?[T] According to Newton’s law of universal gravitation, the force F between two bodies

Chapter 3, Problem 149

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[T] According to Newton’s law of universal gravitation, the force F between two bodies of constant mass \(m_{1}\) and \(m_{2}\) is given by the formula \(F=\frac{G m_{1} m_{2}}{d^{2}}\), where G is the gravitational constant and d is the distance between the bodies.

a. Suppose that G , \(m_{1}\) , and \(m_{2}\) are constants. Find the rate of change of force F with respect to distance d .

b. Find the rate of change of force F with gravitational constant \(G=6.67 \times 10^{-11}\) \(\mathrm{Nm}^{2} / \mathrm{kg}^{2}\) , on two bodies 10 meters apart, each with a mass of 1000 kilograms.

Text Transcription:

F = Gm_1m_2 / d^2

G=6.67x10^-11