Third Law, Part 1 13.Newton's Third Law, Part 2 porcelain enamel ceramics. References Ehrlich, Robert, "Why Toast Lands Jelly-Side Down," 1997 (Princeton University Press, Princeton) Ehrlich, Robert, "Turning the World Inside Out," 1990 (Princeton University Press, Princeton) Taylor, Beverley A.P., Poth, James, Portman, Dwight J., "Teaching Physics with Toys," 1995 (Learning Triangle Press, Middletown, OH) Bloomfield, Louis A., "How Things Work," 1997 (John Wiley & Sons, New York) 1. Speed, Velocity, Acceleration Speed: The change in distance over a given time interval, measured in km/sec, or m/sec (for example). Velocity: 1) The change in distance in a given direction over a corresponding change in time; 2) Speed with an attitude. Acceleration: A change in the magnitude or direction of the velocity. Materials Wind-up toy Ruler Stop watch Procedure Using the ruler and the stop watch, find the speed of the toy by calculating the distance (in millimeters) the wind-up toy moved over a given time interval. Demonstrate or explain "speed," hopefully keeping the wind-up toy going in a certain direction. Demonstrate or explain "acceleration." Use the equations: speed = [distance traveled] / [time it took] s = x/t Put in some figures and calculate the speed (average velocity). Questions How do you know something is moving? When you see a object moving backward or forward or sideways or up or down. What does it mean to say something is moving faster or slower than something else? Accelerating is moving faster and decelerating is moving slower. When something is moving faster at 55 mph or slower at 30 mph. How does velocity differ from speed? Velocity is a measure of a bodies speed and direction Velocity is galaxies moving farther away from each other is known as the red shift. As light from distant galaxies approach earth there is an increase of space between earth and the galaxy, which leads to wavelengths being stretched. The Hubble Law is a observed relationship between recession velocity determined from redshifts and distance determined independently using standard candles, etc. the object's recessional velocity. What is acceleration (deceleration)? Acceleration is speeding faster, and deceleration is slowing down. Acceleration is a change in a bodies speed or direction of motion When radar catches you going above the speed limit, are you getting a ticket for "speeding" or "velocitying"? Yes for speeding. 2. Acceleration Due to Gravity Materials Marbles of various sizes An extremely light ball of comparable size to one of the marbles Procedure Newton's law of universal gravitation is written as: Fg = G (M1M2)/D2 Explain each symbol and the whole equation. For an object on or near the surface of the Earth, D is approximately equal to the radius of the Earth. F is for force g is for gravity G gravity M is Mass 1 M is Mass 2 D Distance. Marbles small size can be tossed in the air faster. Explain the basics of the universal law of gravity: one explains then moon's orbit by reasoning from the motion of a falling apple by measuring how far it falls in one second. Newton's laws of motion and his law of universal gravitation provided a theoretical explanation for Kepler's empirical laws of planetary motion. Because the Sun and a planet feel equal and opposite gravitational forces by Newton's third law, the Sun must also move (by Newton's first law).

astro101a02.html Assignment 2 Review and Thought Questions From the text: pages 54-55: 4, 5, 9, 11, 12 (#21 is optional) Chapter 2 4. Explain how Kepler was able to find a relationship (his third law) between the periods and distances of the planets that did not depend on the masses of the planets or the Sun. Kepler's third law States that the square of a planet's orbital period is proportional to the cube of its average distance from the Sun (semimajor axis), which tells us that more distant planets move more slowly in their orbits. In its original form, written p2 = a3. See also Newton's version of Kepler's third law. 5. Write out Newton's three laws of motion in terms of what happens with the momentum of objects. Newton's first law of motion States that, in the absence of a net force, an object moves with constant velocity. Newton's second law of motion States how a net force affects an object's motion. Specifically: force = rate of change in momentum, or force = mass acceleration. Newton's third law of motion States that, for any force, there is always an equal and opposite reaction force. 9. What is the momentum of a body whose velocity is zero? How does Newton's first law of motion include the case of a body at rest? Newton's first law of motion States that, in the absence of a net force, an object moves with constant velocity. 11. A body moves in a perfectly circular path at constant speed. Are there forces acting in such a system? How do you know? You float while inside a space station. Your in a free falling weightless environment. Gravity is less inside a space station while gravity is strong on Earth. 12. As air friction causes a satellite to spiral inward closer to the Earth, its orbital speed increases. Why? Friction and Gravity may have a effect on the satellite by causing the satellite to fall into the earth faster.. 21, Newton showed that the periods and distances in Kepler's third law depend on the masses of the objects. What would be the period of revolution of the Earth (at 1 AU from the Sun) if the Sun had twice its present mass? Activity 1: "The Universe in a Toy" A Student Activity Using Toys to Demonstrate the Physics of the Universe Introduction Modern-day astronomy is the application of terrestrial physics to the rest of the Universe. The move from superstition and astrology to a mathematical view of our cosmos was secured by the extensive work of Sir Isaac Newton. The work of Newton and others to follow led to our understanding of the physical Universe. So fundamental are these concepts today and so pervasive in our everyday life, the physics can be demonstrated using toys! One of the top ten reasons to become a physicist: you get to play with toys (sometimes really big toys, like rockets, or for astronomers, huge telescopes). Each of the following topics leads to a demonstration of that concept. Look around you. Do you know how much physics is involved in your everyday playing? You are going to find out. You will also learn that it is not such a huge step to apply the physics we use here on Earth to objects and processes in the Universe.

Procedure Listed below are 14 topics, each leading to a different demonstration using toys. The idea is for you to take the time and demonstrate (whether just for yourself, or your friends and family) the physics. It won't be the same if you just think about doing it-you simply will not learn as much, and the demonstration won't mean as much (you have our permission to play). So, pick two (2) of the demonstrations. It would be more economical if you picked those where you actually have the toys around, or similar items that may be substituted. What to Turn In A one- or two-paragraph summary of how the demoue to the planet's gravitational pull. Every mass attracts every other mass through the force called gravity. The force of attraction between any two objects is directly proportional to the product of their masses. The force of attraction between two objects is inversely proportional to the square of the distance between them. Show that objects of different sizes and weights all fall with the same acceleration. The reason needs Newton's second law of motion, a = F/m, to explain completely. You can show this empirically or mathematically (or both). Questions In your own words, state why the balls all hit the floor at the same time. The surface gravity of the Moon is about one-sixth that of Earth. Will objects fall with the same acceleration on the Moon as they do on Earth? The balls hit the earth at the same time due to the gravity. and the force involved when dropping the balls onto the floor at the same time. Objects do not have the same acceleration on the moon. The Moon has no atmosphere. What will happen if you drop a hammer and a feather on the Moon (the Apollo 15 astronauts demonstrated this)? Floating feather on the moon. a hammer and feather falling at the same rate in the lunar vacuum. hammer hits the ground first on Earth. Your weight is the measure of the Earth's force of gravity on you (and of your force pulling back on the Earth). Would this force be slightly greater or slightly less if you were standing on top of Mt. Everest? Explain. What's wrong with this statement: "There is no gravity in space." Answer convincingly. Earth's force of gravity would be less on you if you were on top of Mt. Everest since you are farther above the surface of the Earth. Kinetic Energy: The energy possessed by an object in motion. Materials 4 Candy Bars (keep 3 in a paper bag) Procedure The kinetic energy of an object is equal to half of its mass times its velocity squared; or, more simply: KE = 1/2 mv2. For this demonstration, emphasize how the kinetic energy of an object depends on its mass and its velocity. Give a couple of everyday examples of your choosing before moving onto the candy bar. Mention the unit measure for energy, the joule. We are actually familiar with a joule, even though we don't use the term: a watt is 1 joule per second. So, a 100-watt light bulb produces 100 joules of energy per second. This is a mathematical demonstration. You may wish to keep three of the candy bars in the paper bag while going through the following steps: Metabolizing a candy bar releases about a million joules of energy for your body (!). For simplicity, assume the candy bar has a mass of 0.1 kg. Hold up the candy bar and ask, "How fast must I throw the candy bar to have the same amount of kinetic energy?" Throw slowly. Turn the problem around. You now want to throw the candy bar at 2 times the original velocity. How many candy bars must you eat to obtain the same amount of energy? (Answer: 4 candy bars) Questions Two asteroids are heading towards Earth at the same velocity. One asteroid is twice as massive as the other. How much more kinetic energy does it have than the other one? 2 times more kinetic energy. Two identical comets are heading towards Earth, but one has twice the velocity as the other. How much more kinetic energy does it have? 2 times more kinetic energy. You drop a ball from a ledge. Where does it get its kinetic energy? During the time when the ball starts to drop from the ledge. A ball sitting on the side of a ledge contains stored energy. How are kinetic energy and momentum related? Kinetic Energy is the energy of motion Momentum is a quantity which is mass times the velocity of an object. Give another realistic example where you compare the kinetic energy of two objects. you tip the rock and it rolls down the hill, converting the potential energy into kinetic energy. Force is a quantity which can change the momentum of an object. Energy is a measure of the amount of work a system can do. 4. Thermal Energy (Temperature and Heat) Thermal Energy: Energy contained within a substance as measured by its temperature. Materials Stove Water Pan Procedure When the water is cool, the average kinetic energy of the particles (temperature) is small. As we apply heat to the water, the thermal energy from the heating element is transferred to the water molecules and increases their kinetic energy. As more heat is applied, the kinetic energy continues to increase. Heat the water until boiling, 100 degrees Celsius or 212 degrees Fahrenheit or 373 Kelvin. Heat your oven to the same temperature. Mentally picture what would happen if you stuck your hand in the boiling water versus into the middle of the oven. Questions What is the difference between temperature and heat? Temperature is 212 degrees telling you how hot the water is or 30 degree is how cold the water is. Or 80 degrees outside weather. Heat is you feel how warm it is in the summer or how cold it is in the winter, Why would your hand get burned if placed momentarily in the boiling water, but not if you stuck your hand in a 100 degree Celsius oven? The boiling water is 212 degrees hot water that can burn a hand. The Celsius oven contains no water to burn a hand. Pressure cookers are making a comeback. Why does the pressure increase in the cooker as the contents get hotter? It's pressure inside the pressure cookers when the lid is secured on top. It is thousands of degrees in low-Earth orbit; however, astronauts must wear heated spacesuits and gloves. Why do the astronauts feel cold despite the high temperature? Because it is very cold well below -212 degrees below 0 degrees. Very cold weather makes it feel so cold when no outside heat is present. This is meant to be an easy question: you fill the cold porcelain bath tub with very hot water. Why does the water cool and the tub heat? Explain what happens on the particle (microscopic) level. The material of the bathtub is made of porcelain enamel ceramic materials keeps the water cool. Cool water can quickly have change in hot water. 5. Gravitational Potential Energy Gravitational Potential Energy: Energy stored for later release as kinetic energy as a function of the objects mass, the strength of gravity, and the distance the object falls. GPE = mass * gravity * height. GPE = mgh Materials Two balls of the same size but different mass. Small step ladder or a book shelf Procedure The purpose of this demonstration is to define gravitational potential energy (GPE; also called gravitational energy) and show how this potential energy gets gradually converted into kinetic energy and finally thermal energy. The conversion of gravitational potential energy into kinetic (and thus to thermal energy) helps explain everything from the speed at which objects fall to the ground to the formation processes of stars and planets. Measure the height of the step ladder or the book shelf and mark the levels at 1/2, 1/3, and 1/4 the total height. Compare the relative GPE of one of the balls at different heights (these are estimates since you probably do not know the exact mass of each ball). Compare the relative GPE of the two balls at the same height. Discuss where the balls have the most GPE; where they have a combination of GPE and KE, and where the balls have all kinetic energy. Questions Will it hurt more if you fall out of a window on the 1st floor or the 2nd floor of your house? Why, exactly? It would hurt more from fall out of the 2nd floor window it is higher above the ground compared to the first floor window. What happens (theoretically; don't really do this experiment) to the gravitational potential energy you had before you fell? The energy disappears from you, decreases. At what point do you have the greatest kinetic energy? What happened to that kinetic energy (since energy is conserved) after you hit the ground? When I start falling is when I have the greatest kinetic energy. When hit the ground is when having the greatest kinetic energy since the ground stops your free fall. Rain drops actually heat the air they fall through, albeit a miniscule amount. Why? Rain drops heat due to sunlight or the heating of the air. Somethings heat when they are in motion. Friction. Heat. Gravity. Harder question: If dropped from the same height, which ball will have the greatest kinetic energy just before it hits the floor and why? The smaller ball would have the greatest kinetic energy it is smaller in size and moves faster. 6. Electric Potential Energy Electric Potential Energy: Energy accumulated and stored through the movement of an electrical charge. Materials Balloon Tissue paper or packing popcorn Head of dry hair Procedure Blow up the balloon. Shred the tissue paper or break the packing popcorn into smaller pieces. Demonstrate and explain what is happening when the balloon is rubbed on (non-oily, not-hairsprayed, unconditioned, fly-away) hair and held over the tissue pieces. The balloon gets charged as your hair adds electrons to the surface. When the balloon nears the tissue, the negative charge of the balloon attracts the positive charges of the atoms or molecules (actually, the negative charge repels the negative charges in the atoms or molecules, but the end effect is the same). There is electric potential energy built up between the balloon and the tissue pieces. Questions What is electric potential? negative charge and positive charges in the atoms or molecules. energy built up between the balloon and the tissue pieces. What eventually happens to the potential energy built up on the balloon? When you take the balloon away, some of those electrons stay with the balloon, giving it a negative charge. What does it mean when we state that an electron in an excited atom has potential energy? excited electron cascades back down to the ground state, the atom may emit many photons, each with a different energy and a different color, and the resulting spectrum shows many distinct spectral lines. the energy causes an electron to jump a higher excited state Excited State an electron orbital at a higher energy than the ground state What are the "energy levels" for electrons in atoms? excited state and ground state. Static electricity built up in your clothes dryer when fabric softener is not used, and your socks stick to your towels and sheets. As you pull the socks off, you are generating electric potential energy between the charged items. What happens to this potential energy? Where does it go? The potential energy is being transferred into ground states or is being transferred to socks. 7. Momentum and Force Momentum: The mass of an object times its velocity. Force: Anything that causes a change in momentum (a net force will cause acceleration). Materials Large toy car Small plastic bug Large marble or comparably sized rock Procedure It is hard to believe that the momentum of a very massive object will be changed by a very small object, but since momentum is conserved, this must be true. Write down the mathematical equation for momentum and explain it. Demonstrate and compare the effects of having a bug hit the windshield of your car vs. a big marble. Both transfer some of their momentum to the car. Which one transfers more? Why? Which will exert the greatest force on the car? (We are talking about linear momentum here, as opposed to angular momentum.) The marble would transfer more momentum to the car since the marble is larger compared to the bug which is smaller. More force on the car comes from the marble. Questions: Assume the bug has a mass of 0.001 kg. Assume the large marble has a mass of 0.1 kg. Let's say the marble hit the car with a velocity of 10 m/sec. How fast would the bug have to be traveling to exert the same force? (Hint: the force is the change in momentum of the bug. Since the bug has zero momentum after the hit, the force will be equal to the momentum of the bug the instant before it hits.) 20 m/sec. Two trucks are traveling down the highway at the same speed. One truck is a triple-trailer, long-haul, 18-wheeler while the other is a small pick-up truck. Which truck will be harder to stop, and (using the correct words) why? The small pick-up truck would be harder to stop since it is not as big of a truck. Your 80-pound lab retriever is so happy to see you that he runs up at full speed and jumps on you. Do a physics "play-by-play" describing what happens. Use words like momentum and force in your description. If you were standing still, what was your momentum before your lab hit? The force of the full speed is slowed down by the momentum once the lab retriever jumps on you. My momentum was normal. A bug hits your windshield while driving and the bug does not bounce off. The car changed the momentum of the bug. Since the bug originally had some velocity, it also had kinetic energy. Since energy is conserved, where did the kinetic energy of the bug go? The kinetic energy of the bug went into the bug. The asteroid Ida has a tiny moon named Dactyl. Assume Ida is approximately 900 times as massive as Dactyl. (This is very rough as both are irregularly shaped and we don't know their densities very accurately.) If both are traveling towards Earth at the same velocity, how much more momentum does Ida have than Dactyl? Which one will take more force on our part to divert from crashing into the Earth? Ida has about a lot more momentum. Ida would be harder to divert due to it's size. 8. Conservation of Energy and Momentum Conservation of Momentum and Energy: Energy can change from one form to another, but the total energy in a (closed) system stays the same. The total momentum in a closed system stays the same. Materials Basketball Tennis Ball Paper towel roll cut to about 1-inch height Procedure Balance the tennis ball on top of the basketball using the cut paper towel roll to keep the tennis ball from rolling off. The tennis ball should be exactly on top of the basketball. Predict how high the tennis ball will bounce before you drop the two balls. Drop the basketball (again, making sure the tennis ball is exactly on top). The two balls will fall with the same acceleration to the floor. The basketball hits and has its momentum changed. Since the tennis ball has less mass and momentum is conserved, the momentum from the basketball gets translated into an increase in the tennis ball's velocity. The tennis ball bounces roughly 3-4 times higher than the height from which it was dropped. Questions Think about the various kinds of energy present in this demonstration: GPE, KE + GPE, KE; elastic energy; KE. What does it mean when energy is conserved when applied to this toy? The energy is conserved somewhere inside the toy. Potential energy turns into kinetic energy if the toy is moving, What would happen if you dropped two basketballs in a similar fashion, one on top of the other? (If you are not sure, then any two alike balls will test your hypothesis.) The ball falling on top of the ball would roll off the ball causing both balls to move. What would happen if the differences in the sizes and masses of the balls were even greater than a basketball and a tennis ball? It would be in slower motion since they are heavier. Research the chapter and future lecture on supernovae explosions. Briefly summarize what happens during the collapse and explosion stages. supernovae? Is there more than one way for a supernova explosion to occur? The answer is yes. To understand the alternative supernova mechanism, we must reconsider the long-term consequences of the accretion-explosion cycle that causes a nova. A nova explosion ejects matter from a white dwarfs surface, it does not necessarily expel or burn all the material that has accumulated since the last outburst. there is a tendency for the dwarfs mass to increase slowly with each new nova cycle. How does the material from a supernova explosion (the super-energetic explosion of a massive star) obtain such high velocities? supernovae violent death of a star, they tend to form lots of strange elements. The material in this meteorite could have been formed by being near a supernova when it exploded there is naturally a huge blast wave which accompanies this stellar explosion. In addition to scattering strange elements like this into our neighborhood, the blast wave itself. 9. Conservation of Angular Momentum Angular Momentum: The mass of an object spinning, times its speed around the circle, times the radius of the circle (mass * v * r). In the absence of a torque (a twisting force), angular momentum is conserved-the total angular momentum of a system remains constant. Materials Plastic tube Fishing line Weight Large washer as a pull Procedure Angular momentum conservation is especially important in astronomy. It explains the motions of planets in eccentric orbits, the rapid spin of a neutron star, an accretion disk in a binary system, and the formation of a galaxy. The string should be through the tube, with a weight on one end of the string, and a pull on the other. With the string at its greatest length, whirl the weight around. As it spins, slowly pull the string through the tube, shortening the line. Since the mass of the weight does not change and since the radius of the circle is decreasing, the velocity must increase. Be sure to write down the equation, and describe what is happening. mass velocity The string was pulled away from under the weight. Questions How is this example like an ice skater? How is it different? When a ice skater decides to spin around on the ice the ice skater would start out spinning fast, and eventually slowing down. The conservation of Angular Momentum When a spinning figure skater brings her arms in their distance from the spin center is small so her speed increases. When her arms are out their distance from the spin center is greater so she slows down. High divers must use the conservation of angular momentum in order to avoid a "belly flop," especially when doing a number of spins or rolls. Explain how they control their motion. Explain another common, everyday experience we might have that shows the conservation of angular momentum. Can control motion using hands, and legs. Regaining your balance without falling all the way down. Problem: Let's suppose a neutron star is formed from a star whose radius was originally 1,000 times greater than that of the neutron ball that remained. Assuming that there was no significant change in mass (not a good assumption, but never mind), how much faster must the neutron star be spinning than the original star? spinning faster. When the Sun turns into a red giant, it will be approximately 100 times its present size (radius will be 100 times greater). Will it be spinning faster or slower than it is today? Explain. spinning slower, The larger the object is the slower it spins. Due to less energy, and the size. 10. Inertia (Newton's First Law) Inertia: 1) An object at rest stays at rest; an object in motion stays in motion, at a constant velocity, until acted upon by an outside force; 2) Objects resist changes in their current state; 3) Newton's First Law; 4) Couch potato law. Materials: Rollerskate Stuffed toy Long board Brick or stack of books. Procedure Demonstrate and explain the law of inertia. Include a "crash test" where the skate stops but the stuffed toy keeps moving. Include a second crash test where the skate has more speed. Predict whether the toy will go farther in this case. What's Happening Both the skate and toy have inertia. A force must be applied initially to get them moving (otherwise, what would happen?). They would eventually both stop moving. Once moving they both have the same speed. When the skate stops, nothing prevents the toy from continuing to move.

