A first-order secular theory for the post-Newtonian two-body problem with spin – II. A complete solution for the angular coordinates in the restricted case

Article

A first-order secular theory for the post-Newtonian two-body problem with spin – II. A complete solution for the angular coordinates in the restricted case

Biscani, F.; Carloni, S.

Mon. Not. R. Astron. Soc. 446, 3062-3077 (2015)

Abstract

Building on the results of a previous paper, we compute for the first time a full first-order
perturbative solution for the angular coordinates in the restricted post-Newtonian two-body
problem with spin. The analytical integration of the angular coordinates, based on the theory of
the Weierstrassian functions, allows us to investigate thoroughly the spin–orbit and spin–spin
interactions, and to derive several new results. The application of our solution to a selection
of idealized physical systems of interest reveals a rich variety of dynamical behaviours driven
by purely relativistic effects. In particular, we highlight a new relativistic nutational motion
resulting from the combined spin–orbit and spin–spin interactions.

Keywords

gravitation – relativistic processes – celestial mechanics.

Institute authors

Carloni, Sante

BibTeX

@article{UTF542,
  author        = {Biscani, F. and Carloni, S.},
  title         = {{A first-order secular theory for the post-Newtonian two-body problem with spin – II. A complete solution for the angular coordinates in the restricted case}},
  journal       = {Mon. Not. R. Astron. Soc.},
  volume        = {446},
  pages         = {3062-3077},
  year          = {2015},
  doi           = {10.1093/mnras/stu2258},
}