At what altitude above the earth's surface would the acceleration due to gravity be 4.9 m/s^2? Assume the mean radius of the earth is 6.4x10^6 metres and the acceleration due to gravity 9.8m/s^2 on the surface of the earth.

Question

Physics

Abbey Schmitt

14 November, 10:35

At what altitude above the earth's surface would the acceleration due to gravity be 4.9 m/s^2? Assume the mean radius of the earth is 6.4x10^6 metres and the acceleration due to gravity 9.8m/s^2 on the surface of the earth.

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Nevaeh Wilkins · Answer 1

We apply the gravity calculation expressed in the formula: g=GM/r2

where G is the gravitational constant, m is the mass and r is the radius

r=√GM/g

(1) Radius = √6.674e-11*5.972e24/8 = 7058 kms Earth radius or surface of earth from center of earth = 6400 kmsSo r = 658 kms from surface of earth.

Gravity 8m/s2 will be at 658 kms from surface of earth.

(2) half gravity = 9.8/2 = 4.9 m/s2 Radius=√6.674e-11*5.972e24/4.9 = 9019 kms Half Gravity will exist at 9019-6400 = 2619 kms from surface of earth.