Gravitation....

Question

By how much does the gravitational force between two objects decrease when the distance between their centers is doubled? Tripled? Increased tenfold?

Answer 1

Hi Cathy,

For this problem, you will want to refer to the universal law of gravitation, which tells us that the magnitude of the gravitational force is proportional to 1/r².

So, if you double the distance between the two objects, the force will decrease by 1/4 since 1/r² would become 1/(2r)² = 1/(4r²) = 1/4 x 1/r².

If you triple the distance, then you'd have 1/(3r)², which would become 1/(9r²) = 1/9 x 1/r², and so the force would decrease by a factor of 1/9.

Likewise, when you increase the distance by a factor of 10, the force would decrease by a factor of 1/10² = 1/100