A Preliminary Study on Earth and Other Planets Shape Determination: Comparison of Classical and Relativistic Gravitational Effects

Abstract

A first introduction is presented to the comparison between classical and relativistic gravitationaleffects related to planetary shape characterization. The Earth and the giant planets are the examplesconsidered. The analysis is mainly devoted to relativistic and classical predictions of periastron shiftsfor equatorial or almost equatorial orbits around the Earth and the giant planets, which can be used astools for determinations of the shape and density distribution. The ratios between relativistic (up to theLense–Thirring order correction) and classical (resulting from the harmonic expansion) effects and theirdependence on the orbit parameters are analyzed in order to identify the conditions improving the possibilityto resolve mixed effects. In a complementary approach, predictions for freely falling test particles fromrelativistic corrections and classical harmonic expansions of the Earth and other planets are comparedwithin the same shape characterization framework.