Chapter 8, Problem 8.35P

Consider a satellite in elliptical orbit around a planet of mass M, and suppose that physical units are so chosen that GM D 1 (where G is the gravitational constant). If the planet is located at the origin in the xy-plane, then Explain the equations of motion of the satellite? Let T denote the period of revolution of the satellite. Kepler’s third law says that the square of T is proportional to the cube of the major semiaxis a of its elliptical orbit. In particular, if GM D 1, then?

If a particle be describing an ellipse about a centre of force in the centre, show that the sum of the reciprocates of its angular velocities about foci is constant.

Consider a satellite of mass m moving in a circular orbit around the Earth at a constant speed v and at an altitude h above the Earth’s surface as illustrated as shown. (A) Determine the speed of the satellite in terms of G, h, RE (the radius of the Earth), and ME (the mass of the Earth).