ISSUE ON MEASURING THE LIGHT SPEED IN VACUUM

Based on the proposed differential equations of the interaction of the electric signal with the gravitational field, the observed phenomena are known as the gravitational lens and the Shapiro effect are investigated. The deflection of a light ray in the field of the Sun is simulated. It is shown that a moving photon undergoes in the gravitational field not only a transverse action, which causes a curvature of the trajectory but also a longitudinal one, implementing the acceleration-braking processes. As a result, the instability of the speed of light in a vacuum was revealed.

Speed of light on a rotating platform

In this paper, some analogies between the Shapiro effect in the solar gravitational field and the Sagnac phase shift have been found. Starting from Einstein equivalence principle (EEP), which states the equivalence between the gravitational force and the pseudo-force experienced by an observer in a noninertial frame of reference, we imagine an observer on a rotating platform immersed in a gravitational field. In the Shapiro effect, for example, we know that the speed of an electromagnetic signal, calculated from the Earth, is less than [Formula: see text], but, if we calculate the speed using a clock at rest in the solar gravitational field, where the photon is passing, we get that the speed of light is [Formula: see text]. Similarly, by considering the fictitious gravitational field of the rotating platform, if we look for a clock with respect to which the signal speed is [Formula: see text], we can interpret the time delay as a gravitational effect.

Test of gravitational redshift based on tri-frequency combination of frequency links between Atomic Clock Ensemble in Space and a ground station

<p>Atomic Clock Ensemble in Space (ACES) is an ESA mission designed mainly to test gravitational redshift with high-performance atomic clocks in space and on the ground. Here we develop tri-frequency combination (TFC) method based on the measurements of frequency shifts of three independent microwave links between ACES and a ground station. The potential scientific object requires an accuracy of at least 3×10<sup>-16</sup>, thus we need to consider various effects including Doppler effect, second-order Doppler effect, atmospheric frequency shift, tidal effects, refraction caused by atmosphere, Shapiro effect, with accuracy level of tens of centimeters. The ACES payload will be launched in middle of 2021, and the formulation proposed in this study will enable us to test gravitational redshift at an accuracy level at least 2×10<sup>-6</sup> level, one order more higher than the present accuracy level. This study is supported by NSFCs (grant Nos. 41721003, 41631072, 41874023, 41804012, 41429401, 41574007) and Natural Science Foundation of Hubei Province of China (grant No. 2019CFB611).</p>

Tests in the solar system

This chapter describes observable relativistic effects in the solar system. In the solar system we can, as a first approximation, neglect the gravitational field of all the stars except the Sun. In Newtonian theory, the planet trajectories are then Keplerian ellipses. Relativistic effects are weak because the dimensionless ratio characterizing them is everywhere less than GM⊙/c² R⊙≃ 2 × 10–6, and so they can be added linearly to the Newtonian perturbations due to the other planets, the non-spherical shape of celestial bodies, and so on. The chapter first describes the gravitational field of the Sun using a Schwarzschild spacetime, before moving on to look at the geodesic equation. It also discusses the bending of light, the Shapiro effect, the perihelion, post-Keplerian geodesics, and spin in a gravitational field.

Relativistic models for the BepiColombo radioscience experiment

To test General Relativity with the tracking data of the BepiColombo Mercury orbiter we need relativistic models for the orbits of Mercury and of the Earth, for the light-time and for all the spatio-temporal reference frames involved, with accuracy corresponding to the measurements: ≃10 cm in range, ≃2 micron/s in range-rate, over 2 years.For the dynamics we start from the Lagrangian post-Newtonian (PN) formulation, using a relativistic equation for the solar system barycenter to avoid rank deficiency. In the determination of the PN parameters, the difficulty in disentangling the effects of β from the ones of the Sun's oblateness is confirmed. We have found a consistent formulation for the preferred frame effects, although the center of mass is not an integral. For the identification of strong equivalence principle (SEP) violations we use a formulation containing both direct and indirect effects (through the modified position of the Sun in a barycentric frame).In the light-time equations, the Shapiro effect is modeled to PN order 1 but with an order 2 correction compatible with (Moyer 2003). The 1.5-PN order corrections containing the Sun's velocity are not relevant at the required level of accuracy.To model the orbit of the probe, we use a mercury-centric reference frame with its own “Mercury Dynamic Time”: this is the largest and the only relativistic correction required, taking into account the major uncertainties introduced by non-gravitational perturbations.A delicate issue is the compatibility of our solution with the ephemerides for the other planets, and for the Moon, which cannot be improved by the BepiColombo data alone. Conversely, we plan to later export the BepiColombo measurements, as normal points, to contribute with their unprecedented accuracy to the global improvement of the planetary ephemerides.