Refining of the Global Characteristics of the Earth’s Gravitational Field up to the Fifth Approximation of Molodensky’s Theory Based on Analytic Continuation

The global characteristics of the Earth’s gravitational field are refined to the fifth approximation of Molodensky’s theory. The computations were based on analytic continuation of free-air gravity anomalies from the Earth’s physical surface to the reference spherical surface passing through the calculated point, using a Taylor series. Schematic maps of digital global models of gravity anomaly vertical gradients to the fifth order are presented, and global correction terms are obtained for quasigeoid heights and deflections of the vertical (DOV) for the first to fifth approximations of Molodensky’s theory. It is shown that the gradient solution helps refine the global characteristics of the Earth’s gravitational field. When refining quasigeoid heights using the Stokes’ formula, the second approximation of Molodensky’s theory is sufficient for plain areas, while the fourth one is sufficient for mountainous areas. When refining the DOV components in meridian and the first vertical planes, the standard error increases from the second approximation.