Analytical solution of perturbed circular motion: application to satellite geodesy

A short‐arc orbit technique was developed, and a very precise and efficient tool for regional orbit determination with a rigorous error budget is proposed for analyzing the TOPEX/POSEIDON (T/P) and ERS 1 missions. The purpose is to be able to determine very accurately, in some conditions, the local orbit, with a very small error in the radial direction, using satellite laser ranging data. A precision at the level of 2 cm is obtained. With this it was possible to cross validate all the different orbit determination techniques as well as the results of the altimeter calibration, showing the great progress made with the TOPEX/POSEIDON mission. After that the T/P mean sea profiles were computed and improved with high accuracy, thanks also to the short‐arc orbit technique. As a result, a combined mean sea surface using TOPEX/POSEIDON and ERS 1 data has been computed with crossover difference techniques, the T/P mean sea profiles serving as reference. Fine structures of the mean sea surface have been evidenced. Using this combined mean sea surface, the ERS 1 altimeter calibration was performed over the Mediterranean, again using the short‐arc orbit technique. The result is in good agreement with the previous ones (−41.6±7 cm). Finally, the T/P mean sea profiles were computed for different seasons and compared with a yearly averaged mean sea surface. Variations of about 15 cm are evidenced, associated notably with the thermal expansion between fall and winter. The short‐arc orbit technique appears to be well suited for monitoring very accurately the temporal variability of the Mediterranean Sea at a subcentimetric level.