By Newtons law of universal gravitation, the free-fall acceleration a of a body, such as
Chapter 1, Problem 23(choose chapter or problem)
By Newton’s law of universal gravitation, the free-fall acceleration a of a body, such as the satellite shown in FIGURE 1.3.19, 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, \(a=k / r^{2}\), 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.
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