Problem 10.3 A “surface skimming" satellite is in a circular orbit about a spherical planet. The radius of this hypothetical orbit is the same as the radius of the planet. Prove that the period of such a satellite is the same for all planets having the same density. (Since the density of Mars and the density of the Earth are nearly the same, such a satellite has the same period on both planets.)

Problem 10.3 A “surface skimming" satellite is in a circular orbit about a spherical planet. The radius of this hypothetical orbit is the same as the radius of the planet. Prove that the period of such a satellite is the same for all planets having the same density. (Since the density of Mars and the density of the Earth are nearly the same, such a satellite has the same period on both planets.)