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Gravitational anomaly detection using a satellite constellation: analysis and simulation

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Abstract

We investigate the utility of a constellation of four satellites in heliocentric orbit, equipped with accurate means to measure intersatellite ranges, round-trip times and phases of signals coherently retransmitted between members of the constellation. Our goal is to reconstruct the measured trace of the gravitational gradient tensor as accurately as possible. Intersatellite ranges alone are not sufficient for its determination, as they do not account for any rotation of the satellite constellation, which introduces fictitious forces and accelerations. However, measuring signal round-trip time differences along clockwise and counterclockwise signal paths in a Sagnac-type measurement among the satellites supplies the necessary observables to estimate, and subtract, the effects of rotation. Utilizing, in addition, the approximate distance and direction from the Sun, it is possible to approach an accuracy of \(10^{-24}~{\mathrm{s}}^{-2}\) for a constellation with typical intersatellite distances of 1000 km in an orbit with a 1 astronomical unit semi-major axis. This is deemed sufficient to detect the presence of a galileonic modification of the solar gravitational field.

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Code Availability

The simulation code described in this manuscript is published at https://github.com/vttoth/TETRA.

Notes

  1. This form follows directly from the right-hand side of the alternate form of Einstein’s field equation in the Newtonian approximation, specifically the term \(T_{00}-\tfrac{1}{2}g_{00}T\) with \(T_{\mu \nu}=\operatorname {diag}(c^{2}\rho ,-p,-p,-p)\) for an isotropic perfect fluid.

  2. https://github.com/vttoth/TETRA

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Acknowledgements

VTT thanks Slava Turyshev for discussions and acknowledges the generous support of David H. Silver, Plamen Vasilev and other Patreon patrons.

Funding

The authors declare that no funds, grants, or other support were received during the preparation of this manuscript. The authors have no relevant financial or non-financial interests to disclose. The authors consent to publication of this manuscript.

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  1. Ottawa, K1N 9H5, ON, Canada

    Viktor T. Toth

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  1. Viktor T. Toth
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VTT wrote the entire manuscript and developed the software used for analysis.

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Correspondence to Viktor T. Toth.

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Toth, V.T. Gravitational anomaly detection using a satellite constellation: analysis and simulation. Astrophys Space Sci 368, 92 (2023). https://doi.org/10.1007/s10509-023-04248-5

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