Questions You are walking quickly down a path, stub your toe on a big rock, and fall forward. Why did you fall? The rock is big in size, and a lot of force comes from the rock to you when you fall forward. Hurts from rock. Toe has potential energy turns into kinetic energy when falling forward. Why do spaceships sent into outerspace keep moving? Weightless in outerspace no real gravity to interfere with the spaceships. Would the toy have more or less inertia if it weighed more? Less inertia. Think of another example of how we "use" the inertia of objects in our everyday lives. Many times we try to counteract the law of inertia. Far out in space, objects would keep moving, in the same direction, once set in motion. What would have to have happened if an object changed its motion (accelerated)? Something would have to push on the object from behind. 11. Newton's Second Law Force = mass acceleration (F = ma): 1) The acceleration of an object is proportional to the force applied and is in the same direction as the force; 2) given the same force, an object with more mass will be accelerated less. Materials Plastic ball with a plastic bat Heavy rock about the size of a whiffle ball Procedure Making sure that no one is in the direction that you will be "batting," place the rock on a ledge. Swing the whiffle bat and swing to hit the rock off. How far horizontally does it go? Now, place the whiffle ball on the ledge and swing at it. Try to use the same force each time. How far horizontally does the whiffle ball fly? In which direction does each object travel? Explain Newton's Second Law. Manipulate the equation, solving for a, the acceleration. Explain. Explain why, given the same force when thrown, the wiffle ball travels farther than the rock. Questions Explain in your own words why the ball flew in the same direction as you hit it. When I hit the ball it does go forward since a lot of inertia force is going into the ball as the ball flew in the same direction. What would it take, qualitatively, to make the rock go the same distance as the whiffle ball? The same amount of acceleration inertia force. You want to fly due north. There is a strong wind blowing from the west. You keep the same speed going, but find you are off course. Acceleration (recall) also means a change in the direction of the velocity. In which direction is the force acting? In which direction are you being accelerated? In which direction will you end up going? West, East, North East. Who would be easier to push off of a high-dive: a Sumo wrestler or a tiny female gymnast? Why? A tiny female gymnast. Weighs less smaller in mass and size. Which one will need a greater force to change the momentum? Explain in mathematical terms. a Sumo wrestler the mass, size, weight need to be less. 12. Newton's Third Law, Part 1 Newton's Third Law: For every action there is an equal and opposite reaction. Forces come in pairs. Materials Balloon Tape Fishing line Drinking straws Procedure Attach one end of the line firmly to the wall or a door. Blow up the balloon. Securely tape a short piece of a drinking straw to the balloon. Thread the fishing line through the straw. Let go of the balloon. Explain in detail what is happening in terms of action-reaction. Questions What makes a rocket rise above the surface of the Earth? Lots of force in thrust coming from the chemical reactions of hydrogen gas or liquid cooling hydrogen gas. Solid rocket propellant fuel is also used. The more rocket fuel gases being used the more likely the rocket is going to rise above the surface of the Earth. Explain the whole series of action-reaction involved in your sitting in your chair in this classroom. You can be sitting upstraight in your chair. Arms and Legs are bended while your sitting. The Earth has a huge mass compared to us measley humans. Therefore, it must be pulling on us with a much, much greater force than we are pulling on it. What's wrong with this statement? The Earths mass must be a lot since it's mass is pulling on us since we have much smaller mass. How do astronauts in orbit get around during their EVA's (Extra Vehicular Activities)? Explain in terms of action-reaction. When the astronauts float around inside a space shuttle or space station the astronauts hold on to things like a table top while they work from a computer or doing experiments, or other work. They can use their legs to jump up off the floor, or push off the wall with their hands without floating into the wall. Think of the Sun as a series of spherical layers, much like an onion. Explain the action-reaction series clear down to the core. Why do the center layers have to "push back" so hard? The hot temperatures, gravity, 13. Newton's Third Law, Part 2 Newton's Third Law: For every action there is an equal and opposite reaction. Materials Film canister-the kind with the "set-in" lid, not the wrap-around lid Alka seltzer tablets Water Paper towels Procedure Break the seltzer tablet in two pieces, and put one piece in the canister. Fill the canister half full of water. Snap the canister lid on, place the canister lid-side-down, and step back. Explain in detail what is happening in terms of action-reaction. From an unlearned point of view, how might you think this relates to astronomy? Questions How do astronauts in orbit get around during their EVA's (Extra Vehicular Activities)? Explain in terms of action-reaction. Falling freely around the earth in weightless environment above the earth. experience no force relative to the shuttle. accelerate at the same rate. Hands hold onto things to stay in one place in weightless orbit. The astronauts Think of the Sun as a series of spherical layers, much like an onion. Explain the action-reaction series clear down to the core. Why do the center layers have to "push back" so hard? What makes a rocket rise above the surface of the Earth? Force from thrust from the liquid cooling hydrogen gas. Explain the whole series of action-reaction involved in your sitting in your chair in this classroom. What's wrong with the following statement? Your in a sitting position, and your arms and legs are bended. You can move around slowly in a sitting position. The Earth has a huge mass compared to us measley humans. Therefore, it must be pulling on us with a much, much greater force than we are pulling on it. Robert Alberg Assignment 3 Activity 2: The Phases of the Moon Proceed onto the questions for this activity. These are the questions that you will be turning in to your instructor. Questions 1.(1 pt) The Earth spins on its axis once every 24 hours, making our day 24 hours long. We will loosely define a day as the length of time it takes the Sun to return to the same place in the sky at a given location. In Earth days, how long is a Moon day? the moon day is 27.3 days. Sidereal orbital period 27.3217 solar days Synodic orbital period 29.5306 solar days 2.(1 pt) We define a month to mean the length of time it takes the Moon to go through one complete cycle of phases. If you lived on the Moon, how long would it take the Earth to go through one complete cycle of phases? 30 3.(1 pt) Which of the following could never happen? a.An observer seeing a full moon in the middle of the day (local noon) b.An observer seeing a new moon in the middle of the night (local midnight) c.Both of the above observations are impossible for any observer to see. a. An observer seeing a full moon in the middle of the day (local noon). 4.(1 pt) If you see a full moon in the sky at around midnight where you live, what phase of the Moon does someone who lives on the opposite side of the Earth see at around midnight where they live? half moon. 5.(2 pts) Lives and times of the Moon: a.What time of night would it have to be for you to see the Moon at full phase on the meridian?12:A.M. ________ b.What part of the day would you be in if you saw a 1st quarter moon on the meridian? (Hint: Recall the Earth rotates counterclockwise when viewed from above.) 12:A.M. Midnight________________ c.It's noon where you live. You know that the Moon is on the meridian. Why can't you see it? (Be specific and name the phase it is in.) A lot of sunlight blocking out view of the moon.._______________________ d.What part of the day would you be in if you saw a 3rd quarter moon on the meridian? 6:AM___________ 6.(2 pts) One of the common misconceptions about the Moon going through phases is that they occur because the Moon passes through the Earth's shadow during each month. For science, it is sufficient to note just one observation that negates this "shadowed Moon" theory to have the theory thrown out as invalid. Write down one observation that you can make that makes this theory wrong. The Moon's monthly cycle of phases results from the changing angle of its illumination by the sun. The full moon is only visible at night while other phases of the moon are visible during the day. 7.(2 pts) In a well-written, short paragraph, compare what you knew about the phases of the Moon prior to this activity and how that knowledge changed upon completing this activity. I know of the full moon, half moon, and how the sunlight illumination on the moon is causing the phases from different angles. Now I know more about the other phases of the moon the waxing, waning phases. I learned how many days it takes the moon to complete a cycle of phases. I learned it takes 29.5 days for the moon to the new phase from the full phase. Just for your information, here is a table giving the approximate scaled sizes and distances for the Earth-Moon-Sun system. It is easy to see why, if we have an Earth and Moon that we can actually see and work with, we find it difficult to place them at their scaled distances, and impossible to include the Sun. Approximate Scaled Values for Sizes and Distances Earth Diameter Moon Diameter Distance: Earth to Moon Sun Diameter Distance: Earth to Sun Head: 14 cm 4 cm 4 meters 15 meters 1.6 km (1 mile) Paper Model: 7 cm 2 cm 2 meters 7.5 meters 0.8 km (0.5 miles) Sketch: 3 cm 0.8 cm 0.9 meters (1 yard) 3.2 meters 0.35 km If you need technical help, e-mail Program Support Services at You may also call (800) 543-2350; fax (206) 543-0887; or call (206) 543-0898 (TTY). Lesson Three Earth, Moon, Sun, and Sky Assignment 3. Reasons for the Seasons Why does the Earth have seasons? That is, why are the days shorter in the winter in the northern hemisphere and longer in the summer? The cycle of the seasons results from the 23 tilt of the Earth's axis of rotation. At the summer solstice the sun is higher in the sky and its rays come on to the Earth more directly causing the Earth to warm up some more while the sun is up for more than 12 hours.. in the winter solstice the Sun is low in the sky and up for fewer than 12 hours. Are the seasons more extreme at the poles or at the equator? It is more extreme at the poles since it also colder. Why is it hotter in the northern hemisphere in the summer than in the winter? the northern tip of Earth's axis starts to point more towards the Sun. The Sun is higher in the sky never overhead outside of the tropics and it rises north of east and sets north of west. Longer days with more direct sunlight heat up our hemisphere & cause summer. the sun rises exactly in the East & sets exactly in the West. When the northern end of the Earth's axis starts to have a component pointing away from the Sun, we are entering the season of days shorter than 12 hours (Fall). in the northern hemisphere we see shorter days and less direct sunlight this is because the Sun is lower in the sky all day long. It also rises more to the south of east and sets more to the south of west. Since the Sun is lower in the sky, less of its light gets spread over more of the Earth, making the rays less intense. Observations Think about how high the Sun gets in the northern summer versus the winter. Does it ever get directly overhead (at the zenith) where you live? Yes sometimes it does. About how long is the Sun up in the summer? How long in the winter? If during one day it is about 5:AM - 10:PM during the summer June 21 - September 20. If during one day it is about 7:AM - 5:PM during the winter December 21 - March 20. Travels Have you traveled anywhere where the Sun passed directly overhead? Where on Earth was that? I have not notice the sun directly overhead yet. Where would you have to go to have the Sun directly overhead twice during a year? North. What do the Tropics of Cancer and Capricorn represent? Tropic of Cancer is the parallel circle of latitude 23.5� N. Tropic of Capricorn is the parallel circle of latitude 23.5� S. Representing where the constellations Cancer and Capricorn are located. Tropics of Cancer is on the line going around Earth in the north. July 21 Aug 10. Tropics of Capricorn is on the line going around Earth in the south. Jan 21 Feb 16. How long is the night during the northern winter at the North Pole? Now read through the appropriate sections in Chapter 3, and try to answer these questions again. There is a short quiz in the self-review section of these notes that will reinforce these concepts. Phases of the Moon What does it mean, literally, when we say the Moon orbits the Earth? (Draw a sketch; put in the Earth's orbit around the Sun.) Earth is rotating and Moon is revolving Counter-Clockwise. The moon orbits the Earth The Moon moves around the Earth the same direction in which the Earth moves around the Sun. Since the Earth is moving around the Sun while the Moon tries to circle the Earth, we have two distinct months, just like we have two kinds of days solar and sidereal. Would you ever notice a full moon in the middle of the day? Yes sometimes you can see the moon in different phases in the middle of the day. Would you ever notice a quarter moon at midnight? Yes. When the Moon is full in Washington State, what is the phase of the Moon in, say, Bulgaria, on the opposite side of the Earth? New moon. If you were on the Moon, would the Earth go through phases? Yes. The sunlight creates daylight on the earth. One side of the earth is illuminated in daylight from the sun while another side of the earth is in dark. The Moon is about 30' in angular size as seen from Earth. Clearing up a misconception: is there a dark side of the Moon? Yes. It is on the far side other side of the moon is in darkness. Is it the side we never, ever see? Yes. There is a dark side of the Moon-it is the side that is facing away from the Sun. The side we never see because the Moon keeps the same side towards the Earth during its orbit is called the far side or the back side of the Moon. Take a look at this drawing and notice that there is a phase when the dark side and the far side are the same side during a full moon and a phase where we are seeing the dark side of the Moon during a new moon, although we can't see it because it is dark, and because it happens to occur during daylight. Tides; Eclipses of the Sun and Moon Review and Thought Questions From the textbook: Pages 78-79: 1, 3, 9, 11, 12, 21 Chapter 3 Review Questions 1. Discuss how latitude and longitude on Earth are similar to declination and right ascension in the sky? Latitude is the angle north or south of the equator. Longitude is the angle east or west of the prime meridian. declination Celestial coordinate used to measure latitude above or below the celestial equator on the celestial sphere. the altitude & azimuth of a star in advance from another city. The other system is known as the Equatorial system. This uses coordinates centered on the sky. The two coordinates in this system are known as Right Ascension and Declination. Declination is the star's position N or S of the celestial equator and is measured in degrees. Right ascension is measured from the N-S line which passes through the point where the ecliptic and the celestial equator cross Sun's position on the vernal equinox = 1st day of Spring. RA is therefore like longitude and declination is like latitude. 3. Make a table showing each main phase of the Moon and roughly when the Moon rises and sets for each phase. During which phase can you see the Moon in the middle of the morn- ing? In the middle of the afternoon? Full Moon phase Waxing gibbous First quarter Waxing crescent New Moon phase Waning crescent Third quarter Waning gibbous LUNAR PHASES: NEW Dark Moon FULL Whole Moon is visible QUARTER Half of Moon is visible CRESCENT Between New and Quarter GIBBOUS Between Quarter and Full WAXING Bright region of Moon is growing. WANING Bright region of Moon is shrinking. 9. Where are you on the Earth according to the following de- scriptions? (Refer back to Chapter 1 as well as this chapter.) a. The stars rise and set perpendicular to the horizon. b. The stars circle the sky parallel to the horizon. equator e. The celestial equator passes through the zenith.equator d. In the course of a year, all stars are visible. north celestial pole e. The Sun rises on September 23 and does not set until March 21 (ideally). 11, What is the phase of the Moon if it a. rises at 3:00 P.M.? third quarter b, is highest in the sky at 7:00 A.M.? New Moon c. sets at 10:00 A.M.? full moon 12. A car accident occurs around midnight on the night of a full moon. The driver at fault claims he was blinded momentarily by . the Moon rising on the eastern horizon. Should the police be- lieve him? No. 21. Suppose the tilt of the Earth's axis were only 16�. What, then, would be the difference in latitude between the Arctic Circle and the Tropic of Cancer? What would be the effect on of 23�? Where on Earth Are You? Shown below is a pictogram of the Earth, with the labels of various locations on the Earth listed. Match up the locations with the descriptions of the sky from that location. (You may need to review Chapter 1 for some of the answers.) More than one location may apply to each description-pick the most inclusive answer. Location Description of Sky c.Arctic Circle 66.5 deg N latitude n.North of the Antarctic Circle Viewing the Sun from the Earth b.North of the Arctic Circle_____ 1. The Sun can be seen at the zenith twice during the year. d.South of the Arctic Circle_____ 2. The Sun can be seen at the zenith only once during the year. h.North of the Equator_____ 3. The Sun is at the zenith on or about March 21. k.North of the Tropic of Capricorn_____ 4. The Sun is at the zenith on or about September 21. g.South of the Tropic of Cancer_____ 5. The Sun fails to rise above the horizon between March 21 and September 21. l.Tropic of Capricorn_____ 6. The Sun fails to rise above the horizon between September 21 and March 21. j.South of the Equator_____ 7. Location that is closest to the Sun at the winter solstice. o.Antarctic Circle 66.5 deg S latitude_____ 8. Location that is closest to the Sun at the summer solstice. Viewing the Celestial Sphere from Earth _f.Tropic of Cancer____ 9. North circumpolar stars are seen. e.North of the Tropic of Cancer_____ 10. North celestial pole seen at the zenith. i.Equator_____ 11. All stars rise and set. a.North Pole_____ 12. All northern stars are circumpolar. m.South of the Tropic of Capricorn_____ 13. Celestial poles are seen on the horizon. q.South Pole _____ 14. South celestial pole is seen at the zenith. p.South of the Antarctic Circle _____ 15. All southern stars are circumpolar. If you need technical help, e-mail Program Support Services at You may also call (800) 543-2350; fax (206) 543-0887; or call (206) 543-0898 (TTY). Assignment 4 Exercise Questions 1.Comment generally on the similarity and differences of of the four spectra you chose to observe in greater detail. Include in your comments the colors you observed, the intensity of these colors, and how the spacing of these colors differed. Purple was dark was wide in color from side to side. Green was bright was short in width in color from side to side. Yellow was bright and wide in width in color from side to side. Orange was bright in color and short in width from side to side. 2.How does the light that astronomers see from distant stars and galaxies tell them that the same atoms with the same properties exist throughout the universe? Why are spectral lines often referred to as "atomic fingerprints?" each absorption line is caused by a transition of an electron between energy levels in an atom. Each element has a distinct pattern of absorption lines. Once the pattern of the lines of a particular element have been observed in the laboratory, it is possible to determine whether those elements exist elsewhere in the universe simply by pattern matching the absorption lines. 3.Distinguish among emission spectra, absorption spectra, and continuous spectra in how the spectra look. Emission Spectra Electrons can also go from outer orbits to inner orbits. As electrons move closer to the nucleus, they give off energy that appears as photons. Once again, the amount of energy can be determined using E=hf=hc/. An emission spectrum will be observed when an electron goes from an outer state to an inner state. Absorption Spectra Electrons can change orbits, but the closer the electron is to the nucleus, the less energy it has. Therefore, some amount of energy is needed to move the electron to an outer orbit. This energy can come from the light that passes through the gas containing the atom in question. Energy is absorbed having an amount exactly equal to the amount of energy needed to move the electron to a higher orbit. 4.Distinguish among emission spectra, absorption spectra, and continuous spectra in how the spectra are formed physically (not geometrically). Solid bodies or dense gases or liquids give off continuous spectra. Thin cool gas will absorb certain wavelengths of a continuous spectrum of light producing an absorption spectrum. Warm gas emits certain wavelengths producing an emission spectrum. The specific wavelengths emitted or absorbed is uniquely determined by the chemical makeup of the gas. each absorption line is caused by a transition of an electron between energy levels in an atom. Each element has a distinct pattern of absorption lines. A spectrometer is a device that forms a spectrum. 5.Most elementary texts view the atom as an analogue to our solar system, a central "sun" with a number of orbiting "planets." This is a misleading picture of the atom and simply not true. Consult your text and summarize the correct way to view an atom, especially the electrons. Atoms consist of a nucleus containing one or more positively charged protons. All atoms except hydrogen also contain one or more neutrons in the nucleus. Negatively charged electrons orbit the nucleus. The number of protons defines the element (hydrogen, helium, and so on) of the atom. 6.The spectral lines that you see come from many, many hydrogen atoms, and each of those atoms has just one electron. Why then do we see more than just one spectral line (in emission or absorption) in the visible part of the spectrum? (We would see even more lines if we could see at infrared or ultraviolet wavelengths.) Explain, please. (Hint: There is a figure in the text that will help alot.) Three kinds of Spectra When we see a lightbulb or other source of continuous radiation (a) all the colors are present. When the continuous spectrum is seen through a thinner gas cloud the gas cloud's atoms produce absorption the continuous spectrum (b) When the excited cloud is seen without the continuous source behind it its atoms produce emission lines (c). We can learn which types of atoms are in the cloud from the pattern of the absorption or emission lines. Several different series of spectral lines are shown corresponding to transitions of electrons from or to certain allowed orbits. Balmer series absorption, Lyman series emission, Balmer series emission, Paschen series emission, Bracket series emission. n =2 2 3 4The Bohr Model for Hydrogen. 4.16 figure Energies called energy levels. 7.What is the mystery gas? How do you know? 8.Examine the following spectra: Artificial Solar Spectrum Artificial Laboratory Spectum of Iron Assuming that the "artificial" solar spectrum actually represents the true spectrum, what is the evidence for the claim that iron exists in the atmosphere of the Sun? Once the inner core begins to change to iron, our high-mass star is in trouble. Nuclear fusion involving iron does not produce energy, because iron nuclei are so compact that energy cannot be extracted by combining them into heavier elements. In effect, iron plays the role of a fire extinguisher, damping the inferno in the stellar core. With the appearance of substantial quantities of iron, the central fires cease for the last time, and the star�s internal support begins to dwindle. The star�s foundation is destroyed, and its equilibrium is gone forever. Even though the temperature in the iron core has reached several billion kelvins by this stage, the enormous inward gravitational pull of matter ensures catastrophe in the very near future. A supernova can also occur when the iron core of a massive star rapidly collapses. Iron (Fe) only forms in the most massive stars at the end of a long set of reactions involving numerous nuclei. These reactions only occur in the cores of massive stars where the temperatures are extremely high. The spectrum shows a continuous spectrum with hydrogen, magnesium, iron, and sodium absorption lines. There are no emission lines present in the normal solar spectrum. 9.Spectroscopists trying to unravel the composition of stellar atmospheres wish that spectra were so easily interpreted. In reality, most stars with surface temperatures of 10,000 K or less have complex spectra, with the absorption lines of many elements overlapping across the spectrum. Take a look at the complete spectrum of the Sun below, where the spectrum has been "sliced and stacked." Where would you start in figuring out which absorption lines belong to what elements? (Seriously.) I first would look at the different colors since the different colors represent the different types of elements. Dark Purple Orange Yellow Green Dark Blue suna.jpg 10.Examine the sketch of the laboratory spectra of various elements and compare these to the "spectrum of unknown composition." Remembering that each and every line must match exactly for that element to be present: a.What elements are not in the object that produced the "spectrum of unknown composition"? b.Briefly explain the method you used to figure out the answer to the previous question. What were the main difficulties you had? c.Relate this question to the way astronomers use spectra to identify the composition of a star by summarizing the "point" of this whole lab. Review and Thought Questions Light From the text, pages 102-103: 1, 3, 5, 11, 13, 22, 23 Telescopes From the text, pages 126-127: 3, 7, 16 1. What distinguishes one type of electromagnetic radiation The electromagnetic spectrum consists of gamma rays, x rays, and ultravlolet radiadon. 3. What is a blackbody? Is this textbook a blackbody? Why or effect? Explain why. Blackbody: An ideal object that is a perfect absorber of light the name since it would appear completely black if it were cold, and also a perfect emitter of light. Light is emitted by solid objects because those objects are composed of atoms and molecules which can emit and absorb light. They emit light because they are wiggling around due to their heat content (thermal energy). So a blackbody emits a certain spectrum of light that depends only on its temperature. The higher the temperature, the more light energy is emitted and the higher the frequency (shorter the wavelength) of the peak of the spectrum. Photosphere: The surface layer of the sun where the continuous blackbody-type spectrum is produced that we directly observe when we look at the Sun. the brightness of a blackbody decreases with increasing wavelength. The pulsar observations, along with the fact that the radiation is highly polarized, tell us that the pulsar's radiation is not caused by a black body but by something called synchrotron radiation, or non-thermal radiation. 5. Explain how emission lines and absorption lines are formed. from another? V~hat are the main categories (or bands) of the emission (of light) The process by which matter emits energy in the form of light. emission-line spectrum absorption (of light) The process by which matter absorbs radiative energy. absorption-line spectrum A spectrum that co 11. What type of electromagnetic radiation is best suited to ob- serving a star with a temperature of 5800 K? 13. Go outside on a clear night and look carefully at the bright- est stars. Some should look red and others blue. The primary 22. What is the temperature of a star whose maximum light is emitted at a wavelength of 290 nm? 23. Suppose that a spectral line of some element, normally at 500 run, is observed in the spectrum of a star to be at 500.1 nm. How fast is the star moving toward or away from the Earth? Wien's law tells us that the hotter the object, the bluer its radiation. For example (see Figure 3.15), an object with a temperature of 6000 K emits most of its energy in the visible part of the spectrum, with a peak wavelength of 480 nm. At 600 K, the object's emission would peak at a wavelength of 4800 nm, well into the infrared portion of the spectrum. At a temperature of 60,000 K, the peak would move all the way through the visible spectrum to a wavelength of 48 nm, in the ultraviolet range. The strongest emission is from the Balmer alpha transition at 656.3 nm, which is dark red in color. red 740-620 nm are curves corresponding to temperatures of 300 K (room temperature), 1000 K (beginning to glow deep red), 4000 K (red hot), and 7000 K (white hot). we saw something of how astronomers can analyze electromagnetic radiation received from space to obtain information about distant objects. Radiation can be analyzed with an instrument known as a spectroscope. In its most basic form, this device consists of an opaque barrier with a slit in it (to define a beam of light), a prism (to split the beam into its component colors), and an eyepiece or screen (to allow the user to view the resulting spectrum). Diagram of a simple spectroscope. A small slit in the mask on the left allows a narrow beam of light to pass. The light passes through a prism and is split up into its component colors. The resulting spectrum can be viewed through an eyepiece or simply projected onto a screen. This transition produces radiation in the visible region of the spectrum - the 656.3-nm red glow that is characteristic of excited hydrogen gas. Absorption may also boost an electron into an excited state higher than the first excited state. depicts the absorption of a more energetic (higher-frequency, shorter-wavelength) ultraviolet photon, this one having a wavelength of 102.6 nm (1026 �). Absorption of this photon causes the atom to jump to the second excited state. As before, the atom returns rapidly to the ground state, but this time it can do so in one of two possible ways: orange 620-585 nm yellow 585-575 nm green 575-500 nm blue 500-445 nm indigo 445-425 nm violet 425-390 nm UV: Electromagnetic radiation

