By Newtons universal law of gravitation the free-fall acceleration a of a body, such as the satellite

By Newton’s universal law of gravitation the free-fall acceleration a of a body, such as the satellite shown in th4e following figure, falling a great distance to the surface is not the constant g. Rather, the acceleration a is inversely proportional to the square of the distance from the center of the Earth, a = k/r², where k is the constant of proportionality. Use the fact that at the surface of the Earth r = R and a = g to determine k. If the positive direction is upward, use Newton’s second law and his universal law of gravitation to find a differential equation for the distance r.

Transcribed Image Text:

satellite of mass m surface Satellite Earth of mass M