Question

Calculate the acceleration due to gravity at height of 1600km. Given radius of earth is 6400km and the value of g =9.8 m per second square.

Answer 1

u already gave acceleration due to gravity in the question as 9.8m/s²

Answer 2

Gravity follows an inverse-square law, which means that, as an object moves away from the source of gravitation, the magnitude of the force it experiences drops by the square of the distance it has moved.

We can express this mathematically as a relationship between ratios:

g1/g2=r1)^2/r2)^2

In this case,g1is the acceleration due to gravity at the surface of the earth (9.8ms^2), r1 is the distance of the surface from the centre of the earth (which google informs me is ~6400 km), g2 is the acceleration due to gravity at r2 and r2 is 8000 km (1600km above the surface, which is 6400km from the centre of the earth).

Plugging this all in, we get

g1/g2=r1)^2/r2)^2
9.8/g2=8000^2/6400^2
g2=9.8*6400/8000=7.84/s^2
So acceleration due to gravity at height 1600 km is 7.84m/s^2
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