ASTR 1110, Summer 2000

Homework #2

Motions of the Planets

Due at start of class, June 14 (changed from the syllabus).

Formulas & Numbers

Kepler's 3rd law: (orbital period in yr)2 = (average distance in AU)3 Works for bodies orbiting our sun.
Kepler's 3rd law: (orbital period in s)2 = 4 pi2 (average distance in cm)3 / (G (M1 + M2)) Works for all bodies everywhere. M1 and M2 are the mass of the central body and the satellite, and G is the gravitational constant.

This homework set shouldn't require any use of a calculator. Homework solutions should be neatly typed, and be sure to fully explain your answers.

1. Fast and Slow

Ida is the first asteroid ever known to have a satellite orbiting it, named Dactyl. The Galileo spacecraft measured that Dactyl's orbital period was about one Earth month. Astronomers might want to know the asteroid's mass, so we could determine what sort of rock it was made of and where it came from.
a) Which of Kepler's laws could be used to determine Ida's mass? How?
b) Let's assume Ida's mass suddenly doubled -- for instance, if it collided and merged with another asteroid. Would Dactyl suddenly begin to orbit with a longer period, or a shorter one?

2. Moon Phases

If the moon is full, approximately one time of day does it rise? (e.g., 6 AM, noon, 6 PM, midnight)? For approximately how long will the full moon and the sun be in the sky together? Could this configuration be near a solar eclipse, a lunar eclipse, or neither?

You might want to use a moon ball like we did in the planetarium - just stand in the right place, and the solution will pop out.

3. Models of the Solar System

Explain several problems with Ptolemy's model of the Solar System, and what led to the heliocentric model. Why do you think that the geocentric model lasted as the preeminent description of the Solar System for 1300 years?

4. Uranian Weather

Uranus is tilted on its side by approximately 90 degrees, so that its `North' pole doesn't point toward Polaris (like Earth's does). Uranus's orbital period is 84 Earth years and its rotational period about one Earth day.
Describe what the days and years would be like on Uranus if you were positioned on a) one of its poles, and b) its equator. How long would the sun be up for in each case, and what would the seasons in each case be like? Would the sun rise and set every day in each case, or not?

You may find it helpful to get a globe (or some fruit), and think this one out. Once you're set up right, it's easy.


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

Last modified 12-Jun-2000