When the distance between two objects is reduced to half, the gravitational force between them becomes four times stronger.

Quick Scoop

According to Newton’s law of universal gravitation, the force between two masses is inversely proportional to the square of the distance between them.

That is, F∝1r2F\propto \frac{1}{r^2}F∝r21​ (no need to write this in your exam unless asked, but it helps to think with it).

Step-by-step change

  • Let the original distance be rrr, and the original force be FFF.
  • New distance is r/2r/2r/2 (reduced to half).
  • New force F′F'F′ will be proportional to 1(r/2)2=1r2/4=4r2\frac{1}{(r/2)^2}=\frac{1}{r^2/4}=\frac{4}{r^2}(r/2)21​=r2/41​=r24​.
  • So F′=4FF'=4FF′=4F: the force becomes four times the original value.

In simple words: halve the distance → gravitational pull becomes four times stronger.

One-line exam-friendly answer

When the distance between two objects is reduced to half, the gravitational force between them becomes four times its original value because it follows the inverse-square law.

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Learn how the force of gravitation between two objects changes when the distance between them is reduced to half, using Newton’s law of gravitation and the inverse-square law, with a clear, exam-ready explanation.

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