Experimental testing of relativistic effects, variability of the gravitational constant and topography of Mercury surface from radar observations 1964–1989

Abstract

The new analysis of radar observations of inner planets for the time span 1964–1989 is described. The residuals show that Mercury topography is an important source of systematic errors which have not been taken into account up to now. The longitudinal and latitudinal variations of heights of Mercury surface were found and an approximate map of equatorial zone |ϕ|≤120° was constructed. Including three values characterizing global nonsphericity of Mercury surface into the set of parameters under determination allowed to improve essentially all estimates. In particular, the variability of the gravitational constantG was evaluated:

$$\dot G/G = (0.47 \pm 0.47) \times 10^{ - 11} yr^{ - 1} $$

. The correction to Mercury perihelion motion:

$$\Delta \dot \pi = - 0''.017 \pm 0''.052 cy^{ - 1} $$

and linear combination of the parameters of PPN formalism:

$$\upsilon = (2 + 2\gamma - \beta )/3 = 0.9995 \pm 0.0013$$

were determined; they are in a good agreement with General Relativity predictions. The obtained values Δ.π and ν correspond to the negligible solar oblateness, the estimate of solar quadrupole moment being:

$$J_2 = ( - 0.13 \pm 0.41) \times 10^{ - 6} $$

.