The Gravity Field for an Ellipsoid of Revolution as a Level Surface
Abstract
The form of a single level surface that envelops all attracting matter and the value of the potential or of the gravitational attraction at a definite point on or outside the surface determine uniquely the field of force on and outside of the surface. This statement holds good even when we add to the gravitational attraction the centrifugal 'force' due to uniform rotation. Hence, if we assume that the surface of the earth is an exact ellipsoid of rotation under its own attraction combined with the centrifugal force of uniform rotation about the minor axis, the field of force on and outside this ellipsoid is uniquely determined, if we assume, for instance, the value of gravity at the equator. This determination is carried out by means of a rather special set of curvilinear coordinates. In terms of these coordinates the value of the potential at any point in exterior space and the value of gravity are expressible in closed form in terms of Lengendre functions of the second kind with imaginary argument, and these again are expressible in terms of the elementary functions. In practice, however, it is found more convenient to expand the Lengendre functions in series, also the formulas dependent on them. Various incidental developments are given.
Document Details
- Document Type
- Technical Report
- Publication Date
- May 01, 1952
- Accession Number
- ADA075988
Entities
People
- Walter D. Lambert
Organizations
- Ohio State University