1. Homework #2 Covers Chapters 1, 2, and 3
Due Thursday, February 1, 11:59 PM
Covers Chapters 1, 2, and 3
Estimated time to complete: 1 hour 10 minutes (so don’t wait until the last minute!) – can stop and start as you wish
Read chapters, review notes before starting
Some questions have multiple parts – do not skip them
For some of the drag-and-drop ordering questions, two or more of the answers might be in the same location (i.e., two objects might have the exact same age if you are sorting by age). In this case, place the two answers on top of each other, not side-by-side.
Note: Incorrect guesses will count against you from now on.

2. Homework #3 Due Monday, February 12, 11:59PM Covers Chapters 4 and 5
Estimated time to complete: 1 hour (so don’t wait until the last minute!)
Read chapters, review notes before starting
You can still go back and do Homework #1 for partial credit

3. Thermal Energy: the collective kinetic energy of many atomic/molecular particles (for example, molecules in a rock, in air, in water)
Thermal energy is a form of kinetic energy.
Thermal energy is related to temperature but it is NOT the same.
Temperature is the average kinetic energy of the many particles in a substance – a measure of how fast the molecules of a substance are moving (vibrating).
Velocity of moving (vibrating) molecules is dependent on their temperature  hotter objects have more thermal energy than cooler objects (at the same density)
Students sometimes get confused when we’ve said there are 3 basic types of energy (kinetic, potential, radiative) and then start talking about subtypes, so be sure they understand that we are now dealing with subcategories.

4. Thermal energy is a measure of the total kinetic energy of all the particles in a substance. It therefore depends both on temperature AND density.
Example:
We’ve found this example of the oven and boiling water to be effective in explaining the difference between temperature and thermal energy. You may then wish to discuss other examples. You might also want to note that the temperature in low-Earth orbit is actually quite high, but astronauts get cold because of the low density.
Which would you least want to put your hand into?
Note: a typical sauna has a temperature of 160° – 210° F

5. Don’t Confuse Temperature and Thermal Energy
The Sun possesses a very low-density corona with a temperature of 1 million degrees Kelvin.
But the heat in the corona is not enough to warm up a cup of coffee.
Why? There are so few particles per volume that energy can not be easily transferred from the corona to an object in the corona.
Students sometimes get confused when we’ve said there are 3 basic types of energy (kinetic, potential, radiative) and then start talking about subtypes, so be sure they understand that we are now dealing with subcategories.
High temperature does not automatically imply high thermal energy! (Think hot air vs. hot water).

6. 2) Radiative Energy
Energy in the form of light (more on this in Chapter 5) .
Students sometimes get confused when we’ve said there are 3 basic types of energy (kinetic, potential, radiative) and then start talking about subtypes, so be sure they understand that we are now dealing with subcategories.

7. 3) Potential Energy A) Gravitational B) Chemical C) Elastic
D) Mass-energy
Students sometimes get confused when we’ve said there are 3 basic types of energy (kinetic, potential, radiative) and then start talking about subtypes, so be sure they understand that we are now dealing with subcategories.

8. Gravitational Potential Energy
On Earth, depends on:
object’s mass (m)
strength of gravity (g)
distance object could potentially fall
We next discuss 2 subcategories of potential energy that are important in astronomy: gravitational potential energy (this and next slide) and mass-energy.

9. Gravitational Potential Energy
In space, an object or gas cloud has more gravitational energy when it is spread out than when it contracts.
A contracting cloud converts gravitational potential energy to thermal energy.
Less potential energy (more compact)
We next discuss 2 subcategories of potential energy that are important in astronomy: gravitational potential energy (this and next slide) and mass-energy.
More potential energy (more extended)

10. Chemical Potential Energy
Energy in an unlit match is stored chemical potential energy.
Energy in food (breaking apart chemical bonds of starches, carbohydrates, etc.)
We next discuss 2 subcategories of potential energy that are important in astronomy: gravitational potential energy (this and next slide) and mass-energy.

11. Elastic Potential Energy
Coiled spring
Stretched rubber band
Stretched archer’s bow
Bent diving board (just after diver lands on it)
We next discuss 2 subcategories of potential energy that are important in astronomy: gravitational potential energy (this and next slide) and mass-energy.

12. E = mc2 Mass-Energy speed of light mass Energy (potential)
Einstein’s theory of special relativity says that mass and energy are equivalent, and can be converted back and forth into each other. In other words, mass is a form of (potential) energy.

