A high resolution gravity model for Venus: GVM‐1

Abstract

A spherical harmonic model of the gravitational field of Venus complete to degree and order 50 has been developed using the S‐band Doppler tracking data of the Pioneer Venus Orbiter (PVO) collected between 1979 and 1982. The short wavelengths of this model could only be resolved near the PVO periapse location (∼14°N latitude), therefore a priori constraints were applied to the model to bias poorly observed coefficients towards zero. The resulting model has a half‐wavelength resolution of 400 km near the PVO periapse location, but the resolution degrades to greater than 1000 km near the poles. This gravity model correlates well with a degree 50 spherical harmonic expansion of the Venus topography derived from a combination of Magellan and PVO data. New tracking data from Magellan's gravity mission should provide some improvement to this model, although a complete model of the Venusian gravity field will depend on tracking of Magellan after the circularization of it's orbit using aerobraking.

Venus Gravity: 180th Degree and Order Model

“…The common method is to constrain each harmonic coefficient toward 0 with an uncertainty given by the Kaula rule (Kaula 1966) for that particular planet (used, for example, in Konopliv et al 1993, Nerem et al 1993 and for the second and third steps of this solution). The Kaula rule for Venus is 1.2 × 10 −5 /n 2 where n is the degree of the coefficient.…”

“…In support of the Magellan navigation effort, McNamee et al (1992) reprocessed the low-altitude PVO data to produce a 21st degree and order model. Using the low and high altitude PVO data sets, Nerem et al (1993) determined a 50th degree and order field.…”

An improved gravity model for Mars: Goddard Mars model 1

“…The data were processed using the GEODYN/SOLVE orbit determination/ estimation programs [Putney, 1977]. These programs have previously been used in the derivation of a series of gravitational Goddard Earth Models (GEM) [e.g., Lerch et al, 1979;Marsh et al, 1988Marsh et al, , 1990 and have been adapted for the analysis of planetary tracking data [Smith et al, 1990b;Nerem et al, 1993]. GEODYN provides orbit determination and geodetic parameter estimation capabilities, and numerically integrates the spacecraft Cartesian state and the force model partial derivatives employing a high-order Cowell predictor-corrector method.…”

Rotation of the Terrestrial Planets

“…First results suggested a large orientation difference of a few degrees (Bills et al, 1987;Mottinger et al, 1985), much larger than the wobble amplitudes for the Earth and Mars, which are below an arcsec (Munk and MacDonald, 1960, Section 10.04.3). Later studies including Magellan data gave estimated values of about 0.5 (Konopliv and Sjogren, 1994;Konopliv et al, 1993Konopliv et al, , 1999McNamee et al, 1993), although Nerem et al (1993) (see also Konopliv et al, 1993), who only used PVO data, obtained an even smaller amplitude of about 0.1 . Konopliv and Sjogren (1994) quote a formal error of 0.05 for the pole position.…”