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How does the distance between two objects affect the gravitational force between them?

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gravitational lens — gravity A galactic cluster, about five billion light-years away, produces a tremendous gravitational field that “bends” light around it. This lens produces multiple copies of a blue galaxy about twice as distant. Four images are visible in a circle surrounding the lens; a fifth is visible near the center of the picture, which was taken by the Hubble Space Telescope.

The gravitational force between two objects is governed by Newton’s law of gravitation, which states that the force varies inversely as the square of the distance between them.1

Mathematically, the magnitude of the attractive force $F$ is expressed as:
$F = G \frac{m_{1} m_{2}}{r^{2}}$
In this formula, $G$ is the gravitational constant, $m_{1}$ and $m_{2}$ are the masses of the objects, and $r$ is the distance between their centers.12

Because the force is inversely proportional to the square of the distance, the strength of the attraction diminishes rapidly as objects move apart. For example, if the distance between two bodies is doubled, the gravitational force between them is reduced to one-fourth of its original strength. Extensive experimental testing has consistently confirmed that this inverse square relationship holds true across a wide range of distances, from laboratory scales to the orbits of artificial satellites around Earth.34