Question

What the variation of acceleration due to gravity with altitude and depth​

Answer 1

The relation clearly shows that with an increase in height the acceleration due to gravity decreases. Let the point be taken at a depth d below the earth's surface.

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Answer 2

Altitude

Let the point be taken at a height h above the earth’s surface. Applying the shell’s theorem for the figure we can write the acceleration due to gravity at that point as

$\sf \: g = \frac{GM}{ {r}^{2} } = \frac{GM}{(R + h) {}^{2} }$

The relation clearly shows that with an increase in height the acceleration due to gravity decreases.

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Depth

Let the point be taken at a depth d below the earth’s surface. Applying the shell’s theorem for the figure we can observe that only the mass which lies inside the sphere of radius R-d is responsible for the acceleration due to gravity at that point.

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The relation clearly shows that with an increase in depth the acceleration due to gravity decreases.

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