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Gravity field recovery using space technology has evolved during the last two decades. Several dedicated satellite missions have been sent to the space to get more accurate and up-to-date gravity field information, including, Challenging Minisatellite Payload (CHAMP), Gravity Recovery and Climate Experiment (GRACE) and Gravity field and Ocean Circulation Explorer (GOCE), launched on 15 July 2000, 17 March 2002 and 17 March 2009, respectively. GRACE is the extended version of the CHAMP. The major difference is that the CHAMP is an example of high-low satellite-to-satellite tracking (HL-SST) while the GRACE is an example of low-low satellite-to-satellite tracking (LL-SST) system. We observe the inter-satellite range rates of GRACE tandem constellation. The variation in inter-satellite range is due to the gravity field variation underneath the satellites. There are several methods in practice to recover the gravity field from range rate observation such as acceleration approach, short arc approach and energy balance approach. The most accurate and widely used is the variational equation approach, however numerically costly (Keller, 2014). This paper states the variational equation method in detail and compare the performance of the its two different implementation methods i.e. analytical and variation of constant method. The study shows that the computation time for the variation of constant method has reduced tremendously while achieving the same level of accuracy.

Muhammad Athar Javaid, Wolfgang Keller. (2017) Comparison of two gravity recovery algorithms based on the variational equation approach, Journal of Space Technology , Volume 7, Issue 1.
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