Leaderboard

I don't know how to solve this, but I may be able to show that it is not solvable with three questions..

Of the two questions I asked, the first is the more elegant. The answer (contact angle) is the same for any size sphere or any planet. So long as the planet's mass is large compared to that of the sphere. The second question seemed reasonable to ask, and it surprised me a little that its answer (landing point) does depend on size and on gravitational pull. On Earth, the result shows that the apple does not fall far from the tree. I also heard someone remark that the angle (in degrees) is strikingly close to the answer to life and everything. See Hitch-hiker's guide to the galaxy.