Abstract
Three main effects from general relativity (GR) may change the geometry and orientation of artificial earth satellite orbits, i.e., the Schwarzschild, Lense–Thirring, and De Sitter effects. So far, the verification of GR effects was mainly based on the observations of changes in the orientation of satellite orbital planes. We directly observe changes of the satellite orbit geometry caused by GR represented by the semimajor axis and eccentricity. We measure the variations of orbit size and shape of GPS, GLONASS, and Galileo satellites in circular and eccentric orbits and compare the results to the theoretical effects using three years of real GNSS data. We derive a solution that assumes the GR to be true, and a second solution, in which the post-Newtonian parameters are estimated, thus, allowing satellites to find their best spacetime curvature. For eccentric Galileo, GR changes the orbital shape and size in perigee in such a way that the orbit becomes smaller but more circular. In the apogee, the semimajor axis decreases but eccentricity increases, and thus, the orbit becomes more eccentric. Hence, the orbital size variabilities for eccentric orbits are greatly compensated by the orbital shape changes, and thus the total effect of satellite height change is much smaller than the effects for the size and shape of the orbit, individually. The mean semimajor axis offset based on all GPS, GLONASS, and Galileo satellites is − 17.41 ± 2.90 mm, which gives a relative error of 0.36% with respect to the theoretical value.
Highlights
The effects of the Einstein general relativity (GR, Einstein et al 1938) in the parameterized post-Newtonian (PPN) approximation can be considered as perturbing forces acting on earth-orbiting satellites which change the motion, the geometry, and the orientation of the Keplerian orbits (Infeld 1957; Kopeikin and Potapov 1994; Brumberg 2007)
We empirically confirm the theoretical orbit geometry misshaping caused by the effects emerging from GR
The measurements from 83 artificial earth satellites collected by 106 stations were used for the detection of the orbit size and shape changes caused mainly by the Schwarzschild effect with a minor contribution from the Lense–Thirring and De Sitter effects
Summary
The effects of the Einstein general relativity (GR, Einstein et al 1938) in the parameterized post-Newtonian (PPN) approximation can be considered as perturbing forces acting on earth-orbiting satellites which change the motion, the geometry, and the orientation of the Keplerian orbits (Infeld 1957; Kopeikin and Potapov 1994; Brumberg 2007). The satellite orbits of the Global Navigational Satellite Systems (GNSS), such as GPS, GLONASS, and Galileo, are determinable with an exceptionally high accuracy allowing for the recovery of small-scale perturbations with magnitudes below 1 0–9 m/s2 (Hugentobler and Montenbruck 2017; Bury et al 2020). GPS Solutions (2022) 26:5 period of 14h05m, the satellites orbit at heights between 17,180 and 26,020 km with an inclination of 50° and a revolution period of 12h56m (Steigenberger and Montenbruck 2017; Sośnica et al 2018; Hadas et al 2019). The Galileo satellites with differences between the perigee and apogee heights of 8,840 km (Fig. 1) constitute perfect probes for verifying effects emerging from the GR due to high-precision onboard clocks and two techniques for precise orbits determination, broadcasted L-band GNSS signals and Satellite Laser Ranging (Bury et al 2019b; 2021; Sośnica et al 2019). The onboard clocks require, calibration of biases and corrections to the orbit modeling errors
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