In general, an integral average of some continuous function f(t) over an interval T is given by

Beginning with an expression for the integral average. prove that

A binary system's gravitational potential energy, averaged over one period, equals the value of the instantaneous potential energy of the system when the two masses are separated by the distance a, the semimajor axis of the orbit of the reduced mass about the center of mass. Hint You may find the following definite integral useful:

(()) = = f* f(1) dr. (U)=-G Mu a 1. d0 1+ ecos@ 27 1-e