The strength of the gravitational force FFF between two objects depends on their masses and the distance between them, according to Newton's law of universal gravitation:
F=GM1M2d2F=G\frac{M_1M_2}{d^2}F=Gd2M1M2
where:
- GGG is the gravitational constant,
- M1M_1M1 and M2M_2M2 are the masses of the two objects,
- ddd is the distance between their centers.
Given that all pairs are separated by the same distance ddd, and the asteroids on the left are identical and relatively small (same mass), the ranking of gravitational force acting on the left asteroid depends primarily on the mass of the other object in each pair. Ranking the gravitational force from strongest to weakest:
- Pair where the right object has the greatest mass — because force is directly proportional to the mass of the other object.
- Pairs with intermediate masses on the right — forces decrease as the mass of the right object decreases.
- Pair where the right object has the smallest mass — weakest gravitational force.
Since the left asteroid's mass is constant, the force strength ranking mirrors the mass ranking of the right objects. Summary:
- The gravitational force on the left asteroid is strongest when paired with the most massive object on the right.
- It is weakest when paired with the least massive object on the right.
- Distance is constant, so it does not affect the relative ranking.
This follows directly from the formula F=GMleftMrightd2F=G\frac{M_{\text{left}}M_{\text{right}}}{d^2}F=Gd2MleftMright and the assumption that all left asteroids have the same mass and all pairs have the same separation ddd
