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3 Gravitation and Kepler's Laws
In this chapter we will recall the law of universal gravitation and will then derive the result that a spherically symmetric object acts gravitationally like a point mass at its centre if you are outside the object. Following this we will look at orbits under gravity, deriving Kepler’s laws. The chapter ends with a consideration of the energy in orbital motion and the idea of an effective potential.
3.1 Newton's Law of Universal Gravitation
For two particles of masses m1 and m2 separated by distance r there is a mutual force of attraction of magnitude Gm1m2
r2 ;