Representation of the Earth's Gravitational Potential

Details Representation of the Earth's Gravitational Potential Representation of the Earth's Gravitational Potential

Dec 1971

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1971cemec...4..348v&link_type=abstract

Celestial Mechanics, Volume 4, Issue 3-4, pp. 348-367

Astronomy and Astrophysics

Astrophysics

1

Scientific paper

The paper represents the Earth's gravitational potentialV, outside a sphere bounding the Earth, by means of its difference δV from the author's spheroidal potential. The difference δV is in turn represented as arising from a surface density σ on the sphere bounding the Earth. Because of the slow decrease with ordern of the normalized coefficients in the spherical harmonic expansion ofV, the density anomalies from which the higher coefficients arise must occur in regions close to the Earth's surface. The surface density σ is thus an idealization of the product of the density anomaly Δϱ and the crustal thicknessb. Values of σ are computed from potential coefficients obtained from two sources, Rapp and the Smithsonian Astrophysical Observatory. The two sources give qualitative agreement for the values of σ and for its contour map. The numerical values obtained for σ are compatible with the idea that the responsible density anomalies are reasonably small, i.e., less than 0.05 g/cm3, and occur in the crust alone.

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