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How does Newton’s law of gravitation depend on the masses of two objects?

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Geocentric system — Celestial mechanics Ptolemaic diagram of a geocentric system, from the star atlas *Harmonia Macrocosmica* by the cartographer Andreas Cellarius, 1660.

According to Newton’s law of gravitation, the magnitude of the attractive force between two objects is directly proportional to the product of their masses.12

In the mathematical expression of this law, the force $F$ is calculated as:

$F = G \frac{m_{1} m_{2}}{r^{2}}$

In this formula:
* $m_{1}$ and $m_{2}$ represent the masses of the two objects.1
* $G$ is the gravitational constant.1
* $r$ is the distance between the centers of the two masses.13

Because the force is proportional to the product of the masses, doubling the mass of one object doubles the gravitational force between them, while doubling the mass of both objects increases the force by a factor of four. This relationship ensures that the gravitational force is consistent with the observation that all objects accelerate toward a massive body, such as Earth, at the same rate regardless of their individual mass.13