Classical Mechanics Puzzler

The orbital equation we derived this week for r(q) was

where B is a constant and e is the eccentricity given by

Now consider two identical objects with identical total energy E. One has a circular orbit (e = 0) while the other has an elliptical orbit (0 < e < 1). By considering the equations above:

1. What can you say about the angular momentum (G) of one relative to the other? Are they the same? If not, which has the greater angular momentum?
2. Consider the orbits for each case? How does the pericenter (closest approach) and apocenter (farthest retreat) of the elliptical orbit compare to the radius of the circular orbit?

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