Astronauts put their spaceship into orbit about a planet. Theyfind that the acce

Question

Astronauts put their spaceship into orbit about a planet. Theyfind that the acceleration of gravity at their orbital altitude isone fourth that at the planet's surface. How far above the planet'ssurface are they orbiting? Answer in terms of the planet'sradius.
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Astronauts put their spaceship into orbit about a planet. Theyfind that the acceleration of gravity at their orbital altitude isone fourth that at the planet's surface. How far above the planet'ssurface are they orbiting? Answer in terms of the planet'sradius.
??Rp

Explanation / Answer

Accleration die gravity at height h is g ‘ = g /4

Where g = acceleration due to gravity on the surface ofthe planet

We know g ‘ = g [ R ^ 2 / ( R + h ) ^ 2]

            g / 4 = g [ R ^ 2 / ( R + h ) ^ 2]

R ^ 2/ ( R + h ) ^ 2 = 1/ 4

R / ( R + h ) = 1/ 2

           2R = R + h

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