Question

If the distance of the moon to earth were 0.25 times its current distance, the moon would exert a gravitational force on the earth how many times larger than its current value?

Answer 1

The new force will be 16 times the current value.

Step-by-step explanation:

Lets say,

Mass of the Earth = M

Mass of the Moon = m

Distance between Earth and Moon = r

Gravitational force between the two = F

The gravitational force between the two is given as,

`F = (G* M* m)/(r^(2))`

where, G = Gravitational constant

The new distance = 0.25r

So, the gravitational force (F') will be,

`F' = (G* M* m)/((0.25r)^(2))`

`F' =(1)/(0.0625) * F`

F' = 16 F

The new force will be 16 times the current value.