### University of Colorado Cycles in the Sky and Gravity and Light Questions

(1) Kepler’s 2nd Law

(3 pts.) A comet is only visible when it is sufficiently heated by the Sun (more about this later in the course). Use Kepler’s 2nd law to explain why comets, which tend to have very eccentric orbits, are generally only visible for a small fraction of their orbit.

(2) Kepler’s 3rd Law

(3 pts.) (a) There is an asteroid that orbits the Sun in a circle, once every 15.4 years. Using Kepler’s 3rd law, calculate distance between this asteroid and the Sun. Don’t forget the units of your answer. No credit for an answer without showing how you derived it.

(3 pts.) (b) There is an asteroid that that orbits the Sun in a circle at a distance of 22.5 AU from the Sun. Using Kepler’s 3rd law, calculate how much time it takes for this asteroid to orbit the Sun. Please show your work for this problem as well.

(3)Galileo
Galileo’s observations of the phases of Venus is a classic example of the scientific method. Look at the figure below which shows the phases of Venus for the heliocentric and geocentric models of the solar system. The geocentric model predicts that Venus will go through a certain group of phases, while the heliocentric model predicts that Venus will go through a different group of phases.

(4 pts.) (a) Describe in words what phases the geocentric model predicts that Venus will go through.

(3 pts.) (b) Describe in words what phases the heliocentric model predicts that Venus will go through.

(2 pts.) (c) Describe in words the observations that Galileo made by studying Venus with his telescope: What phases did Venus actually go through?

(2 pts.) (d) Describe in words the explanation of the observations – what could Galileo conclude?

(3 pts.) (e) Galileo also observed that at certain times in the Venus cycle, Venus appeared much larger, and at other times, it appeared much smaller. Galileo attributed this change in apparent diameter to the changing distance between the Earth and Venus. If Ptolemy’s geocentric model was correct, would Venus appear to grow larger and smaller in our sky, or would it remain at the same same size throughout a cycle?

(4) What to do?!
(3 pts.) You are dressed up in a spacesuit on an EVA outside the space station. A fellow crew member accidentally cuts your life support cable. What can you do? You are floating detached from the space station with little oxygen in your suit. You have a big wrench in your hand. To get back to the space station do you throw the wrench:

(a) side ways

(b) away from the space station

(c) towards the space station

Choose which option is correct and write an explanation that includes at least one of Newton’s Laws of Motion.

(5) Phases and Venus

(4 pts.) Suppose we observe the planet Venus tonight and we see that from our perspective here on Earth, Venus is almost full. At the same time, if there was an observer on Venus who could see the Earth with a telescope, what phase would the Earth appear to be in from the Venus observer’s perspective? (Hint: Draw a diagram of the Earth, Sun, and Venus.)

(6) Floating in Space.

Most people believe that the astronauts float around in the space shuttle because there is no gravity in space, but that’s not true!

(2 pts.) (a) Let’s think about the Moon: Describe how the Moon moves over the course of one month.

(3 pts.) (b) Suppose we magically flipped a switch and turned off all the forces that pull on the Moon. According to Newton’s first law how would the Moon move?

(3 pts.) (c) Assume that the Moon’s orbit around the Earth was a perfect circle. Would the moon be accelerating right now? Use a few sentences to explain your answer. (Hint: Remember that “acceleration” has a different meaning in astronomy than in every day life!)

(2 pts.) (d) A friend of your says, “Wouldn’t it be fun to go out into space where there’s no gravity?” How would you persuade her that there really is gravity in space? (Please use an example other than the Moon.)