# ASTR688R Planetary Science, Fall 2004 Homework Assignment #2

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 kT = 0.14 and Qp =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.