Question

. Find the acceleration due to gravity at a
distance of 20000 km from the centre of the
earth.
​

Answer 1

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

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Explanation: