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# Earth’s Mass

For a point on the surface of the Moon determine the ratio of the acceleration of gravity due to the mass of the Earth to the acceleration of gravity due to the mass of the Moon. The rotational distortion of the Earth’s mass adds a small latitude-dependent term to the gravitational acceleration. This term depends on the excess mass in the rotational equatorial bulge of the Earth. The observed latitude dependence of gm can thus be used to determine this excess mass. In addition, this effect must be removed from observed variations in surface gravity before the residual gravity anomalies can properly be attributed to density anomalies in the Earth’s interior. The model we use to calculate the contribution of rotational distortion to gravitational acceleration is sketched in Figure 5–3. The Earth is assumed to be flattened at the poles and bulged at the equator because of its rotation with angular velocity ω. The mass distribution is assumed to be symmetrical about the rotation axis. Because of the departure from spherical symmetry due to rotation, the gravitational acceleration at a point P outside the Earth has both radial and tangential components. The radial component is the sum of GM/r2 and the term g′r due to rotational distortion of the mass distribution; the tangential component g′t is entirely due to the rotationally induced departure from spherical symmetry. Following our previous sign convention both GM/r2 and g′r are positive if directed inward. Since rotation modifies the otherwise spherically symmetric model Earth only slightly, g′r and g′t are small compared with GM/r2.

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