2021年IOAA理论第9题-冥王星的卫星

英文题目

9.1 The mass of Charon, the biggest satellite of Pluto, is 1/8th the mass of Pluto. Both bodies move in a circular orbit around a common center of mass. In addition, they both are tidally-locked. The distance between the center of the planet and the center of the satellite is $$𝑅 = 19 640 𝑘𝑚$$ and radius of the satellite is $$𝑟 = 593 𝑘𝑚$$.

Let $$g_{0}$$ be the gravitational acceleration on the surface of Charon due only to its mass.Let A be the point on Charon surface directly facing Pluto, and B the point diametrically opposite. Compute the percentage difference between gravitational acceleration at A and B respect to $$g_{0}$$ .(15.0pt)