Question

When the Lunar Module lands on the Moon it does so with retro-rockets, since there is no atmosphere for aerobraking on the Moon. How big a velocity change must it make to get from a low lunar orbit down to the lunar surface? Remember that the Moon rotates very slowly, so you don’t have to worry about taking the Moon’s rotation into account.

Answer 1

On these situation , the low lunar orbit is above 100 km of lunar surface . Using formula v² = G M /R where v is the velocity at low lunar orbit , G is universal gravitational constant , M is mass of Moon and R is the height of orbit from center of Moon i..e radius of Moon plus height of orbit from lunar surface. Mass of Moon is 10²⁴ kg and R is 1838 km or 1838000 m ( taking R on meters) with G gives orbital velocity of 6000 meters per second. So on landing at lunar surface the module will have to change velocity from this value to zero at surface to not to strike .