The attractive gravitational force between a spherical body of mass M and another spherical body of mass m is given by F = GMm/r² where r is the distance between the centers of the two masses, and G is the gravitational constant. You are told that a satellite of small mass m orbits the earth (mass M) with a frequency f revolutions per second. You are told that the satellite is a distance h above the surface of the earth and the radius of the earth is RE. If you are given the values of m, G, f, h and RE. Can we determine the mass of the Earth? What assumptions (if any) do we need to make? Does the mass of the satellite matter?
The attractive gravitational force between a spherical body of mass M and another spherical body of mass m is given by F = GMm/r² where r is the distance between the centers of the two masses, and G is the gravitational constant. You are told that a satellite of small mass m orbits the earth (mass M) with a frequency f revolutions per second. You are told that the satellite is a distance h above the surface of the earth and the radius of the earth is RE. If you are given the values of m, G, f, h and RE. Can we determine the mass of the Earth? What assumptions (if any) do we need to make? Does the mass of the satellite matter?
Classical Dynamics of Particles and Systems
5th Edition
ISBN:9780534408961
Author:Stephen T. Thornton, Jerry B. Marion
Publisher:Stephen T. Thornton, Jerry B. Marion
Chapter9: Dynamics Of A System Of Particles
Section: Chapter Questions
Problem 9.17P
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