?The force of gravitational attraction between the Sun and a planet is

Chapter 5, Problem 205

(choose chapter or problem)

The force of gravitational attraction between the Sun and a planet is \(F(\theta)=\frac{G m M}{r^{2}(\theta)}\), where m is the mass of the planet, M is the mass of the Sun, G is a universal constant, and \(r(\theta)\) is the distance between the Sun and the planet when the planet is at an angle \(\theta\) with the major axis of its orbit. Assuming that M, m, and the ellipse parameters a and b (half-lengths of the major and minor axes) are given, set up-but do not evaluate-an integral that expresses in terms of G, m, M, a, b the average gravitational force between the Sun and the planet.

Text Transcription:

F(theta)=G m M/r^2(theta)

r(theta)

theta