if r is the radius of the earth and g is the gravitational acceleration at the earth's surface, what is the gravitational acceleration at altitude h above the earth's surface?

In physics, gravitational acceleration is the speed at which a body falls freely in a void (and thus without experiencing drag). This is the constant acceleration brought on just by the gravitational pull. Gravimetry is the measurement and study of these rates. All bodies accelerate at the same rate in vacuum, independent of their masses or compositions.The combined effects of gravity and the centrifugal force from Earth's rotation determine the strength of Earth's gravity at a fixed place on its surface.

Let, gₙ be the acceleration due to gravity at height h.

gₓ be the acceleration due to gravity at depth x.

The acceleration due to gravity on the surface of Earth is

g= GM/R^2

where,R is the radius of Earth,M is mass of Earth and G is gravitational constant.

∴g ∝ 1/R^2

gₙ ∝ 1/(R+ h) ^2

thus gₙ/g = R^2/(R+ h) ^2

Hence

gₙ = g.R^2/(R+ h) ^2

For more info on gravitational acceleration refer to:

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