3 [Note: this is a version of a test problem in a previous year]. An aging billionaire decides to try to outlive the rest of us by means of time dilation. So he arranges to live the last 20 years of his life on a satellite orbiting the Earth at a distance of 10,000 kilometers (distance measured to the center of the Earth).

a) Assuming the satellite is in a circular orbit, calculate how fast it is moving around the Earth.

b) Calculate how much longer the billionaire lives in comparison to people on Earth and their clocks. In making this calculation, is it appropriate to use the post-Newtonian term only? Explain why or why not.