Question

The distance between two bodies is doubled. How is the magnitude of

gravitational force between them affected?

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Answer 1

force will become one forth.Because force is inversely proportional to the square of distance between the objects

Answer 2

Let m1 = mass of a body , m2 = mass of another body

r = distance between the bodies of masses m1 and m2 from their center

Gravitional Force between the bodies
F1 =( G × m1 × m2 ) / ( r ^2 )

When distance gets doubled
=> r1 = 2 × r = 2r
New Gravitional Force
F2 = ( G × m1 × m2 ) / ( r1 ^2 )
= ( G × m1 × m2 ) / (( 2r) ^2 )
= ( G × m1 × m2 ) / ( 4r^2 )
= 1 / 4 { ( G × m1 × m2 ) / ( r ^2 ) }
= 1 / 4 × F1

The new gravitional force become 1/ 4 times than the original force...

Or

New forced will reduce to 1/ 4 times than original force