Question

Radius of Moon's orbit is 240000 miles and period of revolution is 27 days, diameter of Earth is 8000 miles and the value of gravity on its surface 32 ft/sec2. Verify the statement that the gravitational force varies inversely proportional to square of distance.

Answer 1

The velocity of the Moon is

v = 2r / T

Here, radius of the orbit of the Moon is r and period of revolution is T.

The centripetal acceleration of the Moon which acts towards the centre of the Earth is

Substitute 240000 miles for r and 27 days for T in the above equation,

Consider the distance r varies to the power of n in accordance with the gravitational law.

Let R be the radius of the Earth.

Then,

R = 8000 miles / 2

    = 4000 miles

For the value of g on the surface of the Earth in accordance with the gravitational law,

It follows that

Substitute 240000 miles for r, 4000 miles for R, 0.009189 ft/s² for a_M and 32 ft/s² for g in the above equation,

Rounding off to one significant figure, the value of n is 2.

Thus,

This shows that accelerations are inversely proportional to the square of the distances.

Therefore, the gravitational force varies inversely proportional to square of distance.