1. Problem 1.3.I Assume that the planet's spin
axis is perpendicular to its orbit for all parts of this problem.
2. Problem 2.2.I (Optional)
Do this one if you have not seen a derivation of this before or if you want some problem solving practice!
3. Problem 2.4.I For part a), calculate also the
velocity (relative to Earth) necessary to i) hit the Sun, ii) leave
the Solar System, iii) go into a circular orbit about the Sun at i~90
degrees, and iv) reach Mercury's orbit. Rank in order of increasing
difficulty. Which have our spacecraft done? Note: the
first edition of the book does not have parts d) and e)!
e) (Optional)
If you do this, you could write a code to calculate for an arbitrary planet.
4. Problem 2.10.I
b) Warning: N-body integration code required. Start early on this one. Try to match your analytic calculation by making the same assumptions as you did in part a).
5. Problem 2.16.I (Optional)
This is a classic problem, the answer to which can be found in
many places. Do it if you have not done it before. Try to do it on
your own, using direct integration or Gauss' Law. You can also search
for clues online if you get stuck.
b) Now, work out the
potential at any point interior to a spherical shell.
c) Can you work out the potential at any point interior to an ellipsoidal shell?
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