Question

We know that are we are bound the earth because of gravity how do you think the gravitational pull of earth extends

Answer 1

The gravitational force of the earth varies with height and depth.
It is not the same at all points.

First, there is the variation of gravity with latitude that you alluded to: you weigh about 0.5% more at the poles than on the equator.


Second, gravity does indeed change with altitude. The gravitational force above the Earth's surface is proportional to 1/R², where R is your distance from the center of the Earth. The radius of the Earth at the equator is 6,378 kilometers, so let's say you were on a mountain at the equator that was 5 kilometers high (around 16,400 feet). You would then be 6,383 kilometers from the Earth's center, and the gravitational force would have decreased by a factor of (6,378 / 6,383)² = 0.9984. So the difference is less than 0.2%.

g' = g (1 – d/R)

So as depth d increases, the value of acceleration due to gravity falls.