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# Free - Free-fall Acceleration If the mass density of the...

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Free-fall Acceleration If the mass density of the earth depends only on the distance from the center of the earth (homogeneous shells), we can easily calculate the net gravitational force acting on a particle of mass m, located at an external point, a distance r from the center of the earth: where M is the mass of the earth. For a particle on the earth surface, r = R e , the gravitational force is given by We conclude that the free-fall acceleration depends on the mass of the earth and its radius: The measured value of g = 9.8 m/s 2 and R e = 6.37 x 10 6 m gives which is in good agreement with the accepted value of 5.98 x 10 24 kg. In reality, the situation is more complicated: The earth's crust is not uniform . Precise measurements of the variations of the free-fall acceleration give information about non-uniformaties in the density of the earth. This can suggest the presence of salt domes (which often indicated the presence of oil). The earth is not a sphere . The earth is an ellipsoid. It is flattened on the poles and bulging at the equator (difference in radius is 21 km). The free-fall acceleration is larger

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Free - Free-fall Acceleration If the mass density of the...

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