GRAIL gravity field recovery based on the short-arc integral equation technique: Simulation studies and first real data results

The NASA mission GRAIL (Gravity Recovery And Interior Laboratory) makes use of low-low satellite-to-satellite tracking between the spacecraft GRAIL-A (Ebb) and GRAIL-B (Flow) to determine high-resolution lunar gravity field features. The inter-satellite measurements are independent of the visibility of the spacecraft from Earth, and hence provide data for both the nearside and the farside of the Moon. We propose to exploit this ranging data by an integral equation approach using short orbital arcs; it is based on the reformulation of Newton's equation of motion as a boundary value problem. This technique has been successfully applied for the recovery of the gravity field of the Earth from the Gravity Recovery And Climate Experiment (GRACE) project-the terrestrial sibling of GRAIL. By means of a series of simulation studies we demonstrate the potential of the approach. We pay particular attention on a priori gravity field information, orbital arc length, observation noise and the impact of spectral aliasing (omission error). Finally, we compute a first lunar gravity model (GrazLGM200a) from real data of the primary mission phase (March 1, 2012 to May 29, 2012). The unconstrained model is expanded up to spherical harmonic degree and order 200. From our simulations and real data results we conclude that the integral equation approach is well suited for GRAIL gravity field recovery.