# Why does the acceleration of gravity decrease with increasing height above the Earth’s surface?

The free fall acceleration g is directly proportional to the force F acting on the body and inversely proportional to the body mass m:

g = F / m.

The force of attraction between two bodies (the law of universal gravity):

F = GM3 * m / R ^ 2,

where G is the gravitational constant,

Mz is the mass of the Earth,

m – body weight,

R is the distance from the body to the center of the Earth.

g = GM3 * m / R ^ 2) / m = GM3 / R ^ 2 (1)

From (1) it follows that g is inversely proportional to the square of the distance to the center of the Earth. Distance R can be represented in the form of two terms: the Earth’s radius Rz and the height above the surface h:

g = GM3 / (R3 + h) ^ 2.

As the height h increases, the sum of the distances increases, and the acceleration g decreases.

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