On the foundations of general relativistic celestial mechanics

TL;DR

This paper reviews the modern formulation of celestial mechanics within general relativity, focusing on the decomposition of the N-body problem, effacement properties, and implications for solar system dynamics.

Contribution

It introduces a comprehensive framework for splitting the N-body problem into internal and external dynamics using relativistic coordinates and discusses the effects of general relativity on classical celestial mechanics.

Findings

Development of a global and local chart framework for N-body dynamics

Analysis of effacement properties enabling problem decoupling

Assessment of relativistic modifications to the three-body problem

Abstract

Towards the end of nineteenth century, Celestial Mechanics provided the most powerful tools to test Newtonian gravity in the solar system, and led also to the discovery of chaos in modern science. Nowadays, in light of general relativity, Celestial Mechanics leads to a new perspective on the motion of satellites and planets. The reader is here introduced to the modern formulation of the problem of motion, following what the leaders in the field have been teaching since the nineties. In particular, the use of a global chart for the overall dynamics of N bodies and N local charts describing the internal dynamics of each body. The next logical step studies in detail how to split the N-body problem into two sub-problems concerning the internal and external dynamics, how to achieve the effacement properties that would allow a decoupling of the two sub-problems, how to define external-potential-effacing coordinates and how to generalize the Newtonian multipole and tidal moments. The review paper ends with an assessment of the nonlocal equations of motion obtained within such a framework, a description of the modifications induced by general relativity of the theoretical analysis of the Newtonian three-body problem, and a mention of the potentialities of the analysis of solar-system metric data carried out with the Planetary Ephemeris Program.