The earth's orbit is nearly circular, but not quite.The radial motion oscillates in a narrow range around the minimum of the effective potential Ueff.We call this radius r*. If this range is narrow enough, Ueff may be approximated as A(r-r*)^2 - B, so the radial motion is simple harmonic motion.

a) Find the coefficient A in terms of the strength of the gravitational potential Gm1m2/r*.

b) Find the period of the simple harmonic radial motion.

c) Compare with the angular revolution time 2pi/ derivative phi .