Solved: By Newtons universal law of gravitation the free-fall acceleration a of a body

Chapter 1, Problem 21

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By Newtons universal law of gravitation the free-fall acceleration a of a body, such as the satellite shown in Figure 1.3.18, 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 kr2 , 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 Newtons second law and his universal law of gravitation to find a differential equation for the distance r

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