Chapter 5 3. When astronomers discuss the apertures of their telescopes, they say bigger is better. Explain why. As with an optical telescope the only way to improve the resolving power is to build a bigger tele- scope. Consequently radio telescopes must be quite large. big telescopes are important because they allow us to see very faint objects. 7. Why do astronomers place telescopes in Earth orbit? What are the advantages for different spectral regions? atmosphere turbulence and light pollution.on earth effect telescopes. the Earth's atmosphere absorbs X-rays, solar X-rays can only be studied from spacecraft above our atmosphere. the ability of a telescope to see detail is limited by the earth's atmosphere. This is why the Hubble Space Telescope is important because it is above the atmosphere and is not affected by the distortion caused by it. The larger the objective, the better the telescope can resolve detail. 36 inch telescope to make infrared observations. Earth's atmosphere opaque to X-rays, so observations must be made from space. Light pollution on Earth effects viewing stars in outer space. I6. Radio astronomy involves wavelengths much longer than those of visible light, and many orbiting observatories have probed the universe for radiation of very short wavelengths. What sorts of objects and physical conditions would you expect to be associated with radiation emissions of very long and very For example, let's say that the CME moved towards the upper left-hand corner from coordinates near the Sun of (150, 150) to (100, 90). The actual number of pixels in "x" and "y" that this corresponds to is (50, 60). Therefore, (502 + 602) = (distance in pixels)2. Take the square root of the right-hand side of this equation. You will get a Exercise: Calculations and Questions 1.Using the time given in each image, list the images you used. The clump was directly behind the black circle in c3_20020104_0942.gif. The clump was halfway above the edge of the left corner of the black circle in c3_20020104_1045.gif. The clump was just about all the way above the edge of the left corner of the black circle in c3_20020104_1142.gif. The clump was all the way above the edge of the left corner of the black circle in c3_20020104_1242.gif. The clump was farther away in c3_20020104_1342.gif again in c3_20020104_1442.gif. 2.What is the scaling factor for the images? You would measure from the black circle in the center of the image to each area that the clump was moving in a north west direction toward the upper left hand corner of the image. in millimeters image c3_20020104_1045,gif 6 mm image c3_20020104_1142.gif 11 mm image c3_20020104_1242.gif 16 mm image 2 it was image 3 it was 0.8 inches. image 4 it was 0.12 inches 3.Over how many millimeters or pixels did the clump move, and what is the corresponding distance in kilometers? 4.How much time did it take for the clump to travel this far? 5.What was the speed of this clump? 6.Give your general reaction when you found out the speed of the clump. Were you surprised? 7.Recall Newton's First Law. Is it valid to assume that the clump traveled at roughly the same speed (essentially escaping from the gravitational pull of the Sun) in all of the images you used? Explain your answer. 8.Light travels at roughly 300,000 km/sec. At this speed, it takes about 8.5 minutes (distance divided by the speed divided by the number of seconds in a minute) for the light from the Sun to reach the Earth. How much notice would we have if the CME were traveling directly towards the Earth; that is, how much time would pass between when the light reaches us and the charged material reaches us? 9.What assumption did you need to make in calculating the answer to the above question? 10.If your methods differed slightly from those given above, summarize what you did and how it worked for you. If you used the exact steps given, what improvements would you make to this activity? Self-Review (not submitted) 1.Here is a cartoon from the media and graphics center at NOAA Space Environment Center. For each of the systems, add a short paragraph summarizing exactly how these systems are affected. After your summaries, pick the system that, in your opinion, would be the most critical, should that system be completely knocked out for a total of three days. Support your position. 2.Pretend that you have traveled with our spacecraft through the core of the Sun and are now heading back out. Note the characteristics of each region of the Sun. How is radiation transported through each region? Granulation from the shuttle_dive.gif shows Hot ^ Cooler is going down arrow Plasma in blue box dark lettered. Plasma in red letters Rising Sinking Hot Cooler Plasma Plasma Rising Sinking Hot Cooler Plasma Plasma 3.The Sun's process of maintaining hydrostatic equilibrium is much like a thermostat that regulates heat in a house. Describe how these two processes are analogous. The gravity-pressure balance that supports the sun is a fundamental part of stellar structure known as the law of hydrostatic equilibrium. It says that, in a stable star like the sun, the weight of the material press- ing downward on a layer must be balanced by the pressure of the gas in that layer. Hydro implies that we are discussing a fluid-the gases of the star. Static implies that the fluid is stable-neither expanding nor contracting. The law of hydrostatic equilibrium can prove to us that the interior of the sun must be very hot. Near the sun's surface, there is little weight pressing down on the gas, so the pressure must be low, implying a low temperature. As we go deeper into the sun, the weight becomes larger, so the pressure, and therefore the temperature, must also increase. 4.It is summer where you live. You are laying on a large beach towel, lathered sufficiently in SPF 45 sun lotion. Your best friend has joined you for a day of relaxation. It is approximately 1:30 in the afternoon; the Sun is high above the horizon. There are no clouds in the sky. The temperature is 85 degrees F (about 35 degrees C, or 308 degrees Kelvin). You have just had some bread, cheese, and fruit for lunch, washed down with a bit of fine brew. Your previously active conversation has lulled for a moment. Your friend (who, by the way, has never taken an astronomy class at the University of Washington) is basking in the heat of the Sun. Unexpectedly, your friend turns to you and asks, "Where, do you think, the Sun gets all of its energy?" You ponder the question for a few minutes, your brain temporarily numbed by the beauty of the day and the magnitude of your friend's question. At last, the neural pathways of your cerebral cortex kick in, and you start relating all that you learned in Astronomy 101 about the billions of nuclear fusions occurring in the core of the Sun every second. What do you answer to your friend? You need to be fairly comprehensive, but you also need to put your explanation into words your friend will understand. Review and Thought Questions From the textbook: Pages 148-149: 5, 6, 7, 8 Pages 167-168: 3, 5, 6, 11, 18, 20 Assignment 6 Lab Exercise 3: Distances to the Stars in Leo Objective To determine the distances to seven of the brightest stars in the constellation Leo using the method of spectroscopic parallax; to compare the results to the more accurate distances derived from measured parallaxes. Introduction If the distance to the star is known via its measured parallax, it is a trivial matter for astronomers, or anyone else for that matter, to determine the absolute magnitude of the star using the magnitude equation. The Hipparcos Satellite has cataloged more than 2.5 million stars and measured parallaxes as small as 0.001 of an arc second. Recall just how small an arc second is. The angles that this satellite measured are 1000 times smaller. This small angle belongs to stars 1000 parsecs away. Our galaxy is approximately 30,000 pc in diameter, which means that the majority of the stars are too far away to have a measurable parallax. In these cases, the distance to the star must be determined by some other method. Before we start this exercise, let's take a close look at an actual image of the constellation of Leo, one with the general pattern outlined and the names of some stars included. Since this is an actual image, refer to the unlabeled image at's pretend that this is all you have to work with to find the distances to the stars. You would first go to a catalog and see what stars have had their parallaxes measured. (Excellent first step!) After doing that research, however, you find out that some of these stars have no measured parallax because they are too far away. What is your next step? You note that R Leo looks very red in color, Regulus looks bluish-white, and Al Gieba A orangish. (The image linked at shows the colors even better.) If you could locate a spectrum of these stars, you could determine their spectral types and luminosity classes and compare these characteristics to similar stars. Assuming that stars do not vary in their characteristics across the Galaxy, maybe this will just work. We can use our knowledge of the H-R Diagram and our analysis of a star's spectrum to determine stellar distances. From the strength of the lines in a star's spectrum, we can give it a spectral type and luminosity class. We can use the luminosity to find its absolute magnitude and thus its distance. Finding the distances to stars based upon their spectral type and luminosity is known as the method of "spectroscopic parallax" (even though it has no parallax measurement involved). This method is not easy nor is it exact; however, it has proved to be one of the best ways to learn about the more distant stars. The first part of this method involves determining the star's spectral type and luminosity class. Astronomers can determine a star's spectral type based on the absorption lines in the spectrum of the star. The hottest stars, spectral types O and B show weakened hydrogen lines (too hot-hydrogen atoms are ionized) with some helium lines. Spectral type A stars have extremely strong hydrogen lines (temperatures just right). As stars get cooler, more lines will appear as heavier elements-calcium (Ca) and iron (Fe), for example-recapture their electrons. The singly-ionized calcium atoms (Ca II) are especially strong in spectral type G stars. Spectral type K stars have very weak hydrogen lines (too cold) but strong iron lines and similar heavy elements. The width of a line can be used to determine an approximate luminosity for a star. For a given element, supergiant stars will have the narrowest line. These same lines become much broader as we move to main sequence stars, and white dwarf stars will have the broadest lines of all. Here is an example of the luminosity effect for spectral type A0 stars, from A0 Ia to A0 V, and a white dwarf. Note that the lines of the white dwarf are so broad that they are smeared out. Thought Question: after looking at this effect, how accurate do you think astronomers are in determining the luminosity of a star this way? Important note: the spectra shown in this lab are negatives: absorption lines appear bright while the background continuum appears dark. Spectra are from An Atlas of Representative Stellar Spectra, 1978, (Halsted Press, all rights reserved) Exercise What you will be turning in, via e-mail or as an attachment to an e-mail message: Table 1 and answers to the questions. Table 1 lists 14 stars in Leo. As you will note, 7 of the stars have already been classified, and absolute magnitudes and distances calculated. Your mission is to fill in the details for the other seven stars. Check the data for the first seven stars to verify the process you are to use. Table 1 as a MS Word document Table 1 as an Excel spreadsheet Table 1 as plain text 1.Figures 1 and 2 show a series of standard spectra used to classify stars (Fig. 1 linked) and the seven stars in Leo that have already been classified as well as those seven that you need to classify (Fig. 2 linked). You may either classify the stars working with the online frames, or print each frame and work with the hard copies. 2.First, take a look at the seven stars in Leo that have already been classified, and compare each to the corresponding standard spectrum. 3.Use the examples shown in Fig. 1 to guide you in classifying the remaining seven stars, shown in Fig. 2. Note: because of the need to keep the image sizes small, some image quality had to be sacrificed. Note, too, that there may be a shift in some of the spectra, and with respect to the "line key" at the top of the page. By resizing the browser window (wider or narrower), you can eliminate some of the misalignment. Let the line patterns and strengths guide you in your classification. Also, the standard spectra are for luminosity class "V" only. Do not worry about being extremely accurate-this is not an exact science! 4.List your best guesses as to the spectral types in Column 3 of Table 1. The luminosity classes are already given for you (these would be way too difficult for us to figure out). 5.After you have given your best effort at classifying the stars, check your guesses against the correct spectral types (no cheating!). Fill in the correct spectral types in Column 4, and use these values for the rest of the exercise. How did you do? 6.Assign each star an absolute magnitude based on its spectral type and luminosity class. You must use the H-R Diagram to do this. Fill in Table 1. 7.Solving for the distance in the magnitude formula, M = m - 5 * log(d) + 5, we get: Solve for the exponent of 10 first, then either punch the "inv log" keys or the 10x key on your calculator. If you do not have a scientific calculator, then calculate the number for (m - M + 5)/5 and enter that number into the space below. The program automatically calculates 10 raised to that power. Click on "Answer in Parsecs" for the distance in parsecs. (Remember: calculate the values within the parentheses first, then divide by 5. Use a maximum of two significant figures.) Calculate the distance to each of the seven stars based upon the absolute magnitude from spectroscopic parallax. 8.For the seven unclassified stars, fill in Table 1 for the distances determined from the measured parallax values, where d = 1/parallax (d is in parsecs for parallax measured in seconds of arc). Questions Answer the following questions and include the questions along with your answers either in the body of an e-mail message, or as an attachment. 1.Pretend you need to tell your non-scientist roommate how distances are determined using spectroscopic parallax (in other words, summarize what you just did). Do so in terms that he or she will understand. To find out how faraway planets, and stars are, and the measurements give information as to how big in size the universe is. One way to measure the distance is Parallax measurements of the distances to the stars nearest Earth use as a baseline. The distances to the nearest stars can be measured using parallax Observation of the universe is seeing many galaxies, objects, planets, stars. 2.In your own words, summarize why the spectroscopic parallax method is an important tool for astronomers. spectroscopic parallax Method of determining the distance to a star by measuring its temperature and then determining its absolute brightness by comparing with a standard H-R diagram. The absolute and apparent brightnesses of the star give the star's distance from Earth. 3.The major disadvantage of the spectroscopic parallax method is that it is not very accurate. Why is this? Consider specifically the errors or uncertainties you might expect at each step in the process. Parallax Describe what is meant by parallax. Measure the parallax of a nearby object with your cross-staff and determine its distance. 