A planet's density from its moon
- Round
- Theory
- Points
- 10
- Level
- Bronze
- Taught in
- Section 3.7
Adapted from IOAA 2015 (Magelang), theory problem 2. We have restated it in our own words and kept the original data. The solution was last checked on 21 October 2026.
A moon of a planet has a period of 7 days, 3 hours and 43 minutes, and its semi-major axis is 15.3 times the mean radius of the planet. The Moon has a period of 27 days, 7 hours and 43 minutes and a semi-major axis 60.3 times Earth's mean radius. Ignore the masses of the moons next to their planets. What is the ratio of the planet's mean density to Earth's?
- By (3.2),
- The periods are 10 303 minutes and 39 343 minutes.
- The ratio of densities is
AnswerThe planet's density is 0.238 times Earth's. The data fit Jupiter and its moon Ganymede, and a density a quarter of Earth's shows that Jupiter is mostly hydrogen and helium.
This problem also appears among the olympiad problems of Section 3.7, Two bodies, collisions and slow changes, which teaches the ideas it uses. Equation and figure numbers refer to the course.