You are asked to verify Kepler's Laws of Planetary Motion. For these exercises, assume that each planet

Question:

You are asked to verify Kepler's Laws of Planetary Motion. For these exercises, assume that each planet moves in an orbit given by the vector- valued function r. Let r = ||r||, let G represent the universal gravitational constant, let M represent the mass of the sun, and let m represent the mass of the planet.

Using Newton's Second Law of Motion, F = ma, and Newton's Second Law of Gravitation

show that a and r are parallel, and that r(t) × r'(t) = L is a constant vector. So, r(t) moves in a fixed plane, orthogonal to L.