13. Mass-Energy
E = mc2
A small amount of mass can release a great deal of energy
Concentrated energy can spontaneously turn into particles (for example, in particle accelerators)
This is how stars make energy – we will talk about this a lot in later chapters.
0.1 kg of material

14. Summary of Types of Energy
Kinetic Radiative Potential
Energy of motion
(moving objects)
Gravitational (potential
to fall in a gravitational
field)
Light (Chapter 5) + +
Chemical (matches, batteries, energy stored within food)
Thermal energy
(energy of vibrating atoms/
molecules at temperature T)
You might wish to go through the example tracing the energy of a baseball back through time, as described on p. 90 of the text. +
Elastic (coiled springs) +
Mass-energy (E = mc2) – convert mass to pure energy, and back

15. Conservation of Energy
Energy can be neither created nor destroyed.
It can change form or be exchanged between objects.
The total energy content of the Universe was determined at the time of the Big Bang and remains the same today.
Important concept!
You might wish to go through the example tracing the energy of a baseball back through time, as described on p. 90 of the text.

16. Conservation of Energy
At top of arc, ball has lots of gravitational potential energy and little kinetic energy.
Just before the ball hits the table, it has less gravitational potential energy, but more kinetic energy (it is moving faster).
Conservation of energy tells us that sum of kinetic energy + gravitational potential energy of ball is the same at all times.
We next discuss 2 subcategories of potential energy that are important in astronomy: gravitational potential energy (this and next slide) and mass-energy.

17. Same concepts apply to space!
Near the Sun, planet has less gravitational potential energy and more kinetic energy (it is moving faster), than when planet is far away from the Sun (but PE + KE always a constant). This is just Kepler’s 2nd law of planetary motion!

18. Kepler’s 2nd Law is Simply a Restatement of the Conservation of Momentum
Conservation of angular momentum:
Mass x velocity x radius = constant
m x v x r = constant
If r goes down, v must go up
If r goes up, v must go down
(think of an ice skater pulling in her arms)
Orbits cannot change spontaneously without an external force.

19. Suppose you stepped off a cliff, and landed on a trampoline
Suppose you stepped off a cliff, and landed on a trampoline. Your kinetic energy is greatest _________, while your gravitational potential energy is greatest _________.
A) just after you step off; just before you land on the trampoline.
B) half way down; half way down.
C) just before you land on the trampoline; just after you step off
D) actually neither your kinetic nor gravitational energy vary during the process
We next discuss 2 subcategories of potential energy that are important in astronomy: gravitational potential energy (this and next slide) and mass-energy.

20. Suppose you stepped off a cliff, and landed on a trampoline
Suppose you stepped off a cliff, and landed on a trampoline. Your kinetic energy is greatest _________, while your gravitational potential energy is greatest _________.
A) just after you step off; just before you land on the trampoline.
B) half way down; half way down.
C) just before you land on the trampoline; just after you step off
D) actually neither your kinetic nor gravitational energy vary during the process
We next discuss 2 subcategories of potential energy that are important in astronomy: gravitational potential energy (this and next slide) and mass-energy.

21. Newton’s Second Law and Gravity
The Universal Law of Gravitation:
Every mass attracts every other mass.
Attraction is directly proportional to the product of their masses.
Attraction is inversely proportional to the square of the distance between their centers.
G = Gravitational constant of Nature

22. Gravity (An Example)
Suppose M1 doubles in mass, M2’s mass is cut in half and the distance between the two masses is doubled. What happens to the gravitational force between them?
Now, new mass_1 = 2M1, new mass_2 =1/2 M2, and new distance = 2d
New Force Fg = G * (2M1)(1/2 M2)/(2d)2 = G * M1M2/4d2
= 1/4 G* M1M2/d2 = 1/4 G* M1M2/d2 =1/4 Old Force Fg
Gravitational force would be diminished by a factor of 4.

23. Clicker Question
Suppose the mass of M1 is tripled, while M2 mass remains unchanged, and the distance between the two masses triples. What happens to the gravitational force between them?
A) It remains the same C) It is 1/9 as strong.
B) It is 1/3 as strong D) It is 3 times stronger.

