Comparison of Newton, Einstein and Brans–Dicke Gravitational Effects Associated with Earth and Other Planets Shape Determination

A comparison between classical, relativistic and Brans–Dicke gravitational effects related to planetary shape characterization is presented. The periastron shifts for orbits around the Earth and the giant planets which can be used as tools for determinations of their shape and density distribution, are the main object of our analysis. The conditions on the parameters improving the possibility to resolve mixed effects are studied. Differing from the approach in a previous work, we now include the observational errors for the classical expansion parameters \(J_{n}\)—which are of particular relevance for the ice giants Uranus and Neptune—as well as the corrections to gravitomagnetic effects resulting from a slight inclination of the satellite orbits. Also, some non-orbital considerations are carried out for the coefficient \(J_{3}\) associated to the South-North asymmetry of the mass distribution of the other two giant planets and the Earth.