The high‐resolution gravity anomaly of the lunar topography

Abstract

By lowering the altitude of Lunar Prospector to about 10–20 km the spacecraft will provide measures of the Moon's gravity field at very high resolution, enabling us to derive a spherical harmonic representation that includes harmonics of degree 360 and demanding precise calculation of the gravity field of the topography at such low altitudes. We present a method to determine the gravity field of the topography at low altitudes, which is very efficient even for higher degree harmonics and is also applicable for topography with laterally and radially varying density. The method is applied to three simple models; namely, an unfilled basin, a basin with mare filling, and a topography specified by a tesseral harmonic of degree 60 and order 30, before applying it to the actual topography of the Moon. It is shown that the gravity of the topography calculated by the surface‐mass density approximation (a conventional method) is sufficient for harmonics of degree up to about 100 but becomes increasingly inadequate as the degree of the harmonics increases. The method is also applied to internal density interfaces, such as a possible Moho undulation, and it is concluded that the surface‐mass density approximation becomes less appropriate once the degree of the harmonics exceeds about 20. We also calculate the free air gravity anomaly of the lunar topography at 10 km altitude using this method and the available 90 degree spherical harmonic model of the topography. Although the surface topography of Venus has been expanded in terms of the spherical harmonics of degree up to 360 [Rappaport and Plaut, 1994], its gravity field is measured at altitudes greater than 150 km [Sjogren et al., 1997], which is much larger than the surface topography or possible undulation of the crust‐mantle boundary. The results of our method and the conventional method may not differ significantly for Venus.