GRAVITATIONAL SPECTRA FROM DIRECT MEASUREMENTS

A simple rapid method is described for determining the spectrum of a surface field (in spherical harmonics) from harmonic analysis of direct (in situ) measurements along great circle arcs. The method is shown to give excellent overall trends (smoothed spectra) to very high degree from even a few shortarcs of satelite data. Three examples are taken with perfect measurements of satellite tracking over a planet made up of hundreds of point masses using 1) altrimetric heights from a low-orbiting spacecraft, 2) velocity (range rate) residuals between a low and a high satellite in circular orbits, and 3) range rate data between a station at infinity and a satellite in a highly eccentric orbit. In particular, the smoothed spectrum of the earth's gravitational field is determined to about degree 400 (50-km half wavelength) from 1o x 1o gravimetry and the equivalent of 11 revolutions of Geos 3 and Skylab altimetry. This measurment shows there is about 46cm of geoid height (rms worldwide) remaining in the field beyond degree 180. -Authors