find the acceleration due to gravity at a distance of 20000km from the centre of the earth
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Answer:
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Answer:
Newtons law of Gravitation states that the force of gravitational attraction between two bodies of mass M and m separated by a distance d, is proportional directly to the product of masses and inversely proportional to the square of the distance between them.
Newton's law of Gravitation: F = G M m / d²
G = Universal Gravitational constant = 6.674 * 10⁻¹¹ N m²/kg²
M = Mass of a body
m = mass of the 2nd body
d = distance between the centers of mass of the two bodies
Let R = radius of Earth = 6,400 km
h = altitude above Earth = 12,800 km
d = distance from center of Earth = 19,200 km
We know that on the surface of Earth, gravity is:
g = G M / R² = 9.81 m/s²
g' = acceleration due to gravity at distance d = G M / d²
=> g'/g = R²/d²
=> g' = g R² / d²
= 9.81 * 6400²/19200²
= 1.09 m/s²