Question

If the moon were twice as far from the earth as it is now, the gravitational force it

exerts on the earth would be​

Answer 1

One-fourth of the original gravitational force.

Step-by-step explanation:

The gravitational force between two objects of masses
`m\textrm{ and }M` is given as:

`F_(g)=(GmM)/(r^2)`

Where,

`G\rightarrow \textrm{gravitational constant}\\r\rightarrow \textrm{distance between the masses}`

Therefore, the gravitational force is inversely proportional to the square of the distance between the masses.

Now, if the distance is doubled, then the force has to be reduced by a factor of one by four or gravitational force will one-fourth of the original.

Let us verify it.

If
`r = 2r`, then new gravitational force is,

`F_(g,new)=(GmM)/((2r)^2)=(GmM)/(4r^2)=(1)/(4)(GmM)/(r^2)`

As seen above, new gravitational force is one-fourth of the original gravitational force between moon and Earth.