1. Problem 2.9.**I**: Go to the "Binary Star Integrator"
(from the class webpage, click on "Astronomy Workshop", "Orbital
Integrators" and "2D Orbits". Check your answers to part b) and show
examples of tadpole and horseshoe orbits if they exist. View these in
both the rotating and inertial systems to help you understand what is
going on. Check your answer to part c) by starting the third particle
on a circular orbit 60 degrees ahead of Jupiter and varying its
semimajor axis. Make a table showing which values of the semimajor
axis allow the particle to cross Jupiter's orbit and which do not.

2. Problem 2.15.**E**

3. Problem 2.17.**E** Do this problem by writing a
short computer code in any language. Turn in a copy of your code and
its output. Check your answers in as many ways as you can think of
and discuss your results.

4. Problem 2.23.**I** All satellites within
synchronous orbit have nearly circular orbits, so you can assume
e=0. Before starting this problem, make a plot of Eq. 2.44
vs. distance. What are the main features and do they make sense
physically? After solving the problem, calculate the impact timescale
for Mars' moon Phobos. Assume k_{T} = 0.14 and Q_{p}
=86, and get other values that you need from the Satellite Calculator at
http://janus.astro.umd.edu/astro/calculators/scalc.html. Comment
on your numerical result.

5. Problem 2.32.**I** Instead of parts a) and b),
derive the general result for launch from a distance r along an elliptical
orbit. Show that the special cases a) and b) follow from your more
general result.

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