24. Clicker Question
Suppose the mass of M1 is tripled, while M2 mass remains unchanged, and the distance between the two masses triples. What happens to the gravitational force between them?
New Force Fg = G * (3 M1)*(M2)/(d)2 = G * 3 M1M2/9d2
= 3/9 G* M1M2/d2 = 1/3 Old Force Fg
Force decreases to 1/3 original value (Answer B)

25. Kepler’s Third Law
More distant planets orbit the Sun at slower average speeds, obeying the relationship
p2 = a3
p = orbital period in years
a = avg. distance from Sun in astronomical
units (AUs)
This relation falls naturally from Newton’s law of gravitation (or any 1/d2 force law) and applies to all orbiting objects.

26. The Acceleration of Gravity
All falling objects accelerate at the same rate (not counting friction of air resistance) because of gravity at a rate g.
On Earth, g ≈ 10 m/s2: speed increases 10 m/s with each second of falling for all objects, regardless of mass.
Of course, value of g is different if you go to the Moon, Jupiter, etc.

27. Why do all objects fall at the same rate?
Different mass objects feel different gravitational forces from the Earth, but they all feel the same acceleration.

28. The Acceleration of Gravity (g)
Galileo showed that g is the same for all falling objects on Earth, regardless of their mass (but most likely not from dropping objects from the Leaning Tower of Pisa).
When you show this video clip, be sure to point out what is going on since it is not easy to see…
Apollo 15 demonstration
David Scott, James Irwin*, Alfred Worden
*no relation to me!

29. How is mass different from weight?
Mass – the intrinsic amount of matter in an object
Weight – the force that acts upon an object, depends on your local g value (you weigh more on Earth, less on the Moon, etc.)
You are weightless in free-fall, although you obviously have mass and are experiencing gravity.

30. Compared to Earth, on the Moon……
A) You would have the same mass and the same weight.
B) You would have a different mass and a different weight.
C) You would have a different mass but the same weight.
D) You would have the same mass but a different weight.

31. Compared to Earth, on the Moon……
A) You would have the same mass and the same weight.
B) You would have a different mass and a different weight.
C) You would have a different mass but the same weight.
D) You would have the same mass but a different weight.
We next discuss 2 subcategories of potential energy that are important in astronomy: gravitational potential energy (this and next slide) and mass-energy.
Mass is a measure of how much of you there is, while weight is a measure of the gravitational force you feel (which can vary with location).

32. Astronomy Myth #6
“Astronauts float around the Space Shuttle or International Space Station because there is no gravity in space.”

33. Astronomy Myth #6 There is gravity in space.
“Astronauts float around the Space Shuttle or International Space Station because there is no gravity in space.” WRONG!
There is gravity in space.
Weightlessness is due to a constant state of free-fall.
Astronauts are literally “falling around” the Earth
Astronauts must conserve angular momentum – they can’t just fall straight down

34. Question: If gravity is always attractive, why does Earth
not fall into the Sun?
Answer: Angular momentum must be conserved. The Earth cannot fall straight into the Sun.
Same answer as to why astronauts appear to float in space -- they are actually falling around the Earth (they feel gravity even though they are weightless).

35. How does Newton’s law of gravity extend Kepler’s laws?
Kepler’s laws apply to all orbiting objects, not just planets, not just our Solar System.
Ellipses are not the only orbital paths. Orbits can be:
bound (ellipses)
unbound
parabola
hyperbola

36. Escape Velocity
If an object gains enough orbital energy, it may escape (change from a bound to unbound orbit).
Escape velocity from Earth ≈ 11 km/s from sea level (about 40,000 km/hr).
Escape and orbital velocities don’t depend on the mass of the cannonball.
Can use this to discuss how adding velocity can make a spacecraft move to a higher orbit or ultimately to escape on an unbound orbit.

37. Center of Mass
Because of momentum conservation, orbiting objects orbit around their center of mass
In our Solar System, planets move on large orbits, and Sun moves on a tiny orbit around the center of mass of the Solar System.
We next discuss 2 subcategories of potential energy that are important in astronomy: gravitational potential energy (this and next slide) and mass-energy.

38. The center of mass between two gravitating objects is:
A) Closer to the more massive object.
B) Closer to the less massive object.
C) Midway between the two objects.
D) At the center of the more massive object.
We next discuss 2 subcategories of potential energy that are important in astronomy: gravitational potential energy (this and next slide) and mass-energy.

39. The center of mass between two gravitating objects is:
A) Closer to the more massive object.
B) Closer to the less massive object.
C) Midway between the two objects.
D) At the center of the more massive object.
Think of a heavier child on a teeter-totter – heavier child must sit closer to the balancing (fulcrum) point to balance lighter child.