(a) The degree- part of the Earth's anomalous gravitational potential has a known…

PHYSICS · Subjective · Fermi University Physics · Mathematical Methods for Physics · Earth, Climate & Energy Physics · The solid Earth: structure, fields and thermal history

The Solid Earth, Ch The shape and gravity of the Earth: potential, geoid, isostasy and flexure

Problem

(a) The degree-

n = 10

part of the Earth's anomalous gravitational potential has a known amplitude at the surface, radius

a = 6371\,\mathrm{km}

. Using the exterior radial decay factor

(a/r)^{n+1}

for the potential of a degree-

n

term, estimate the fraction of that potential amplitude still present at a satellite at radius

r = a + 200\,\mathrm{km}

. (b) A broad geoid low, taken to be produced by a single compact mass deficit, has a half-width of

x_{1/2} = 900\,\mathrm{km}

. Using the geoid half-width rule for a point source,

x_{1/2} = \sqrt3\,z

, estimate the greatest depth at which such a source could lie.

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