Open AccessGravitational and magnetic fields of some simple solids of revolution
Author(s) -
Parker Robert L.,
Shure Loren
Publication year - 1985
Publication title -
geophysical journal of the royal astronomical society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.302
H-Index - 168
eISSN - 1365-246X
pISSN - 0016-8009
DOI - 10.1111/j.1365-246x.1985.tb05115.x
Subject(s) - conic section , circular symmetry , spherical harmonics , symmetry (geometry) , convergence (economics) , gravitational field , simple (philosophy) , classical mechanics , mathematical analysis , point (geometry) , gravitational potential , gravitation , physics , geometry , mathematics , philosophy , epistemology , economics , economic growth
Summary. Exact spherical harmonic expansions are given for calculating the gravitational and magnetic fields associated with certain uniform solids of revolution. The figures are those made by rotating a conic section about one of its principal axes. The coefficients in the expansions can be computed accurately and efficiently and this approach leads to a very satisfactory method for calculating the fields of geological bodies with approximate circular symmetry about a vertical axis. A complete theory of convergence is given for the expansions. Somewhat unexpectedly, the sphere of convergence is determined by the location of a number of equivalent point or line sources that lie within the body or on its edges.