Question

The variation of acceleration due to gravity is given as g'=g(1-(2h/R)) while the acceleration due to gravity at a height 'h' is given as g'=g(R/R+h)^2. why is these two formulas different eventhough they mean the same?

Answer 1

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The variation of acceleration due to gravity is given as g'=g(1-(2h/R)) while the acceleration due to gravity at a height 'h' is given as g'=g(R/R+h)^2. why is these two formulas different eventhough they mean the same?

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Under the gravitational influence on two bodies, the mass in terms of mass is given by,. FA = GMmA/r2, ... GMm/(R+h)2.

⇒ gh= GM/[R2(1+ h/R)2 ] . . . . . .

(2). The acceleration due to gravity on the surface of the earth is given by;

. g = GM/R2 .

Answer 2

Explanation:

The “real” formula can be derived from Newton’s Law of gravity:

F=GmMr2

where m is the mass of the object, M the mass of the earth, r the distance between the centers of mass of both, F the force applied and G the gravity constant.

Because F=ma , a=Fm , which means a=Gmr2 . If we call R the radius of the Earth, then we do find

g=GmR2

But what happens if the distance is at a height h above R ? Then the formula becomes

g′=Gm(R+h)2

This is the exact formula for the gravity acceleration at a height h above the surface of the Earth. But where does your formula comes from? It’s actually an approximation of this formula when h≪R :

g′=GmR21(1+hR)2

=g11+2hR+o(hR)

=g(1−2hR+o(hR))

Therefore, when h≪R , we do have

g′≈g(1−2hR) .