Abstract

The first pair of satellites belonging to the European Global Navigation Satellite System (GNSS)—Galileo—has been accidentally launched into highly eccentric, instead of circular, orbits. The final height of these two satellites varies between 17,180 and 26,020 km, making these satellites very suitable for the verification of the effects emerging from general relativity. We employ the post-Newtonian parameterization (PPN) for describing the perturbations acting on Keplerian orbit parameters of artificial Earth satellites caused by the Schwarzschild, Lense–Thirring, and de Sitter general relativity effects. The values emerging from PPN numerical simulations are compared with the approximations based on the Gaussian perturbations for the temporal variations of the Keplerian elements of Galileo satellites in nominal, near-circular orbits, as well as in the highly elliptical orbits. We discuss what kinds of perturbations are detectable using the current accuracy of precise orbit determination of artificial Earth satellites, including the expected secular and periodic variations, as well as the constant offsets of Keplerian parameters. We found that not only secular but also periodic variations of orbit parameters caused by general relativity effects exceed the value of 1 cm within 24 h; thus, they should be fully detectable using the current GNSS precise orbit determination methods. Many of the 1-PPN effects are detectable using the Galileo satellite system, but the Lense–Thirring effect is not.

Highlights

  • General relativity (GR) predicts a number of effects that could not be explained by the classical Newtonian theory of gravity

  • The masses of artificial satellites are negligible with respect to the mass of the central body, the velocities of artificial Earth satellites are much smaller than the speed of light (v2/c2 < 6.8·10−10), the size of the Earth and the satellite heights are much larger than the Earth’s Schwarzschild radius; all of which allow for a simplification of the GR effects in the post-Newtonian approximation (PPN)

  • The simulation results were compared with the first-order perturbations for 24 h intervals, that is, the interval typically used for deriving precise Global Navigation Satellite System (GNSS) orbits by the International GNSS Service, because very long arcs of GNSS orbits, exceeding 1 week, are typically affected by systematic errors of solar radiation pressure modeling (Teunissen and Montenbruck 2017; Bury et al 2019)

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Summary

Introduction

General relativity (GR) predicts a number of effects that could not be explained by the classical Newtonian theory of gravity. These include, e.g., deflection of light, Shapiro time delay of light, gravitational waves, time dilation, and effects explaining the peculiar motion of celestial bodies (Einstein et al 1938; Will 2014). Despite that the usefulness of these satellites for navigation is limited, these can be used for the verification of the effects emerging from general relativity due to the variable distance from the Earth, high-quality onboard hydrogen masers, and rubidium atomic clocks (Delva et al 2018; Herrmann et al 2018), as well as two independent techniques for orbit determination: GNSS and SLR

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