A first-order secular theory for the post-Newtonian two-body problem with spin -- I: The restricted case

Abstract

We revisit the relativistic restricted two-body problem with spin employing a perturbation scheme based on Lie series. Starting from a post-Newtonian expansion of the field equations, we develop a first-order secular theory that reproduces well-known relativistic effects such as the precession of the pericentre and the Lense-Thirring and geodetic effects. Additionally, our theory takes into full account the complex interplay between the various relativistic effects, and provides a new explicit solution of the averaged equations of motion in terms of elliptic functions. Our analysis reveals the presence of particular configurations for which non-periodical behaviour can arise. The application of our results to real astrodynamical systems (such as Mercury-like and pulsar planets) highlights the contribution of relativistic effects to the long-term evolution of the spin and orbit of the secondary body.

14 pages, 3 figures, Published in MNRAS

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Cited by in corpus (6)

• Effective two-body approach to the hierarchical three-body problem
• Effective two-body approach to the hierarchical three-body problem: quadrupole to 1PN
• The Stark problem in the Weierstrassian formalism
• On the astrodynamics applications of Weierstrass elliptic and related functions
• The Influence of General Relativity on the Spins of Celestial Bodies in Inclined Orbits
• Hamiltonian normal forms for the post-Newtonian binary problem