Originally posted by sonhouse
Kirby, our intrepid lunar explorer is driving his solar powered rover on the equator of the moon and notices his solar cells are going bad. He finds he has to keep the cells aimed right at the sun full bore or the power drops below the level required for his life support equiptment. He finds he has to turn off his radios, lasers and such and is alone on the ...[text shortened]... long does it take to get back to his base halfway round the moon?
So how fast in Km/hr is that?
Where is the base situated? The latitude is very important for solving this problem. And where is he himself at? At the antipode of the base perhaps?
There is no need for him to be at local moon noon at all. It's only important for him to have the sun over the horizon, that’s enough. The moon has no atmosphere that block sun light as her on Good ol' Earth where the sun becomes fainter near the horizon.
If he is near to the lunar north pole or south pole (depending of the season) he have eternal sun shine and do not have to move at all. He just have to stay put, mace a call to the base to come and pick him up when they have the time.
A day on the moon is some 14 (earth) days long and the night is as long (not considering any seasonal effect), this is an important clue to the solution of the problem.
He should prefer going on the maria which is relatively flat and straight forward, and avoid the more rocky regions of the lunar surface.
So the most efficient route from where he is to the base is, with this circumstances, not possible to calculate, the same with his velocity.