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Kerry Browne: Questions sometimes arise about how satellites change from one orbit to another. The following worksheet, cforbits_changing.mw, based on cforbits.mw can be used to explore the process of changing orbits by applying tangential thrust. This worksheet may be particularly useful for discussion of the NASA homework problem.

Kerry Browne: Note: When using the spiral orbits, $U(r) = -\frac{k}{r^2}$, if you get an error from dsolve saying, ”…cannot evaluate … right of x, probably a singularity”, where x is some integer. You can manually set maxt to a value slightly less than x and the worksheet will calculate.

Comments by Mary Bridget Kustusch (post-doc and co-instructor, Winter 2012)

This year, we transitioned to a Mathematica worksheet instead of a maple worksheet. There were still kinks that needed to be worked out, but this allowed the students to “break” the program, which led to some good discussions about what happened and why. In particular, when you lower the energy below the potential, you move into a “forbidden zone” and mathematica just stops. Also, many students were trying to raise the energy to get an hyperbolic orbit, but the program was not designed to deal with orbits with a really long (or infinite) period.


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