The high-resolution gravity anomaly of the lunar topography

By lowering the altitude of Lunar Prospector to about 10-20 km the spacecra ft will provide measures of the Moon's gravity field at very high resolutio n, enabling us to derive a spherical harmonic representation that includes harmonics of degree 360 and demanding precise calculation of the gravity fi eld of the topography at such low altitudes. We present a method to determi ne the gravity field of the topography at low altitudes, which is very effi cient even for higher degree harmonics and is also applicable for topograph y with laterally and radially varying density. The method is applied to thr ee 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, b efore applying it to the actual topography of the Moon. It is shown that th e gravity of the topography calculated by the surface-mass density approxim ation (a conventional method) is sufficient for harmonics of degree up to a bout 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 d ensity approximation becomes less appropriate once the degree of the harmon ics 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 top ography of Venus has been expanded in terms of the spherical harmonics of d egree up to 360 [Rappaport and Pla ut, 1994], its gravity field is measured at altitudes greater than 150 km [Sjogren et al., 1997], which is much lar ger than the surface topography or possible undulation of the crust-mantle boundary. The results of our method and the conventional method may not dif fer significantly for Venus.