4.Reconsider the measured parallax method. For stars within a measurable range, what primary factor contributes to the errors or uncertainties with this method? Distance to a star or the true brightness luminosity of the star. 5.As an astronomer, you are asked to choose between the spectroscopic parallax and measured paralax methods. Which one would you choose and why? We can now use the H-R diagram again, the temperature tells us where the star lies horizontally while the width of the spectral lines tells us the luminosity class (dwarf, giant, supergiant). From this we can infer the luminosity. Then, given luminosity and the apparent brightness, we ge the distance. This is called the spectroscopic parallax method-->if you determine the brightness and luminosity using the spectrum, you can therefore determine the distance. This is important because it can be used to find the distance to any star for which you can obtain a spectrum. Supplying the hobbyist, professional pyrotechnician, industry, and schools since 1998. "We specialize in small orders" Americium 241 Sealed, Radioactive Test Source If you're looking for a clean, accurate, certified radiation source, here it is. Americium is a man-made metal (atomic number 95) produced when plutonium atoms absorb neutrons in nuclear reactors, and in nuclear weapons detonations. Americium has several different isotopes, all of which are radioactive. The most important isotope is Am-241, with a half-life 432.7 years. Americium - 241 is a strong Alpha, and weak Gamma radiation emitter. If you're thinking about making a Cloud Chamber, or engineering your own Spinthariscope, this source is ideal. Americium - 241 does not emit harmful penetrating radiation. It's strongest output is Alpha particles which are the basis of many fascinating nuclear experiments & demonstrations. The compound used in the source is an oxide of Americium... and is not water soluble, so it is not dangerously toxic like many other isotopes are. The source itself is permanently sealed in a heavy brass housing and cannot be removed. The combined Alpha & Gamma radiation output is over 60,000 CPM! Our Americium Source measures 15 mm in diameter, and features a recessed, Mylar radiation exit window that is 4 mm in diameter. A strong beam of Alpha particles is emitted from the 4 mm exit window. Due to its long half-life, this source will continue to function for over 400 years. Your Americium-241 source comes with a clear plastic storage case as shown above, along with the Certificate of Measured Radiation as shown below. Direct contact with this material is not hazardous, but if the source unit is crushed and ground into a powder, ingestion or inhalation of the dust may be hazardous. This is an NRC "exempt quantity" of radioactive material and disposal in public landfills is permissible. Principle Emission: Gamma: 13.9 KeV (42.7%) & 59.5 KeV (35.9%) Alpha: 5,443 KeV (12.8%) & 5,486 KeV (85.2%) Americium 241 1 uCi Radioactive Source: $25.00 - The worst bioterrorism attack in U.S. history was perpetrated through the mail two years ago. Five people died and 17 were sickened by anthrax-infected letters sent to media companies and the Capitol Hill offices of Democratic Sens. Tom Daschle of South Dakota and Patrick Leahy of Vermont. Ricin is derived from the castor bean plant, is relatively easy to make and can be deadly in very small doses. When inhaled or ingested, fever, cough, shortness of breath, chest tightness and low blood pressure can occur within eight hours. Death can come between 36 and 72 hours after exposure. There is no antidote. Ricin has also been used in crimes in the United States that have no connection to terrorism. Last summer a Washington state man was convicted of making and possessing about 3 grams of ricin, enough to kill 900 people. radio.gif Aircraft and Shipping boats bands. AM radio. Shortwave radio. TV and FM radio. pe_ke.gif Potential energy turns into Kinetic Energy when ball rolls off ledge toward to the ground below. first_quarter.gif 89.853 degrees betwen the Earth and star. Angle between star and moon. Angle is larger than what is shown. 90 degrees. earth from the star and moon. horsehead2_side_graphic.gif . < A . < B . < C Telescopes reflect6.gif Eye piece Primary mirror Secondary mirror refract.gif a tube like telescope. big to small 2 sections. earth1.gif 6 lines north to south going around one side of globe. Longitude Lines. 3 lines east to west going around one side of the denverdistance.gif Denver to Mazatlan = length of the shadow radius of the Earth height of the obelisk spectanalysis.html Summary The student observes and records a continuous spectrum and the emission lines of various gases, identifies a particular gas based upon its emission spectrum and identifies the composition of a "star" based upon its absorption spectrum. Materials Rainbow glasses or slide-mounted grating Colored pencils or crayons Background and Theory In many respects, light exhibits a wave-like behavior. As with waves in water, this means light waves have a velocity (c in a vacuum; 300,000 km/s), a wavelength (lambda), and a frequency (nu). The distance a light wave travels in one second is its velocity, expressed in meters per second (m/s); the distance between two wave crests (or troughs) is the frequency (number/second). velocity = wavelength * frequency is the fundamental relationship between these three quantities Wavelengths shorter than those corresponding to infrared light are usually measured in nanometers. One nanometer is one-billions of a meter (1 nm = 10-9 m). The wavelength of the light determines the color. A wavelength of around 650 nm corresponds to red light; 500 nm, to green light; 450 nm, to blue light. The human eye responds to the wavelength range of around 400 - 700 nm. 300 nm 400 nm 500 nm 550 nm 575 nm 600 nm 625 nm 650 nm A transmission grating is a piece of transparent glass or plastic ruled with many finely spaced lines. A grating will break up light into a spectrum just like a prism, but will form multiple spectra. The image of the object will go straight through the grating, forming what is known as the zeroth image. The spectrum formed beside the zeroth image is called the first-order. The next one out is called the second-order, etc. As one looks toward the higher-order spectra, the spectra become become fainter and more dispersed (spread out). A rainbow is formed when rain drops break the Sun's light into the component colors. Light passing through a prism also forms a rainbow, but in this case we call it a spectrum (plural: spectra). A spectrum of the Sun or a light bulb (both approximately behaving like blackbodies will have all of the colors of the rainbow. These spectra are called continuous spectra. Procedure Print out the Worksheet. Part 1: Pre-exercise Exercise: 1.Fill in the blanks and answer the questions in Part 1 on the worksheet. Part 2: Observing Spectral Lines in the Lab 1.Your instructor will place a clear plastic box containing antifreeze on the overhead projector -- magically transformed into a large spectroscope1 -- and project the light from the projector, through a slit in a piece of cardboard, through the antifreeze, and through a large diffraction grating onto the screen. Describe the spectrum of colors before and after the antifreeze is placed in the light path. Comment on the relative intensities of each color. 2.Your instructor will place various colored filters over the slit. Describe what happens for each filter. 3.Practice viewing -- discuss the following observations with your teammates: a.Using a slide-mounted grating or a pair of "rainbow" glasses, observe any light source. Can you see the first order spectra, one on each side of the zeroth order? What do you need to do to see the two spectra? How do the colors of the two first-order spectra differ? Can you see a second order spectrum? Second orders are hard to see as they must be viewed way off to each side and are faint. b.Optional Use a quantitative spectroscope to observe a light bulb, a neon light, or a street light. Look about 15 degrees to the side of the zeroth image to see the wavelength scale. What wavelength range do you see? 4.Continuous spectrum: use the colored pencils or crayons and sketch the spectrum seen of an ordinary light bulb; for example, that used in an overhead projector. 400 nm (blue) 500 nm 600 nm (red) 700 nm 5.Make a sketch of each spectrum from the gas discharge tubes. Be sure to reflect the correct intensity of each line, the correct spacing, the relative positions, etc. Note: If all of the spectra look exactly the same, or you do not see a large number of red lines for neon, you may be using the spectroscope incorrectly or your spectroscope may be faulty. Check with your instructor. Type of Gas Sketch of the Spectrum Wavelength 400 nm 500 nm 600 nm 700 nm 6.Your instructor will insert an unknown gas emission tube into one of the power boxes. Examine the pattern and colors of the emission spectrum, mentally compare it to the gases you just observed. What is the unknown gas? ______________ Part 3: Questions Answer the following questions on your worksheet. 1.Comment specifically on the similarity and differences of each of the spectra that you have observed. Include in your comments the colors you observed and how the spacing of these colors differed. 2.Examine the following spectra: Artificial Solar Spectrum Laboratory Spectum of Iron What is the evidence for the claim that iron exists in a relatively cool outer layer of the Sun? Once the inner core begins to change to iron, our high-mass star is in trouble. Nuclear fusion involving iron does not produce energy, because iron nuclei are so compact that energy cannot be extracted by combining them into heavier elements. In effect, iron plays the role of a fire extinguisher, damping the inferno in the stellar core. With the appearance of substantial quantities of iron, the central fires cease for the last time, and the star�s internal support begins to dwindle. The star�s foundation is destroyed, and its equilibrium is gone forever. Even though the temperature in the iron core has reached several billion kelvins by this stage, the enormous inward gravitational pull of matter ensures catastrophe in the very near future. A supernova can also occur when the iron core of a massive star rapidly collapses. Iron (Fe) only forms in the most massive stars at the end of a long set of reactions involving numerous nuclei. These reactions only occur in the cores of massive stars where the temperatures are extremely high. The spectrum shows a continuous spectrum with hydrogen, magnesium, iron, and sodium absorption lines. There are no emission lines present in the normal solar spectrum. 3.How does the light that astronomers see from distant stars and galaxies tell them that the same atoms with the same properties exist throughout the universe? Why are spectral lines often referred to as "atomic fingerprints"? each absorption line is caused by a transition of an electron between energy levels in an atom. Each element has a distinct pattern of absorption lines. Once the pattern of the lines of a particular element have been observed in the laboratory, it is possible to determine whether those elements exist elsewhere in the universe simply by pattern matching the absorption lines. 4.How can a hydrogen atom, which has only one electron, have so many spectral lines? Three kinds of Spectra When we see a lightbulb or other source of continuous radiation (a) all the colors are present. When the continuous spectrum is seen through a thinner gas cloud the gas cloud's atoms produce absorption the continuous spectrum (b) When the excited cloud is seen without the continuous source behind it its atoms produce emission lines (c). We can learn which types of atoms are in the cloud from the pattern of the absorption or emission lines. Several different series of spectral lines are shown corresponding to transitions of electrons from or to certain allowed orbits. Balmer series absorption, Lyman series emission, Balmer series emission, Paschen series emission, Bracket series emission. n =2 2 3 4The Bohr Model for Hydrogen. 4.16 figure Energies called energy levels. 5.Distinguish among emission spectra, aborption spectra, and continuous spectra. Emission Spectra Electrons can also go from outer orbits to inner orbits. As electrons move closer to the nucleus, they give off energy that appears as photons. Once again, the amount of energy can be determined using E=hf=hc/. An emission spectrum will be observed when an electron goes from an outer state to an inner state. Absorption Spectra Electrons can change orbits, but the closer the electron is to the nucleus, the less energy it has. Therefore, some amount of energy is needed to move the electron to an outer orbit. This energy can come from the light that passes through the gas containing the atom in question. Energy is absorbed having an amount exactly equal to the amount of energy needed to move the electron to a higher orbit. 6.Examine the following spectra: What elements are present in the object that produced the "Spectrum of Unknown Composition"? Explain your method and relate this activity to the way astronomers use spectra to identify the composition of a star. 1 To find out more about this 'magical' transformation, see Philip M. Sadler. Projecting Spectra for Classroom Investigations. The Physics Teacher, 29(7), 1991, pp. 423 � 1999 University of Washington Revised: 3 February, 2000 lec3.html Lecture 3 Notes Main Points Be able to identify phases of the Moon. Understand the orientation of the Earth-Moon-Sun. Be able to predict: Rise/set times of different phases. Location of the Moon at different phases at different times of the day. Know the different types of eclipses and why they occur. Definition: Sidereal Month The amount of time for the Moon to orbit the Earth once. It takes 27 1/3 days. Phases of the Moon Occur in a constantly repeating pattern. Due to specific orientations of the Earth, Sun and Moon. The orbital motion is shown in the diagram below. The Sun is drawn on the right hand side. Note the rotation of the Earth is counter-clockwise. This is the view when looking down on the north pole. Study the above diagram carefully. Do you see how half of the circle is yellow in color, and the other half is black? This is important, as the only side of the Moon (or the Earth) that will be lit up is the side facing the Sun! For one full rotation of the Earth, the Moon in its orbit does not more very much. This means that all observers on Earth see the same phase in one 24 hour period. Play the following animation to see the orientation of an observer on Earth and the time of day. ANIMATION: Earth Rotation This is the perfect world I described in the first day of class. Sunrise is at 6 A.M., sunset is at 6 P.M., the other times can easily be broken down as well. Now let's add the Phase line to the above image: By drawing a line that is tangent to the Moon's orbit around the Earth, we see what part of the Moon is visible to an observer standing on Earth. The important thing is that we are stuck on Earth, we cannot suddenly leave our planet and view the Moon from some other location, so the red line divides the front half from the back half. In this case, we see more than half of the moon lit up. This is a phase we call Gibbous. There is another term to add as well, but we will come to that later. Now that you have seen how the phase line works, print out a copy of this set of lecture notes. In the figure below, draw a phase line for each of the smaller circles. Shade in the dark side of the moon. Can you see another Gibbous phase? What about Full? or even New? How about the phase we call Crescent? What about the Quarter phases? The labeled diagram can be found here. Don't look at it until you have tried to label them yourself! Moon Phase Diagram Now we can identify the terms Waxing and Waning Waxing = to increase (grow) Waning = to decrease (diminish) From New to Full, the Moon appears to grow in light. These phases are called Waxing. After the Moon has reached Full, the amount of surface lit becomes smaller and smaller. These phases are called Waning. Each set of phases starts at the New Moon phase. Hence the first time half the Moon is lit is called the 1st Quarter phase. Definition: Synodic Month The amount of time to go from New Moon to the next New Moon. This takes about 29.5 days. This is longer than the Sidereal Month because the Earth does not sit still in space, it is also in orbit around the Sun. Rise and Set Times Using our perfect world, the moon is above the horizon for 12 hours and below the horizon for 12 hours. Sunrise is at 6 a.m., and Sunset is at 6 p.m. Noon is 12 p.m., and midnight is 12 a.m. The time to reach the meridian is always 6 hours. In the phase diagram above, each phase shown is when it is on the meridian. Full Moon is on the meridian at 12 a.m. It rises at 6 p.m., and sets at 6 a.m. New Moon is on the meridian at 12 p.m. It rises at 6 a.m., and sets at 6 p.m. What about the first quarter moon? When determining the rise and set times, either subtract 6 hours or add six hours to the time the phase is seen on the meridian. Eclipses Two types: Solar and Lunar. Only occur during a new moon or a full moon. Due to Moon's orbit around Earth, eclipses do not happen every month. Instead they occur in seasons There can be anywhere from 4 to 7 eclipses in one year, but never less than 4. Background on shadows: Sun is physically larger than the diameter of the Moon's orbit around the Earth. Shadows end up being coned shape: Umbra = central (darker) region of the shadow cast by an eclipsing body. Penumbra = region surrounding the umbra. Above, we see how the type of eclipse seen depends on where you are standing in the shadow cone. Only those in the umbra will see a total eclipse! With a tilt of 5.2 degrees, the Moon is only in position for an eclipse when it is on the line of nodes. Click here to learn more about the alignment. Solar Eclipses: Types possible: total, partial, or annular. Moon passes in front of the Sun...New moon phase. Sun is blocked from view. Annular eclipses are when the Moon appears smaller in size on the sky and does not completely block out the full disk of the Sun. Solar eclipses only last a few minutes because the Sun and Moon appear to be about the same time. It does not take long for them to pass each other. Lunar Eclipses: Types possible: total or partial Moon passes through the shadow cast by Earth...Full moon phase. Moon is still just changes color. Last longer than solar eclipses because the Earth's shadow is much larger than the moon. ANIMATION: Solar Eclipse Definition: Saros Cycle The time between nearly identical eclipses. This comes out to be almost 18 years and 11 1/3 days or 223 Synodic months. This means the Sun and Moon are back in the same configuration. Back to Lecture Listing These pages are maintained by Dr. Jeannette M. Myers. The contents of this page has not been reviewed or approved by FMU. about the Earth? How does the force of gravity in the Russ- ian space station Mir (orbiting 500 km above the Earth's surface) compare with that on the ground?

