Global lunar gravity recovery from satellite-to-satellite tracking

Abstract

A feasibility study is presented of high resolution and accuracy determination of the global grayity field of the Moon from a combination of low-low satellite-to-satellite range-rate observations and conventional tracking from stations on Earth. The European Moon ORbiting Observatory (MORO) mission, studied as a candidate for the third mediumsized science mission (M3) under the European Space Agency's Horizon 2000 scientific programme, is adopted for the simulation purposes. Global coverage and mapping of the fine details of the gravity field is achieved by satellite-to-satellite tracking (SST) of a small sub-satellite deployed by MORO in its 100 km polar orbit, whereas the long-wavelength features are obtained from Earth-based tracking. The combination of SST and Earth-based tracking therefore represents a powerful tool over a wide range of wavelengths. Moreover, tracking from Earth provides a clear reference for the satellite orbits, which are hard to determine from SST data only. The baseline mission proposal foresees a co-orbiting satellite pair in which the two satellites follow each other in essentially the same orbital plane with only a small spacing in time. The MORO gravimetry experiment requirements prescribe a surface level radial acceleration accuracy of a few mGal with a surface resolution of 50–100km. A number of satellite tracking configurations has been investigated and the influence of noise and systematic errors has been studied. Using perfect measurements and in the absence of systematic model errors the gravity field of the Moon, assumed to be pertectly represented by the 60 × 60 Lun60d model of Konopliv et al. (1993) with a surface resolution of 91 km, has been recovered with a radial acceleration accuracy better than 0.003 mGal using a 3° in-plane satellite spacing. Introducing uncorrelated random noise to the tracking links and a 10% model error in the direct solar radiation pressure model, still an accuracy better than 5 mGal can be achieved. Finally, it is shown that a small angular separation in right ascension of the ascending node of the orbital planes of MORO and its sub-satellite adds extra cross-track information to the SST range-rate signal and thus enables better determination of high sectorial and near-sectorial terms of the gravity field.