Enter an expression for the magnitude of the acceleration due to gravity near Ea

Question

Enter an expression for the magnitude of the acceleration due to gravity near Earth, in terms of RE, ME, the altitude above the Earth’s surface, H, and the gravitational constant, G

Calculate the magnitude of the acceleration due to gravity, in meters per second squared, at sea level on Earth.

Calculate the magnitude of the acceleration due to gravity, in meters per second squared, near Earth at an altitude of H = 7 km above sea level.

The strength of the gravitational field of a source mass can be measured by the magnitude of the acceleration due to gravity at a field point. Thus the gravitational field strength at a point depends on the distance from the source mass. For this problem assume that Earth’s mass is concentrated at its center and that Earth has a radius of RE = 6,378 km at sea level and a mass of ME = 5.972×1024 kg. Ignore any forces due to Earth’s rotation or due to other astronomical bodies.

Enter an expression for the magnitude of the acceleration due to gravity near Earth, in terms of RE, ME, the altitude above the Earth’s surface, H, and the gravitational constant, G

Calculate the magnitude of the acceleration due to gravity, in meters per second squared, at sea level on Earth.

Calculate the magnitude of the acceleration due to gravity, in meters per second squared, near Earth at an altitude of H = 7 km above sea level.

Explanation / Answer

g'= g/(1+( h2/r2)^³/²

H/R = 0.0010987

H²/R² = 1.20720(10^-6)

(H²/R²) = 1.4345 (10^-19)

g'= 9.8/1+0.0000000014345

g'= 9.8/1.0000000014345

g'= 9.7999 m/s²

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