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UW Extension Distance Learning

Two Little Gravity Quizzes


The Earth

You and the Earth

Your weight is a measure of the force that the Earth exerts on you and that you exert on the Earth. In terms of Newton's Second Law:

F = mg

where g is the acceleration due to gravity, approximately 9.8 m/s2. In terms of the mass of the Earth, M, your mass, m, and the radius of the Earth, R (ignoring "big G"), this equation can be written as:

This equation is read as the "force is proportional to the mass of the Earth times the mass of the object (you), and inversely proportional to the radius of the Earth squared." Interestingly, solid spherical bodies act as if all of their mass is concentrated right at the center! Figure out what would happen in a relative sense in the following scenarios (answers given at the end of the quiz):

  1. The Earth suddenly doubles in size (radius)
    1. Your weight stays the same
    2. Your weight doubles
    3. You weigh 1/4 as much
    4. You weigh 1/2 as much

  2. You eat so much that you now have twice as much mass (Earth stays the same)
    1. You weigh twice as much
    2. You weigh 4 times as much
    3. You weigh the same
    4. You weigh 1/2 as much

  3. The Earth is now twice as massive, but your diet leaves you with only 1/2 your original mass
    1. You weigh exactly the same as before the changes
    2. You weigh 4 times as much
    3. You weigh 1/2 as much
    4. You weigh 1/4 as much

  4. The Earth balloons to twice its size (radius) and also gains twice its mass
    1. Your weight doesn't change
    2. You weigh twice as much
    3. You weigh 1/2 as much
    4. You weigh 4 times as much

  5. The Earth is 1/2 its current size, but twice its current mass.
    1. Your weight doesn't change
    2. You weigh 8 times as much
    3. You weigh 1/8 as much
    4. You weigh 1/4 as much


The Sun

The Sun and the Earth

We can calculate the gravitational force between the Sun and the Earth by using the mass of each object, Msun and mearth and the distance between them, D. Again, ignoring "big G," the force is represented by:

Figure out what would happen in a relative sense in the following scenarios (answers given at the end of the quiz):

  1. The Sun suddenly moves two times farther away
    1. The force stays the same
    2. The force doubles
    3. The force is 1/4 as much
    4. The force is 1/2 as much

  2. The Sun stays in the same place, but the Earth suddenly has twice as much mass
    1. The force is twice as much
    2. The force is 4 times as much
    3. The force is the same
    4. The force is 1/2 as much

  3. The Sun is now twice as massive, but the Earth has only 1/2 its original mass
    1. The force is exactly the same as before the changes
    2. The force is 4 times as much
    3. The force is 1/2 as much
    4. The force is 1/4 as much

  4. The Earth moves two times farther away and also gains two times its original mass
    1. The force doesn't change
    2. The force is twice as much
    3. The force is 1/2 as much
    4. The force is 4 times as much

  5. The Sun goes to 1/2 its current distance, but twice its current mass.
    1. The force doesn't change
    2. The force is 8 times as much
    3. The force is 1/8 as much
    4. The force 1/4 as much

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Astronomy C101: Comparison of EPE and GPE UW Extension Distance Learning

A Comparison of Electric Potential Energy and Gravitational Potential Energy

Page 1

The energy levels of an electron in an atom are roughly analogous to the steps of a ladder. An electron jumping to higher energy levels can be compared to a workman climbing up a ladder. We are going to compare the energy levels of an electron in a hydrogen atom to a vertical ladder braced upon a wall.

