2021

Gravity on the two faces of Charon

Round: Theory
Points: 15
Level: Silver
Taught in: Section 3.8

Adapted from IOAA 2021 (Bogotá, held online), theory problem 9. We have restated it in our own words and kept the original data. The solution was last checked on 21 October 2026.

Charon, the largest moon of Pluto, has one eighth of Pluto's mass. Both move on circular orbits round their common centre of mass, and both are tidally locked. The distance between their centres is $R = 19 640$ km, and Charon's radius is $r = 593$ km. Let $g_{0}$ be the acceleration due to Charon's own gravity at its surface. Let A be the point of Charon's surface facing Pluto, and B the point opposite it. Find the difference between the accelerations at A and B as a percentage of $g_{0}$ .

I solved it without the solution

AnswerThe accelerations at A and B differ by about 0.004% of $g_{0}$ . Each is about 0.07% less than $g_{0}$ , and the near side is reduced slightly more than the far side.

This problem also appears among the olympiad problems of Section 3.8, Tides and the Roche limit, which teaches the ideas it uses. Equation and figure numbers refer to the course.