Astronauts put their spaceship into orbit about a planet. Theyfind that the acce
ID: 1669804 • Letter: A
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.??Rp
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