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The newtonian formula to calculate gravitation force between two objects of mass M1 and M2 with distance R between then is
F = (G×M1×M2)/(R^2)
So when distance is doubled, R becomes 2R
So F' becomes (G×M1×M2)/((2R)^2) = F/4
Hence we have proved the first statement.
Now when the distance is halved, R becomes R/2
So F" becomes (G×M1×M2)/((R/2)^2 = 4F
Hence we have proved the second statement
F = (G×M1×M2)/(R^2)
So when distance is doubled, R becomes 2R
So F' becomes (G×M1×M2)/((2R)^2) = F/4
Hence we have proved the first statement.
Now when the distance is halved, R becomes R/2
So F" becomes (G×M1×M2)/((R/2)^2 = 4F
Hence we have proved the second statement
Astrobolt:
Note: Here 'G' is the Universal Gravitational Constant = approx 6.67 × 10^(-11)
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