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