CHAMP and GRACE resonances, and the gravity field of the Earth

Abstract

Using orbital data far more precise than existed a quarter of a century ago, we have derived values for lumped geopotential harmonic coefficients from the passage of the satellites CHAMP (Challenging Minisatellite Payload) and GRACE (Gravity Recovery And Climate Experiment) through particular resonances. Due to orbit decay, CHAMP first passed through the 46/3 resonance (orbit repeating after 46 revolutions over three days) and then, in due course, 77/5, 31/2 and 47/3; indeed it passed through 31/2 three times, following orbit raises to extend the satellite’s useful lifetime. The orbit data we used for CHAMP came from the retrospectively computed and highly accurate state vectors, but for GRACE (both satellites) only the routine (less accurate) TLEs (Two-Line mean Elements) have so far been available, being used for 61/4 analysis. Values for the lumped harmonics come from analysis of the large variation in the orbital inclination (and to a lesser degree the nodal right ascension) that they cause. Our main success has been for the 31/2 resonance, including the implicit 62/4, but in all cases our lumped values agree well with values based on the complete CHAMP and GRACE high-degree global gravity models (Eigen-3p and Eigen-Grace02s, respectively), though essentially independent of them. This confirms both the validity of our method and the high quality of the new global models.