Question1

A lunar landing craft approaches the moon’s surface. Suppose that one-third of its weight is fuel, that exhaust velocity from its rocket engine is 1500 m/s, and that acceleration of gravity at the lunar surface is one-sixth of that at the earth’s surface. How long can craft hover over the moon’s surface before it runs out of fuel?

Question2

Planet Mercury (m = 0.3301 x 10^24 kg ) is in a circular orbit about the sun (M = 1.989 x 10^30 kg ) at r = 57.91 x 10^6 km.
demonstrate that this slight shortening of period amounts to the observed precession (gradual rotation of the semi-major axis ) of Mercury's orbit that is 43 seconds of arc per century. This contract between Einstein's calculations and observed precession was one early piece of proof confirming Einstein's relativity.