Classical and relativistic n-body problem: from Levi-Civita to the most advanced interplanetary missions
Dipartimento di Matematica Tullio Levi-Civita, Università degli Studi di Padova, Via Trieste, 63, 35121, Padova, Italy
Accepted: 18 October 2021
Published online: 13 November 2021
The n-body problem is one of the most important issues in Celestial Mechanics. This article aims to retrace the historical and scientific events that led the Paduan mathematician, Tullio Levi-Civita, to deal with the problem first from a classic and then a relativistic point of view. We describe Levi-Civita’s contributions to the theory of relativity focusing on his epistolary exchanges with Einstein, on the problem of secular acceleration and on the proof of Brillouin’s cancellation principle. We also point out that the themes treated by Levi-Civita are very topical. Specifically, we analyse how the mathematical formalism used nowadays to test General Relativity can be found in Levi-Civita’s texts and evolves over the years up to the current Parametrised version of the Post-Newtonian approximation (PPN) which is used in high precision contexts such as important space missions designed also to test General Relativity and which aims to estimate with very high accuracy the PPN parameters.
© The Author(s), under exclusive licence to Società Italiana di Fisica and Springer-Verlag GmbH Germany, part of Springer Nature 2021