[G02-4] Gravity field modelling and applications

[G02-4-03] Satellite gravimetry from tracking: do it right, and for better

^○Peiliang Xu (Kyoto University, Kyoto, Japan)

Satellite gravimetry from tracking has played a key role in precise recovery of global Earth's gravity models. In this talk, (1) We will prove that the standard numerical integration method to reconstruct a precise global Earth's gravity model from satellite tracking measurements, as currently used to produce almost all standard global Earth's gravity models by major institutions worldwide (NASA Goddard Space Flight Center, GFZ, JPL and University of Texas CSR, for example), is incorrect mathematically; (2) Bearing in mind that gravity satellites can be precisely tracked almost continuously by using global navigation satellite systems, we develop a new, measurements-based perturbation method for precise reconstruction of global Earth's gravity model from satellite tracking measurements. This new measurement-based perturbation method is uniformly convergent from the mathematical point of view for arcs of any length and can theoretically extract any small forces from long arc measurements with a very high resolution; (3) We develop three different local solutions to the Newton's nonlinear different differential equations of satellite motion. As a result, the new solutions can serve as starting foundations for global satellite gravitational modelling from satellite tracking measurements; and finally, (4) By directly turning the nonlinear differential equations of satellite motion into the nonlinear integral equations, and recognizing the fact that satellite orbits can now be measured almost continuously at the level of random errors, we further reformulate the links between satellite tracking measurements and the global uniformly convergent solutions to the Newton's governing differential equations as a condition adjustment model with unknown parameters. With all the efforts, we have finally constructed solid mathematical foundations for the next generation of global satellite gravitational models of high precision and high resolution.