Gravimagnetic effect of the barycentric motion of the Sun and determination of the post-Newtonian parameter γ in the Cassini experiment

Abstract

The most precise test of the post-Newtonian γ parameter in the solar system has been achieved in measurement of the frequency shift of radio waves to and from the Cassini spacecraft as they passed near the Sun. The test relies upon the JPL model of radiowave propagation that includes, but does not explicitly parametrize, the impact of the non-stationary component of the gravitational field of the Sun, generated by its barycentric orbital motion, on the Shapiro delay. This non-stationary gravitational field of the Sun is associated with the Lorentz transformation of the metric tensor and the affine connection from the heliocentric to the barycentric frame of the solar system and can be treated as gravimagnetic field. The gravimagnetic field perturbs the propagation of a radio wave and contributes to its frequency shift at the level up to 4 × 10 −13 that may affect the precise measurement of the parameter γ in the Cassini experiment to about one part in 10,000. Our analysis suggests that the translational gravimagnetic field of the Sun can be extracted from the Cassini data, and its effect is separable from the space curvature characterized by the parameter γ.

On the two approaches to the data analysis of the Cassini interplanetary relativity experiment

“…Unfortunately, insufficiently elaborated comparison of the two different mathematical techniques did not allow Bertotti et al [6] to reproduce our results. The goal of the present Letter is to show that the result of Bertotti et al paper [6] exactly coincides with that obtained earlier in our paper [5].…”

“…Hence, [6] believed that [5] missed the velocity-dependent term in front of the logarithmic function in Eq. (5).…”

“…(12)-(15)]). Our equation for the gravitational Doppler shift, z gr , written down in the barycentric coordinates is [5,8] z gr = − (6) where…”

“…This α B β 3 × 10 −13 correction comes from the time derivative of the argument of the logarithmic function in Eq. (5) as shown in [5]. Differentiation of the solar-velocity term in front of the logarithm in Eq.…”

A new laser-ranged satellite for General Relativity and space geodesy: III. De Sitter effect and the LARES 2 space experiment

“…The most accurate determination of γ so far is its measurement by the CASSINI spacecraft in the gravitational field of the Sun [29], with an accuracy of about 2.3 × 10 −5 (for a discussion of the CASSINI test of γ see [30]); we emphasize that the orbital plane of the LARES 2 satellite will be affected by the de Sitter precession due to the mass of the Sun. From Eq.…”