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How does doubling the distance between two objects change their gravitational attraction?

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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.

According to Newton’s law of gravitation, the gravitational force between two objects is inversely proportional to the square of the distance between them. This relationship is defined by the formula:12

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

Because the force follows this inverse square law, doubling the distance ( $R$ ) between two objects results in the denominator increasing by a factor of four ( $2^{2} = 4$ ). Consequently, the gravitational attraction between the objects is reduced to one-fourth of its original strength.2