Question
Planet X has three moons. The gravitational force between the planet and each of its moons is the same. A student draws the diagram below to compare the masses of the moons and to show their distances from Planet X.
image.png
In which of these ways should the diagram be corrected?
Moon B should be smaller.
Moon A should be closer to Moon B.
The orbit of Moon A should be closer to Planet X.
The orbit of Moon C should be farther away from Planet X.
image.png
In which of these ways should the diagram be corrected?
Moon B should be smaller.
Moon A should be closer to Moon B.
The orbit of Moon A should be closer to Planet X.
The orbit of Moon C should be farther away from Planet X.
Answers
GPT-5 mini
Answer: The orbit of Moon C should be farther away from Planet X.
Reason: For equal gravitational force F = G M m / r^2 for each moon, m / r^2 must be the same. That means r^2 ∝ m, so the more massive a moon is the farther from the planet it must be. In the diagram Moon C is drawn the largest (most massive) but not on the largest orbit, so its orbit needs to be moved outward. The other suggested changes are not required.
Reason: For equal gravitational force F = G M m / r^2 for each moon, m / r^2 must be the same. That means r^2 ∝ m, so the more massive a moon is the farther from the planet it must be. In the diagram Moon C is drawn the largest (most massive) but not on the largest orbit, so its orbit needs to be moved outward. The other suggested changes are not required.