Acceleration with respect to displacement?!
Hi. My name is David. I like physics. Recently I ran into a problem that has really begun to bug me. Have you heard of the Northrop Grumman Lunar Lander Challenge? It's really cool. The teams are competing for a purse of like $2 million. For the highest level, the teams must launch their rocket from point A and remain in the air at an altitude of at least 50 meters for 180 seconds. Then they land their rocket at point B. After measuring the accuracy of the landing, the rocket makes a return flight back to point A, again at an altitude at or exceeding 50 meters for 180 seconds. Cool Challenge.
My question relates to how the same force required to suspend a mass for 180 seconds on earth would affect the same mass but starting from rest on the surface of the moon. At first, the same force will be enough to produce an acceleration of 9.8m/(s*s)(earth gravity)-1.62m/(s*s)(moon gravity). I am assuming the rocket is launched vertically away from the moon's surface. The rotation of the moon can be ignored as it is a mere ~10 miles/hour. The difficulty arises as the rocket gains velocity and moves away from the moon. The force of gravity exerted by the moon diminishes as a function of distance. This in turn causes an increase in the acceleration of the craft. This of course relates directly to the distance of the object from the moon. I seem to be caught in a circular loop of dependent factors. Can anyone help me? This isn't homework so don't feel pressured. I just really want to figure this out.
The force of gravity between two objects (aka a rocket and the moon) is equal to G*m1*m2/(r*r) where G is the gravitational constant: 6.67300*10^(-11)*m^(3)/(kg*s*s) and m1 and m2 are the masses of the objects in question and r represents the distance between them. The moon's mass is 7.36*10^(22)*kg and its radius is 1 737.4*km.
Thanks in advance to any kind genius that would like to help me!