Here are hints for problems 2a, 2b in the Kepler assignment:


Hint for 2a:

Use an "obvious" integral to get a formula for A (area)
and also use the pi ab formula too.  You'll get T.

Hint for 2b:

(1) Look at pp. 585, 586 for these equations:

     e = c/(GM)  and d = h^2/c

These are enough to do the first bit (just rearrange the bits)

(2) Look at the top of p. 511 for these equations:

    a^2 = [ ed/(1-e^2) ]^2   and  b^2 = e^2d^2/(1-e^2)

Then use the first (drop the ^2) to get an equation for  ed
and one for  b^2/a^2 (set up the fractions from the equations and
simplify).  Then finally you can get a new equation for ed which will
finish 2(b).

Hope this helps!