If the distance between two masses decreases by one third, the force between them will increase by a factor of 9.
How to calculate the force between two masses?
The gravitational force between two masses is given by Newton's law of universal gravitation.
F = Gm₁m₂ / r²
where;
- G is the universal gravitation constant
- m₁ is the mass of the first object
- m₂ is the mass of the second object
- r is the distance between the two objects
From the equation given above, we can see that force is inversely proportional to gravitational force.
F' = Gm₁m₂ / (¹/₃ r)²
F' = Gm₁m₂ / (¹/₉ r²)
F' = 9Gm₁m₂ / r²
F' = 9F
Thus, if the distance between two masses decreases by one third, the force between them will increase by a factor of 9.