Exam #1 - June 16, 2000

History of Astronomy, Motions of the Sky, and the Terrestrial Planets

Astronomy 1110

Dr. Henry Throop, University of Colorado

"One had to be Newton to realize that the Moon is falling, when everyone sees that it doesn't fall." - P. Vallery, 1966

Formulas & Numbers

Kepler's 1st law: All planets move in ellipses, with the Sun at one focus.
Kepler's 2nd law: The orbit of each planet sweeps out equal area in equal time.
Kepler's 3rd law: (orbital period in yr)2 = (average distance in AU)3, for bodies orbiting the sun.
Kepler's 3rd law: (orbital period in s)2 = 4 pi2 (average distance in cm)3 / (G (M1 + M2))
1 AU = 150 million km (1.5 108 km = 1.5 1013 cm)
1 km = 103 m = 105 cm = 106 mm
Speed of light = c = 3 1010 cm/s
Light year = 1 1018 cm
Velocity = Distance / Time

Instructions: There are 20 questions. The first set should be done on the bubble form, and the second and third sets on the test itself. If you are unclear on anything, please talk to me or Rob. The exam is due at the end of class, 12:35 PM.

Multiple Choice (30 points @ 3 points each)

1. A new asteroid has been discovered with a perfectly circular orbit. Is this a violation of Kepler's first law?
a) No - it's still an ellipse
b) It can't really be a circle, and must be a measurement error
c) Kepler's laws should be fixed
d) It's probably two asteroids orbiting each other, like Ida & Dactyl.

2. Why are many observatories built near the equator?
a) It's warmer and the atmosphere is more stable there.
b) The nights are longer on the equator.
c) Throughout the year, all the stars can be seen from the equator.
d) There is less `light pollution' from street lights.

3. What holds the planets in their orbits?
a) Their momentum and energy.
b) The tug of gravity constantly pulling them toward the Sun.
c) Collisions with asteroids and comets
d) Kepler's second law.

4. Comet Hale-Bopp has an orbital period of about 4,000 years. However, it was only visible to most people on Earth for a few months. Why could this be?
a) We can only see comets standing near the equator.
b) The comet melted as it got closer to the Sun.
c) Greenhouse gases in the comet (methane, carbon dioxide) prevented us from seeing it.
d) An application of Kepler's second law.

5. The Earth's atmosphere has been relatively stable over the age of the Solar System. What is one reason why?
a) Its orbit has always been an ellipse.
b) It is small enough so that it cannot retain an atmosphere for very long.
c) People have recently tried to stabilize it by burning fossil fuels.
d) There has been feedback between its atmosphere and surface.

6. Put these objects in proper order of size (diameter)
a) Milky Way, planet, solar system, star, asteroid, universe.
b) Solar system, asteroid, star, planet, Milky Way, universe.
c) Universe, Milky Way, solar system, star, planet, asteroid.
d) Asteroid, solar system, planet, star, Milky Way, universe.

7. Put these times in proper order
a) Earth orbital period, Lunar orbital period, Earth rotational period, age of Earth, age of Universe.
b) Age of Universe, age of Earth, Earth orbital period, Lunar orbital period, Earth rotational period.
c) Earth orbital period, Lunar orbital period, Earth rotational period, age of Universe, age of Earth.
d) Age of Earth, age of Universe, Lunar orbital period, Earth rotational period, Earth orbital period.

8. Newton's law of gravity says that all bodies attract each other. Why, then if there is a force of gravity between you and the star Deneb, do you stick to the Earth and not orbit Deneb?
a) The Sun is the most massive star in the Galaxy, which is why we orbit it.
b) Gravity doesn't work between gasses, only planets.
c) The distance to Deneb makes its gravitational force unimportant.
d) Gravity works only for planets around the Sun.

9. In which of the following cases are you accelerating?
a) When in orbit around the Sun.
b) When slowing down at a stoplight.
c) When running around a corner at a constant speed.
d) All of the above

10. If you were standing on the South Pole, where would you see Polaris?
a) It's not visible from the South Pole.
b) It rises in the East and sets in the West, like all stars.
c) You can only see it during the winter (southern hemisphere summer).
d) It would be visible, but only just barely above the horizon.

Short Answer Questions (30 points @ 5 points each)

1. You are picnicing outside and see a moon overhead with its east half illuminated (to your left). What meal are you eating?




2. You are building sand castles on the beach and notice that the tides are particularly high always at this time of the month, and regularly destroy your creations. What phase of the moon is it? Do you believe your friend who tells you there's a solar eclipse coming up tomorrow? (Drawing a diagram may help!)




3. Explain what is meant by a `Universal Law' such as Newton's law of gravity.




4. The few top meters of the Earth's crust are called `topsoil' and are a very fine powder (mixed with some water). What most directly causes this on the Earth?




5. The top few meters of the Moon are also a fine powder. Could the the same process be at work, or a different one? If so, which?




6. Assess the statement issued by one recent environmental protester: `We really must stop the greenhouse effect!'




Long Answer Questions (40 points @ 10 points each)

1. Describe retrograde motion of the planets in the sky. How could you observe it, how long would it take to observe, and what causes it? Describe how retrograde motion was modeled in both the Ptolemaic and heliocentric models.

2. Let's imagine astronomers have discovered a new planetary system orbiting the star Beta Centauri, which a few times brighter than our Sun. They can determine that it has four planets orbiting at 0.1 AU, 2 AU, 5 AU, and 100 AU. All planets have the same mass, size, and density of the Earth. Describe what each of the the planets in this system might look like. How would their atmospheres compare? What about their surfaces? What features would you expect to see on the surface of each one? Which ones might be the best place to look for life like our own (which requires liquid water)?

3. Compare and contrast the evolution of the surfaces on Mercury and Venus. Be detailed: which processes are important or unimportant on each one, and what determines which ones dominate? How do you think the surfaces will continue to evolve for the next billion years?

4. Let's say we were standing next to the Sun, and observing Pluto, 45 AU away. If the Sun were to suddently go out, how long (in hours) would it take until Pluto disappeared from our view? In other words, how long would it take the light to go out to Pluto, and return? Show your steps.

C&H cartoon here


Dr. Henry Throop, University of Colorado / throop@broccoli.colorado.edu

Last modified 15-Jun-2000