Chapter 5.3, Problem 205E

The force of gravitational attraction between the Sun and a planet is $F\left(\theta \right)=\frac{GmM}{r^2\theta }$ , 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.