At what distance from the center of the Earth is the acceleration of gravity g / 4?

| August 13, 2021 | education

At what distance from the center of the Earth is the acceleration of gravity g / 4? The acceleration of gravity at the surface of the Earth is g = 9.8 m / s, the radius of the Earth is taken equal to 6400 km

Initial data: a = 0.25g (free fall acceleration at a height h from the Earth’s surface).

Constants: G = 6.67 * 10 ^ -11 m ^ 3 / (kg * s ^ 2); R = 6400 km = 6400000 m; M = 5.97 * 10 ^ 24 kg; g = 9.8 m / s ^ 2.

The desired distance from the center of the Earth can be expressed from the formula:

a = 0.25g = G * M / (h + R) ^ 2, whence h + R = √ (G * M / 0.25g).

Let’s perform the calculation:

h + R = √ (6.67 * 10 ^ -11 * 5.97 * 10 ^ 24 / (0.25 * 9.8)) = 12 748 733 m.

Answer: Free acceleration will be equal to 0.25g at a distance of 12,748,733 m from the center of the Earth.



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