To get to a higher energy level, an electron must gain energy. It does this by absorbing a photon having exactly the right amount of energy for the jump. To climb to a higher step, the workman must use energy. He got this energy from food.

There are some important differences, however. First of all, the energy levels available to an electron are not equally spaced like the steps on a ladder. They get closer together the farther away from the ground state the electron is. If this were a ladder, it would be like stepping smaller and smaller distances as one moved up. The top steps would be barely millimeters apart.

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Continue on to Page 2. Go to Assignment 1

astro101si.html Astronomy C101 Introduction to Astronomy Introduction Look up into the night sky. What do you see? How much of what you see can you describe? How many objects that you can describe are nearby the Earth? How many are extremely far away? Can you describe why the stars appear to rise and set daily and why we see different constellations during the course of a year? What, exactly, is a star anyway? Are the stars we see in the night sky part of our Milky Way, or do they belong to other galaxies? Perhaps the ultimate questions are: "How did we get here to be asking such things, and are there other intelligent beings seeking answers to similar questions?" The study of astronomy, the study of objects and phenomena beyond the atmosphere of the Earth, takes us along an unending road of discovery. It is said that astronomy is the oldest science (which it is) and the youngest science (which it also is!). How can it be both? It is the oldest science in that mankind's attempts to understand the Universe began thousands of years ago with the tracking of the Sun, the Moon, and the seasons. It is the youngest science in that new discoveries are made everyday. New hypotheses must be formed that address these discoveries. As our technology advances-meaning larger telescopes, satellites, lightning-fast computers-so must our attempts to understand nature. An advanced degree is not needed to participate actively in astronomy. You are involved by merely questioning what goes on beyond our home planet. A pair of binoculars, a star map, and curiosity will get you started. The next step will take you beyond visually wandering from constellation to constellation and will involve wanting to understand what you see, wanting to know how we know what we do. The next step is what you are taking by registering for this course. This course is open to everyone, and there are no prerequisites. It is designed for students whose strengths lie in fields other than science or math. Having said that, we must note that mathematics is the language of the Universe, and there are some concepts that can be explained best and most thoroughly with a few equations. In all cases where mathematical formulae are involved, we give a review and examples of how to solve the problems. Course Overview and Goals What is Astronomy? As mentioned above, astronomy typically means the study of objects and phenomena beyond the atmosphere of the Earth. That is a lot of stuff! Astronomers today must and do specialize. The field of observational astronomy has been divided into roughly five disciplines: planetary sciences, solar physics, stellar astronomy, galactic/extra-galactic astronomy, and cosmology. Historically, the teaching of introductory astronomy has tried to cover all of these fields in 10 or 15 weeks! It should come as no surprise to find out that this approach has come under serious attack. The University of Washington has a separate planetary astronomy course, Astronomy 150, and plans are underway for developing a non-major extra-galactic and cosmology course as well. Each course covers a more limited amount of material, but covers it to greater depth. This course emphasizes topics on solar physics, stellar astronomy, and galactic astronomy. Hopefully, you, the student, will develop not only a solid foundation for future independent study but also a desire to take additional astronomy courses. This course will introduce you to what it is that astronomers do. Today, our research consists of working with smaller questions contained within the largest question: "How does the Universe work?" We observe an astronomical object or event and note things that we do not understand. Can we figure it out within the basic physical and mathematical background that we have? If not, what additional observations are needed? We make measurements of the stars and other objects in our galaxy (and in other galaxies). After we make our observations, we must analyze the data. This usually means graphing the data and looking for relationships. (You will study in detail one of the most important graphs in astronomy, the Hertzsprung-Russell diagram, that led to our modern-day view of how stars evolve.) If we discover something that we believe will advance our knowledge of the Universe, even in a small way, we submit our results to a scientific journal for peer review and subsequent publication. As you work through the lessons in this course, you will experience-as much as is possible over a short period of time-what it is like to be an astronomer. You start with learning the elementary physics and mathematics underlying our understanding of the Universe. From there you will step to the Sun and other stars and objects in the Milky Way. The lab exercises pace you through the types of measurements and analyses astronomers do, as well as give you practice in clear, concise writing of your results and your interpretation of them. The goal of the "Teacher's Corner" included with each lesson is to introduce current and future teachers to the astronomy education resources available on line. The inspiration for this follows one of NASA's priorities: "Educational Excellence: We involve the education community in our endeavors to inspire America's students, create learning opportunities, and enlighten inquisitive minds." In short, astronomy education is a "hot topic" today. The listings given at the end of each lesson have been chosen because of the quality of the material at each Web site. Course Objectives By the end of this course, you will be able to explain the concept of the celestial sphere and report on observations of objects in the night sky; connect terrestrial physics to astrophysics by demonstrating-with common, everyday materials-the concepts of conservation of momentum, angular momentum, energy, and the role that forces play in the Universe; discuss the nature of electromagnetic radiation and how that radiation transfers energy and information through interstellar space; show how the relative motion of a source of radiation and its observer can change the perceived wavelength of the radiation-and explain the importance of this phenomenon to astronomy in determining the motions of stars, the masses of stars, and the existence of extra-solar planets; summarize the overall properties of the various regions of the Sun; outline the process by which energy is produced in the Sun's interior; and explain how energy travels from the solar core, through the interior, and out into space; state how a Hertzsprung-Russell diagram is constructed, and summarize the properties of the different types of stars and the evolution of those stars identified by such a diagram; explain how the formation and life of a star is affected by its initial mass by contrasting the evolutionary histories of a high-mass and low-mass star; summarize the composition, physical properties, and characteristics of the interstellar medium-and describe the significance of the interstellar medium to the life cycle of stars; discuss the origin, components, and use of a distance-scale ladder in determining the distances to nearby stars as well as distant parts of the Galaxy; and relate the substructure and components of the Galactic disk to those of the Galactic halo and Galactic bulge. Required Materials Textbook (required): Voyages to the Stars and Galaxies (2nd edition) by Andrew Fraknoi, Sidney C. Wolff, David Morrison. 2001, International Thomson Publishing. This textbook was chosen for its readability. Not every topic will be covered, and some topics will be expanded upon through online lecture notes. Lab Tools: simple scientific calculator 15 cm (6 inch) ruler small package of colored pencils or crayons Lesson Format Reading Assignments Each lesson involves reading one or two chapters, occasionally an outside resource. Lecture Notes with Self-Review Online lecture notes will serve to clarify certain harder-to-understand sections. They will also expand upon certain topics. These online notes also include self-review sections to check the comprehension level and to prepare the student for the exams. Lab Exercises The best way to learn astronomy is to do astronomy. Observational astronomers today take data, graph it, analyze it, and summarize their work. As much as possible, we have replicated this process in the lab exercises and have avoided a "cookbook" approach. Each lab will take approximately two or three hours to complete. You are encouraged to read completely through a lab before starting it. See what materials, review, additional reading, and responses are needed. Answers to some of the questions asked will not be found directly in the text or online notes. You are expected to piece together information and use your own logic to answer many questions. Activities Activities are similar to labs, but are much shorter, taking one-half to one hour to complete and generally focus on only one or two concepts. Teacher's Corner Most lessons include a list of Web sites with quality educational resources and lesson plans related to the concepts covered in that lesson. Overview of Lessons Lesson One As incredible as it might sound, astronomy covers objects spanning sizes from the nucleus of an atom to the farthest reaches of the visible universe: from less than 1 picometer (10-12 meter), to 1026 meters, or equal to a full range of 38 powers of ten. Lesson One covers the major structures of the Universe and the basics of observing the night sky, including the vocabulary, and concludes with brief overview of the history of astronomy. At the end of Lesson One, you will complete your first lab assignment, "Distances in the Universe: The First Step"-within the online notes under Assignment 1: Finding the Size of the Earth and the Distances to the Moon and the Sun. Lesson Two What holds regions of the Universe together? Gravity. In Lesson Two, we set the physical foundations of astronomy, the laws that govern how everything moves and the forces involved. Chapter 2 of the text includes a brief history on how gravity was "discovered," and how we use the effect of one body upon another to determine mass. As part of Lesson Two, you will complete the first activity; you get to play with toys and discover the physics involved-the same physics that governs such things as the collapse of stars! Lesson Three Lesson Three is the next step in setting the foundation for observations. Here we cover the reasons for the seasons, time, phases of the Moon, eclipses, and tides. Each of these concepts has applications in planetary science, stellar astronomy, or both. The assignment for this lesson is an activity on the phases of the Moon. You perhaps have thought about the "dark side of the Moon," or the "far side of the Moon," but what do they mean? When the Moon is full at midnight on one side of the Earth, what is its phase 12 hours later, at midnight, on the opposite side of the Earth? This activity will help you answer these questions. Lesson Four Unlike most other scientists, astronomers cannot bring their test material into the laboratory for controlled experiments. To learn about our universe, we rely upon our knowledge of the nature of light: how it is produced, how it travels through a vacuum and through media, how it behaves when we "capture" it with a telescope. This lesson gives a survey of what we know about radiation, spectra, and telescopes. As part of this lesson, you will complete and submit the lab on spectral analysis, which covers emission, absorption, and continuous spectra. Lesson Five Our favorite star has to be the Sun. It is, by all accounts, just an average star, but extraordinary to us as a giver of life. This lesson covers two chapters in the text, starting first with the overall structure of the Sun and the Earth-Sun connection, and finishing with the nuclear powerhouse that rages in the core of the Sun. The activity that will be submitted as part of the lesson introduces the data we've obtained from the SOHO satellite, which has been monitoring the Sun continuously over the past few years. You will be calculating the tremendous velocity of a solar flare and the time it will take for the energy released to reach and affect Earth. Lesson Six Preparation for your midterm examination. Lesson Seven The backbone of stellar astronomy is the classification of stars and a chart called the Hertzsprung-Russell Diagram (H-R Diagram). The reading that accompanies this lesson introduces a lot of new vocabulary and concepts related to the classification of stars. There is ample self-review in the online notes to help you with this. The lab that will be completed as part of this lesson introduces the cosmic distance ladder; that is, the steps we take to calculate not only the distances to the nearest stars but also stairsteps from the bottom rungs to the edge of the visible universe. In this lab, we learn how we calculate distances using a method called "the spectroscopic parallax of stars." Here you use your knowledge of stellar spectra and the H-R Diagram to find the distances to stars in the constellation Leo. Lesson Eight In a metaphoric sense, stars are as much alive as we are. They are born in an environment that nourishes them until they mature enough to start fusion in their core. They may be alone, or part of a twin, triplet, or even multiple stellar system. Their birth is marked by a physical scream of sorts as they go through a stage of powerful outflows of material. Eventually they calm down and settle in for a life determined by what they weighed at birth (the amount of mass they have). Lesson Seven examines the theoretical ideas of how stars are born and the observational evidence to support these theories. Recent results from the Hubble Space Telescope have given us tantalizing evidence that newly formed stars have material around them that may contain planetary systems. These images plus the recent discovery of planets around dozens of nearby, solar-like stars hint that the formation of planets may be a standard by-product of star birth. The activity included with this lesson will give you an idea of what astronomers must do to detect a planet orbiting another star. Lesson Nine Continuing with our study of the lives of stars, we follow them through their adolescence, old age, and their eventual death. Depending upon the mass they had at birth, some stars live an extremely long time while others go through life fast and furious. The stars that live a long time die without much fanfare compared to the stars that live only a relatively short period of time. The massive, short-lived stars go out in a blast of energy representing one of the most violent explosions in the Universe. Lesson Nine addresses the question, "How do we know all this?" by having the student "walk" through the process of constructing what is known as a "color-magnitude diagram" of two clusters of stars. These diagrams reveal not only the ages of the clusters (and thus the way stars of different masses age) but also the relative distances to the clusters. Lesson Ten Although most massive stars end their lives as neutron stars, a topic we started in the last lesson and finish here, a select few leave behind a remnant so massive that it collapses for eternity. Gravity is the force that stars fight their whole lives, and gravity is what wins in the end. To understand black holes (one of the reasons students take an astronomy course), we must find a way to describe gravity under such extreme conditions. This lesson introduces you to the theory of general relativity as proposed by Albert Einstein. Don't panic! The text goes through the theory in a logical, comprehensible way. You will marvel at yourself as you find you actually understand this whole new way of thinking about gravity. This lesson includes an activity where you probe one of the first pulsars detected-the one in the Crab Nebula. Near the center of this nebula lies the remnant of a star that exploded in the year 1054. Each time the object rotates, which happens roughly 1000 times a second, bursts of energy are directed towards the Earth. Lesson Eleven We end this course with the study of our galaxy, the Milky Way. Up to this point, we have concentrated on gaining the fundamental knowledge needed to understand the stars in the Galaxy and some of the ways they may end their lives. Stars give material back to the interstellar medium whence they came. The "stuff between the stars" was mentioned during the birth of stars, this lesson pursues the topic in greater depth. How do we know the shape and size of the Milky Way? What lies at the very center of our galactic home? The lab exercise assigned to this lesson introduces you to a special type of variable star, called an RR Lyrae variable, that has been instrumental in our measurements of distances within the Galaxy. At the turn of the 20th century, around 1920, astronomers believed that the solar system was close to the c����      !"#$%&'()*+,-./0123456789:;<=>?