Question

Calculate the value of g at a height of 12800 km from the centre of the earth. Radius of earth is 6400 km.

Answer 1

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:

g1g2=r22r21g1g2=r22r12

In this case,g1g1 is the acceleration due to gravity at the surface of the earth (9.8ms^2), r1r1 is the distance of the surface from the centre of the earth (which google informs me is ~6400 km), g2g2 is the acceleration due to gravity at r2r2, and r2r2is 10000km (3600km above the surface, which is 6400km from the centre of the earth).

Plugging this all in, we get:

9.8g2=100002640029.8g2=10000264002

Rearrange to make g2g2 the subject:

g2=9.8∗64002100002g2=9.8∗64002100002
g2=4.01ms2

Answer 2

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