https://doi.org/10.1140/epjp/s13360-025-07269-x
Regular Article
Flyby anomaly in the variational principle of general relativity
Université de Tours, 37200, Tours, France
a
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Received:
22
May
2025
Accepted:
29
December
2025
Published online:
24
January
2026
Abstract
For gravity assist space probes, the trajectory shows phenomenological anomaly on the position and velocity being interacted with the spacetime manifested by a planet. The anomalous velocity deviation of this osculating planetary flyby attracts enough attention as a problem of general relativity. In connection with the rotating weak-field massive source, the Lense-Thirring metric is diagonalised to find the equation of motion from action invariance Hamilton principle in the pure general relativistic theory. The computation for a near Earth flyby hyperbolic trajectory justifies theoretically the energy anomaly over the asymptotic in and out velocity obeying Anderson’s empirical formula!
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© The Author(s), under exclusive licence to Società Italiana di Fisica and Springer-Verlag GmbH Germany, part of Springer Nature 2026
Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.