@ABCDEFGHIJKLMNOPQRSTUVWXYZ[\]^_`abcdefghijklmnopqrstuvwxyz{|~�����enter of the Milky Way, and that our galaxy was the entire universe! By using the special characteristics of the RR Lyrae stars and observations of them in dozens of globular clusters, we learned that we were, in fact, about two-thirds of the way to the edge of our galaxy. The Earth was not the center of the solar system, and now the solar system was not the center of the Galaxy. Lesson Twelve Preparation for your final examination. Submitting Assignments Format The instructions for each assignment give the format for submitting your work or provide a text file where you simply fill in your answers and include it in the body of an e-mail or as an attachment. For the labs, this may include filling in tables and showing some simple calculations along with short or essay-type answers. Your assignments will be graded and returned to you within a week. In the meantime, you should plan on starting the next lesson and assignment. To submit assignments by e-mail, you should send a copy of the assignment to the instructor's e-mail address (see the "About Your Instructor" page). In the subject heading, be sure to include your Distance Learning student number, the course identification number, and the assignment number. Each lesson includes some self-review that is for your personal use for preparing for the exams and is not submitted for grading. Examinations This course includes a midterm and a final examination. The midterm covers lessons one through five; the final exam, lessons six through ten. The final exam is cumulative only in the sense that each lesson has built upon the information that came before. The criteria for grading the exams are included in the section "Course Grade," included as part of this introduction. The exams are closed-book, closed notes, and mostly of multiple-choice format. You may wish to bring a calculator to the exam, although you will probably not need it. You may not use this course guide or other notes in the exams. More details about the exams are supplied in Lessons Five and Ten of this course guide. You will be allowed two hours for each examination. Course Grade (Grading System) 5 Lab Exercises 30 pts each 150 pts total 5 Activities 10 pts each 50 pts total 2 Exams 100 pts each 200 pts total Total Number of Possible Points: 400 points Your final grade will be determined by your overall percentage (interpolate between the values shown, if necessary): 95%+ 4.0 70% 2.0 90% 3.5 65% 1.7 85% 3.0 60% 1.2 80% 2.5 55% 0.7 75% 2.3 < 55% 0.0 Study Tips The principal author of your textbook, Andrew Fraknoi, is a nationally recognized leader in the field of astronomy education. The preface for the student contains a number of suggestions on how to succeed in your studies. Although these suggestions are geared towards the formal classroom, they can be adapted to an online, correspondence course. The bottom line, however, is that nothing beats sitting down and just doing it! Learning the Vocabulary of Astronomy: You will confront what seems like a whole new language. Each lesson contains a list of key terms. Spend the extra time it takes to become familiar with these words and phrases and how they are used in astronomy. Your understanding of the material depends on it. Asking Questions: You may feel isolated from the rest of the students taking this course and from your instructor. This isolation can be minimized by asking questions, as many as you need to ask. A correspondence course has a great advantage over the classroom: you do not have to worry about "asking a stupid question." For your instructor, no question is a stupid question, period. There will be opportunities to post questions where others may read them and respond; we guarantee that other students will be thankful someone was able to put into words what they were having trouble understanding. Review: Each lesson has a review section, usually with answers provided. This review is a measure of whether or not you have adequately studied the text, online notes, and have thought about what was done in the labs and activities. Web Connections At the end of each lesson is a list of relevant and interesting links pertaining to the material covered. In addition, for most lessons, links are also given to educational sites that have related lesson plans and information for K-12 teachers. There are so many interesting internet Web sites covering astronomical topics that it is overwhelming. Almost all of them contain glorious, full-colored pictures and a wealth of information. The internet has complete journal and magazine articles and detailed results of the research of the leading astronomers, not only in our country but also around the world. (There are also a lot of "garbage" sites; hopefully you will never come across these and waste your time.) Texts usually emphasize images taken by large observatories and the Hubble Space Telescope, and the links provided are to Web sites owned by NASA and other government agencies and major universities. We've tried to complement this by providing links to pages maintained by organizations of amateur astronomers and astrophotographers. Planning Your Schedule The course is based upon the Astronomy 101 classes taught at the University of Washington. These courses are completed in one college quarter of 11 weeks (including finals week). If you apply yourself, as students who attend class (usually more than one class) must, you should be able to finish one assignment per week, including exams. Most lessons are designed to require an average of about fifteen hours, the equivalent of five hours of class time and ten hours of study time per lesson for in-class work. It is extremely important that you set your goals and deadlines and then stick to them. Please turn in your assignments on a timely basis; do not wait until you have finished a number of them and submit them all at once. The best way to learn from these assignments is to have feedback shortly after you have completed them. This will not be possible if weeks have gone by since you last looked at them. Learning is next to impossible, and your grade will suffer accordingly, if you wait until near the end of the six-month deadline and then try to complete the course in a month or less. Using E-Mail The advantages of using electronic mail in this course are as follows: You can get personal answers to your questions more quickly than by regular mail. Electronic mail will increase the timeliness of my response to your assignments. Establishing an Electronic Mail Account. If you do not have an electronic mail account, you can establish a UW Uniform Access account by doing one of the following: If you are a matriculated UW student, follow the instructions in the "Getting Started" section of the Guide to Information Technologies and Resources via the University of Washington. If you are not a matriculated UW student, or if you need help setting up your account, call Distance Learning at (206) 543-2350 or (800) 543-2320 (voice), or (206) 543-0898 (TDD). Connecting to the UW For information on establishing an e-mail account, please refer to the Student Handbook. General Questions Once you have an e-mail account, you can address questions about Distance Learning in general to and questions about this particular course to your instructor. If you have any problems using electronic mail, you can get help by calling Distance Learning. You can also send e-mail to Distance Learning at or UW Computing and Communications at About the Course Developer I am Dr. Ana M. Larson, a lecturer in astronomy at the University of Washington as well as the instructor for this course. My research has covered the radial velocity changes seen in stars with the hope of detecting extra-solar planets as well as modeling their atmospheres. My cohorts and I detected suspicious variations in the star known as Pollux or beta Gemini that closely mimic what we would see should it have an orbiting planet. Unfortunately, this star is also what is known as a giant, and giant stars usually have too much going on in their atmospheres to unravel the possibility of a planet. By "modeling their atmospheres," I mean that we are able to set up a computer program that calculates the abundances of elements and the pressure, temperature, and density of a star at various depths in its atmosphere. We then compare the theoretical spectrum to the spectrum we observe and see how close our model comes to the real thing. As a returning student with two pre-school children, my interest in astronomy was initially spawned by correspondence courses in Introductory Astronomy, The Planets, and Life in the Universe. My first degree from the University of Washington was in Business Education. Once my children reached elementary school age, I returned to get bachelor degrees in physics and astronomy. My doctoral work was done subsequently at the University of Victoria, Victoria, British Columbia, where I spent many, many nights at the Dominion Astrophysical Observatory observing nearby stars. Most of my time now is spent with teaching the Astronomy 101 and 150 evening classes at the UW, along with this course. I am also involved with the Old Campus Observatory by teaching undergraduates how to operate it, and how to develop and give presentations during the public observing nights. For more information, please visit my homepage at the Astronomy Department: If you need technical help, e-mail Program Support Services at You may also call (800) 543-2350; fax (206) 543-0887; or call (206) 543-0898 (TTY). � 2002 by UW Distance Learning. All rights reserved. No part of this publication may be reproduced in any form or by any means without permission in writing from the publisher. A Math Refresher Lesson One: Introducing the Scale of the Universe and Our View of the Night Sky Assignment 1: Lab Exercise 1: Finding the Size of the Earth and the Distance to the Sun and Moon Unit Conversion Calculator Lesson Two: Gravity, Energy, Forces Periodic Table of the Elements A Short Gravity Tutorial Assignment 2: Activity 1: "The Universe in a Toy" Lesson Three: Earth, Moon, Sun, and Sky Assignment 3: Activity 2: The Phases of the Moon gravityequation1.gif G M 1 M 2 R2 gravityequation2.gif 6.67 x 10 -11 5.98 x 10 24 70 6.38 x 10 6 2 gravityequation3.gif 6,67 x 10 -11 5.98 x 10 24 70 1.273 x 10 7 2 gravityequation5.gif 6.67 x 10 -11 5.98 x 10 24 70 3.19 x 10 6 2 gravityequation6.gif M 1 M2 D2 gravity_example.html More Practice with Gravity You will need to use your scientific calculator to check the math in the following examples. You may find, like so many students of introductory astronomy, that the hardest thing about exponents is figuring out which buttons to push on your calculator. For the calculator provided with Microsoft Windows, there is an "Exp" key. First, put in the base number (for example, in the number 6.67 �10-11, the "6.67" is the base number). Then click on the "Exp" key and enter the exponent, clicking on "+/-" to make the exponent negative if needed. The Force of Gravity Between You and the Earth The equation that we use for determining the force between the Earth and you is: force = where M1 is the mass of Earth in kilograms; M2, your mass in kilograms; and R, the radius of the Earth in meters. The G is the gravitational constant: 6.67 �10-11 N m2/kg2. Let's not worry too much about the units of measure, however. Examples 1.A realistic example. Your mass is 50 kilograms (70 kg * 2.2 lbs/kg = 154 pounds). The force felt between you and the Earth (equal and opposite) is: force = = = 686 N 2.Let's double the radius of the Earth, so that R = 1.276 � 1013 meters. force = = 171.5 N you would weigh 1/4 as much! 3.Let's triple the radius of the Earth, so that R = 1.276 � 1013. force = = = 76.2 N. you would weigh 1/9 as much (686/9 = 76.2, all numbers are rounded off)! 4.How about a little trick? Let's say the Earth shrank, so that its radius becomes 1/2 of what it was before. Now, the girl, still standing on the surface, is closer to the center of the Earth. Before we go through the calculations, you should predict whether she will weigh a.the same, b.more, or c.less. If you guess "more" or "less," then predict how much more or less. The new radius of the Earth, after shrinking, is 3.19 � 106 meters, so the new force becomes: force = = 2744 N Let's see: 2744 divided by 686 = 4. If the Earth were to shrink to 1/2 of its current radius, you would weigh four times as much! 5. Following this line of reasoning, if the Earth's radius were 1/3 of its current radius, you would weigh 9 times as much. (Remember when we are doing these calculations, the mass of you and the mass of the Earth are not changing.) The force between you and the Earth depends directly on the two masses. It doesn't take a rocket scientist to know that if you ate so much that you ended up with two times your current mass, you would weigh two times as much. The force between you and the Earth would double, and your ankles would ache. You will not be required to solve any equations involving such large quantities with exponents; however, you should have an understanding of how the force between you and the Earth would change should either or both of the masses change, or if the radius of the Earth changed. The Force of Gravity Between Two Worlds You may have wondered during the above examples why we always measured from the center of the Earth to the surface, in other words, used the radius of the Earth. That is because solid, spherical objects act as if all of the mass were contained right in the very center (this is not strictly true, but a good enough approximation for our use). Let's take look at other examples, now involving two spherical worlds. This time let's use some values for the masses that makes our arithmetic a bit more manageable, and get rid of those pesky exponents. Because we want to look at relative changes, we are also going to ignore "Big G." The equation we use here is similar to the one above, but this time we substitute D, meaning the distance between the centers of the two worlds. The equation is force = where this time the two masses, M1 and M2 represent the masses of the two worlds. The worlds are shown here all at approximately the same size, but the radii do not matter, just the distances between the centers. Calculate the force between each of the worlds, substituting the values shown in the figure into the equation above. Do not bother with units of measure here, it's the concept we want to understand. Make sure you try each example before looking at the answers. gravity_example_answers.html Gravity Example Answers Remember the equation we are using: force = A.force = 1 B.force = (1 * 1)/42 = 1/16 C.force = (1 * 1)/22 = 1/4 D.force = (1 * 2)/22 = 1/2 E.force = (1 * 3)/22 = 3/4 F.force = (1 * 4)/22 = 1 G.force = (2 * 3)/22 = 3/2 Note that examples A and F both have a force equal to 1. In example F, the larger mass of one of the bodies offset the fact that they were twice as far away from each other as in example A. astro101a01_math.html A Math Refresher Working with Ratios Finding the ratio of two numbers means dividing one by the other. When we know that one ratio will be proportional to another ratio, and we know the values of three of the numbers, it makes finding the unknown fourth number easy. Here is a simple example: When we work with ratios, some of the units may cancel out: Here is a slightly more difficult example, where the unknown is in the denominator of one of the ratios: After a bit more manipulation we get: Let's look at a more specific problem. Let's say you know that the distance between Seattle and Tacoma is 40 miles. On your map, that is represented by 4 inches. You want to know how far across the country is (as the crow flies). You measure on your map, and find that the distance is represented by 20 inches. Setting the problem up, we say that "40 miles is to 4 inches as x miles is to 20 inches." Or in equation form: Making Measurements When making measurements online, it doesn't matter what part of the cursor you use (for example, the tip of the "finger on the hand" or somewhere on the "palm"), as long as you are consistent with all measurements. A Little Bit of Trigonometry The hardest part about trigonometry these days is trying to figure out which buttons to push on the calculator. A refresher for sine, cosine, and tangent of an angle for a right-angle triangle, in this case the angle represented by the Greek letter alpha, having sides of lengths A, B, and C: Sin(alpha) = opposite/hypotenuse (or A/C) Cos(alpha) = adjacent/hypotenuse (or B/C) Tan(alpha) = opposite/adjacent (or A/B) To solve the problems when you know the angle (such as 0.5 degrees for the angular size of the Sun and Moon), manipulate the equation so that the unknown is on the left-hand side and the known values are all on the right-hand side. Percentage Error Calculating the percentage error is something we all (at least in theory) learned in middle school or earlier, but you may be a bit rusty in this skill. In calculating this error, we compare the value we obtained to the accepted (true) value. The formula to use is: ratio1.gif A 3, A = 3 x 150 = 30 150 15 15 ratio2.gif A = 3 mi, A = 3x 150 km = 30 km 150 km 15mi 15 mi crossed out ratio3.gif 150 km = 3 mi 150 km = x x 3 mi x 15 mi 15 mi ratio4.gif 150 km X 15 = x, x = 750 km 3 ratio5.gif 40 miles = x miles 4 inches 20 inches percent_error.gif my value - true value x 100 = % error true value trigfig.gif A C a B Meteorites: Stones from the Sky Summary To examine 12 different meteorites of 4 different types -- iron, stony, stony-iron, and carbonaceous chondrite -- and to correctly identify 6 unknown meteorites. Background and Theory Meteorites are fragments of other worlds that have survived the entry into the Earth's atmosphere. Most meteorites originate in the asteroid belt from bodies that formed very early in the history of the solar system. Almost all of the information we have learned about the solar system, such as its age, history, and chemical composition, is due to the detailed study of meteorites. Types of Meteorites There are three basic origins of meteorites. This leads to a classification of meteorites into three types: stony, stony-iron, and iron. Meteoriticists recognize many more types of meteorites, and have reconstructed a marvelously detailed history of the solar system from their subtle differences. The images shown here are from this extensive gallery of meteorite images. It is highly recommended that you take the time to visit this site. Iron Meteorites The most easily recognized meteorites are the iron meteorites. Since even a casual examination shows that they are not ordinary rocks, they tend to be very common in collections. However, they are rare in space. They are heavy and, except for a thin crust (made by the melting of the surface by the passage through the atmosphere), they look and feel like metal. Chemically, they are mostly iron with a few percent nickel and a little cobalt. When sawed in half and polished, they display a geometrical pattern called a Widmanstatten pattern (see figure at the left which shows an iron found in Henbury, Australia). This pattern is the result of the meteorite cooling very slowly under very high pressure. Iron meteorites were once the cores of larger, differentiated bodies, most likely asteroids. Because of differentiation, these large asteroids developed an iron core and a stony outer mantle. Between the core and the mantle was a stony-iron region, more iron toward the core, more stony toward the mantle. Collisions in the asteroid belt break up asteroids, sending particles into the inner solar system. Occasionally one of the bits runs into the Earth and falls as a meteorite. The iron meteorites we are handling in class are samples of the cores of worlds formed out beyond the orbit of Mars. Stony Meteorites The most common meteorites that fall to the Earth are called stony meteorites. Many are from the outer parts of an asteroid that was destroyed by collision, but some are pieces of material that was never part