Question

show the acceleration due to gravity at height h above the surface of the earth is gh=g(R/R+h)

Answer 1

Answer:

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)

Answer 2

Answer:

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