of a much larger body. Meteorites that come from such a small, undifferentiated body are called primitive meteorites. The stony meteorites vary in appearance: some are light, some dark, some are coarse grained, some fine grained. Chemically they are also diverse; however, they all have a telltale composition that tells us that they are definitely not from Earth. Their diversity and the fact that they tend to look like ordinary rocks to the untrained eye means that stony meteorites are difficult to recognize in the field. Unless someone sees them fall, they usually go unnoticed. Therefore, although stony meteorites are the most common type out in space, they are rarer than irons in collections on Earth. The stony meteorite shown in the figure at right is from Silverton, Texas. Stony-Iron Meteorites Pieces of material from the boundary zone between the cores and mantles of the now-destroyed asteroids are also found. These very rare meteorites are called stony-iron meteorites. They tend to look like irons with pieces of stone in them, or stones with pieces of iron. This stony-iron meteorite was found in Kansas. This stony-iron meteorite was found in Dalgaranga, Western Australia. Carbonaceous Chondrite Meteorites An especially important type of meteorite is the carbonaceous chondrite. These are stony meteorites of a very special kind, usually black or dark gray in color. They are rich in the element carbon (thus their black color) and they contain small spherical droplet-like inclusions called chondules. They are among the most unchanged (primitive) objects in the solar system, having survived literally untouched for 4.6 billion years. It has been recently learned that some chondrules were formed outside of our solar system and thus were around long before our solar system was even formed. So, not only are carbonaceous chondrite meteorites an important probe into the early history of our solar system, but they may supply us with materials from beyond our solar system. Although carbonaceous chondrites are fairly abundant among meteorites that fall to the Earth, they look enough like Earth rocks that they are rare in collections. They also weather very easily and do not survive long on the surface of the Earth. This is a section of the most famous carbonaceous chondrite, the Orgueil, found in France. It is one of the most studied meteorites; some amino acids (the "building blocks of life") are found in this meteorite. Notice the extremely black color. This is a section of a carbonaceous chondrite found in Allende, Mexico. The small white specks are chondrules. Most of the chondrules are roughly spherical in shape. Procedure The tables in the lab have a number of meteorites of these different types. Examine them carefully with the idea that afterwards you will be identifying meteorites for which the types are not going to be given. Pay particular attention to the densities, colors, fusion crust, chondrules, and metallic materials. On this page, write down the characteristics of the different types of meteorites that will allow you to identify similar ones later. Meteorite Type Location of Find Specific Characteristics Density Colors Chondrules? Metallic? Other Iron Canyon Diablo heavy and, except for a thin crust Odessa Henbury Guadalupe Stony Wellman some are light, some dark, some are coarse grained, some fine grained. Dalgety Downs Millbillillie Cocklebiddy Stony-Iron Dalgaranga look like irons with pieces of stone in them, or stones with pieces of iron. Brenham Carbonaceous usually black or dark gray in color. Chondrite Allende (1) Allende (2) Astronomy 150 Name ______________________________ Meteorite Quiz Now that you have had the opportunity to look over the various types of meteorites, you should be able to apply your newly found knowledge to a possible real-life situation. A good friend of yours has learned that you are taking Astronomy 150 and excitedly invited you over to take a look at his new meteorite collection. The collection has cost him one-month's salary, but he thinks it is worth it. He lays out the six meteorites on the table in front of you and asks you to identify what he has just purchased. Write down what type of meteorite you think each one is and why. What characteristics of each rock lead you to classify it as you did? Unfortunately, you have very bad news for your friend; you suspect that one or more of his purchases are not meteorites at all, but are terrestrial rocks. If you think the sample is not a meteorite, then just write down "rock" as its type. Unknown Meteorite Type Reason for this Identification 1. 2. 3. 4. 5. 6. collected 76.8 kg of rock and soil samples, took photographs, and set up the ALSEP and performed other scientific experiments. This was the first mission which employed the Lunar Roving Vehicle which was used to explore regions within 5 km of the LM landing site. After the final EVA Scott performed a televised demonstration of a hammer and feather falling at the same rate in the lunar vacuum. spacecraft contain contained propellant tanks, reaction control engines, wiring, and plumbing. Five silver/zinc-oxide batteries provided power after the CM and SM detached, three for re-entry and after landing and two for vehicle separation and parachute deployment. The CM had twelve 420 N nitrogen tetroxide/hydrazine reaction control thrusters. The CM provided the re-entry capability at the end of the mission after separation from the Service Module. The SM was a cylinder 3.9 meters in diameter and 7.6 m long which was attached to the back of the CM. The outer skin of the SM was formed of 2.5 cm thick aluminum honeycomb panels. The interior was divided by milled aluminum radial beams into six sections around a central cylinder. At the back of the SM mounted in the central cylinder was a gimbal mounted re-startable hypergolic liquid propellant 91,000 N engine and cone shaped engine nozzle. Altitude control was provided by four identical banks of four 450 N reaction control thrusters each spaced 90 degrees apart around the forward part of the SM. The six sections of the SM held three 31-cell hydrogen oxygen fuel cells which provided 28 volts, an auxiliary battery, three cryogenic oxygen and three cryogenic hydrogen tanks, four tanks for the main propulsion engine, two for fuel and two for oxidizer, the subsystems the main propulsion unit, and a Scientific Instrument Module (SIM) bay which held a package of science instruments and cameras to be operated from lunar orbit and a small subsatellite to be put into lunar orbit. Two helium tanks were mounted in the central cylinder. Environmental control radiator panels were spaced around the top of the cylinder and electrical power system radiators near the bottom. Apollo Program The Apollo program included a large number of uncrewed test missions and 12 crewed missions: three Earth orbiting missions (Apollo 7, 9 and Apollo-Soyuz), two lunar orbiting missions (Apollo 8 and 10), a lunar swingby (Apollo 13), and six Moon landing missions (Apollo 11, 12, 14, 15, 16, and 17). Two astronauts from each of these six missions walked on the Moon (Neil Armstrong, Edwin Aldrin, Charles Conrad, Alan Bean, Alan Shepard, Edgar Mitchell, David Scott, James Irwin, John Young, Charles Duke, Gene Cernan, and Harrison Schmitt), the only humans to have set foot on another solar system body. Total funding for the Apollo program was approximately $20,443,600,000. 3. Kinetic Energy Apollo 17 Soil Mechanics Investigation A trench dug to study soil properties. Soil mechanics is the study of the mechanical properties of soils and the way that these properties affect human activities. Soil mechanics studies were performed on all six of the Apollo Moon landings. The goals of these studies were to improve our scientific knowledge about the properties of lunar soil and to provide the engineering knowledge needed to plan and perform lunar surface activities. Soil mechanics studies took a variety of forms. These included crew commentary while collecting geologic samples and deploying experiments and postmission analysis of photography of these activities. Several experiments were performed specifically to study soil mechanics. These include use of penetrometers, which are rods that measure the force required to penetrate to various depths in the soil. Also, several small trenches were dug to study the soil properties along the trench walls. Finally, studies were performed on samples returned to Earth. For example, analysis of core tubes allowed properties such as density, average grain size, strength, and compressibility to be measured as a function of depth. During landing, the impact of rocket exhaust with the surface produced dust clouds. On some missions, dust became visible 30 to 50 meters above the surface, and during the final 10 to 20 meters of descent, the surface was largely obscured by the dust cloud. On other missions, the dust cloud was not as dense and the surface remained clearly visible throughout the landing. The soil on the Moon is very fine-grained, with more than half of all grains being dust particles less than 0.1 millimeters across. Some of these particles become electrostatically charged and cling to objects (such as space suits and other equipment) that they come in contact with. The dark dust grains absorb sunlight, and equipment that became dust-coated sometimes became excessively hot. Despite the fine-grained nature of the surface, it provided good traction for astronauts as they moved about. Crew mobility, both on foot and in the lunar rover, was affected more by local topography such as craters and ridges than by soil properties. The lunar surface easily supported the weight of the astronauts and their equipment. Typically, astronaut boots and the lunar rover's wheels only penetrated 1 to 2 centimeters into the surface, with penetration reaching five centimeters in some places. The lunar module footpads sank 2 to 20 centimeters into the soil. When astronauts inserted sampling tubes into the soil, they typically found penetration was easy for the first 10 to 20 centimeters and increasingly difficult below that depth. The deepest penetration achieved on a hand-driven core tube was 70 centimeters, which required about 50 blows with a hammer. For sampling at greater depths, the Apollo 15, 16, and 17 crews used a battery-powered drill. This allowed sampling to depths of 1.5 to 3 meters, which was achieved easily on Apollo 16 but with much more difficulty on Apollo 15 and 17. earthcircumference.gif Syene to Alexandria = 7.2 degrees circumference of the Earth 360 degrees epe0.jpg Energy eV ionization 13.6 13.0 12.7 12.0 10.2 0 ground state + fmmd2.gif F x M sm P22 Earth D2 fmmr2.gif F X Mm R2 CelestialNavigation1.htm SKYWATCH PROJECT: CELESTIAL NAVIGATION TIME REQUIRED: Part A: About three hours around noon Part B: About an hour on a clear evening PART A - SOLAR OBSERVATIONS EQUIPMENT REQUIRED: A smooth, sunny location, a stick (at least one foot long), a compass (to find north), a protractor, a watch and a ruler. BACKGROUND: The gnomon, a fancy name for a vertical stick (must be thin and round) stuck in the ground, is the most ancient of all astronomical instruments. It can be used to chart the Sun's motion across the sky so as to determine one's latitude and longitude, as well as the time of true noon. WHAT TO DO: Construct a gnomon in a location that is well exposed to the Sun. A flat, smooth (grass can make things uneven) surface is best; if the gnomon cannot be easily stuck in the ground (as on asphalt), then a small stand will help. A "plumber's helper" turns out to be ideal! Use a compass to find true north (note: compass needles point to magnetic north, which is approximately 18 degrees east of geographic or true north in the Seattle area) and draw a north-south line on the ground through the gnomon. If you can't locate a compass, estimate a north-south line. It will be best to use a large sheet of paper, well secured to the ground to prevent wind problems. A possible setup (bird's eye view) is: From about 11:30 am to about 2:30 pm PDT (or 10:30-1:30 PST) accurately mark the position of the shadow's tip and the time of observation - every 15-20 minutes is sufficient except for 12:30-1:30 PDT (11:30-12:30 PST) when every 5-10 minutes is required. The tip's shadow will be fuzzy: you should try to mark the point halfway between the end of the dark shadow and the end of the "fuzziness". Be sure also to measure the gnomon's length above the ground. Afterwards make a table giving for each observation: (1) time, (2) length of shadow, (3) azimuth of shadow, and (4) altitude angle of Sun (calculated using trigonometry; see diagram above). Make a plot of altitude angle versus time and draw an "eyeball curve" for your data points to estimate the time of maximum solar altitude, which is called local noon. Also make a plot showing how the tip of the shadow moved in azimuth through the day. You probably will find that your measured time for the shortest gnomon shadow (Sun highest) is not exactly 12:00 am PST (1:00 pm PDT), as you might expect. There are several reasons. The first is due to the equation of time, as discussed in lecture, and this correction is supplied for you in a table on page 3. In this table "fast" means that local noon will happen before clock noon. Make this correction (and one for Daylight Savings Time if necessary) to your observed time for local noon. Any difference in your new value from 12:00 is due to the fact that your watch is set to PST, which applies to the center of the Pacific Time Zone at 120�longitude West. You can therefore use this time difference to actually calculate the longitude of your location, remembering that for each four minutes that local noon is observed to be later than 12:00, your location must be 1� of longitude farther west. What longitude do you find for Seattle? How accurate a determination do you think it is? You can also determine your latitude using your gnomon data. Please do so. The method is a basic one used by mariners whenever they "shoot the Sun" with a sextant. Start with your measured value of the maximum altitude (amax) of the Sun. The diagram on p. 3, a fundamental one for the entire course, illustrates that the following formula is true: b = 90� - amax + d , where b is your latitude and d is the declination of the Sun, that is, how many degrees north (positive) or south (negative) of the celestial equator the Sun is on that day. Through the year d changes from -23.5� (northern winter solstice) to +23.5� (summer solstice) as the tilt of the earth's axis changes with respect to the Sun. A second table on p. 3 gives you daily values for d in units of degrees and arcminutes - convert to the nearest one-tenth of a degree by remembering that 0.1� = 6'. Finally, compare your results for latitude and longitude with the accepted (map) values. PART B - POLARIS OBSERVATIONS In this part you use a quadrant to measure your latitude using Polaris on one night. Your angle-measuring device is a homemade affair, as shown in the diagram on p. 2. (The vertical support shown is not really needed.) For the greatest accuracy, use as large a protractor as possible. Rather than attaching an actual protractor, it may be easier to use a large piece of paper (on cardboard) on which you've drawn all of the tick marks for angles such as a protractor shows. Make sure you understand what a scale reading of 0�or 90� means in terms of zenith or horizon. Give your results in terms of the angle above the horizon, called the altitude angle. Sight along the stick with your eye and have a friend read the scale when you say "Now!", or, if you're by yourself, once you're lined up pinch the string so as to "lock" the movable string on the correct reading. To improve accuracy, take several readings and average. Once you have determined your latitude with Polaris, compare your measurement with a value derived from a map and with your gnomon-shadow value. Extra Credit: The elevation of Polaris is approximately your latitude, but since Polaris is not located exactly at the North Celestial Pole (NCP), you can be off by as much as almost one degree. The essence of the correction is illustrated below. Find Cassiopeia at the time of your observation, make a sketch such as that below, and estimate the angle m ; if you forget to do so, you can use a planetarium software package as a substitute. Then, knowing that Polaris is located 50' from the NCP, use simple trigonometry to calculate the difference in altitude t between Polaris and the NCP; in the illustration the NCP is at an altitude t = 50' sin m higher than Polaris, but your situation may be different depending on where Cassiopeia is. CelestialNavigation2.htm Salvaging the Skywatch Project on CELESTIAL NAVIGATION The weather has obviously been even more atrocious this quarter than is usual for Seattle's dismal winter. Thus this assignment is being revised in the following manner. - It is still worth 10% of your total grade, but it is no longer given such importance that you will receive an Incomplete if you do not do it. - You now have two options for the Skywatch, either with simulated data (given below) or, as originally intended, with real data obtained by you in the real world; however, you cannot do both options. The advantage of the real data option is that you get up to 20% extra credit on the assignment. - if you choose the simulated data option and yet have been able to obtain some real data (either Polaris or solar data), then submit a write-up about these data and you can earn some extra credit on the assignment - Due date is still Thu. 11 March, for either option (Skylogs are still due on Thu. 4 March); if you are possibly doing a second skywatch for extra credit (as discussed in the syllabus ; write-ups are available on the class Web site), then it is also due on 11 March. ____________________ The procedure is basically the same as in Part A of the original assignment, except now you have no idea of where you are, except that you were kidnapped several months ago while surfing off the coast of Washington State, and you've been kept in the hold of a ship ever since! But at last you've been able to get up on deck and take the data given below. Moreover, fortunately you have a watch that indicates Greenwich Mean Time (GMT), the time that corresponds to zero degrees longitude. Thus GMT is your basic reference, rather than PST as discussed in the original assignment. You know that the date is 19 Feb 1999 (by making notches in the hold all those months), and you also have a handy table that tells you for this date: Equation of time: sun is 14.0 minutes slow compared to mean time Declination of sun -11�24' = -11.40 � The length of your gnomon is 8.4 cm. Using a plot of altitude angle of the sun versus time, derive your longitude and latitude on planet Earth. Check a map and report in which sea you are located.