Nodal Precession in Closely Spaced Planet Pairs
Abstract
Planetplanet perturbations can cause planets' orbital elements to change on secular timescales. Previous work has evaluated the nodal precession rate for planets in the limit of low α (semimajor axis ratio; 0 < α ≤ 1). Our simulations show that systems at high α (or low period ratio), similar to multiplanet systems found in the Kepler survey, have a nodal precession rate that is more strongly dependent on eccentricity and inclination. We present a complete expansion of the nodal precession rate to fourth order in the disturbing function and show that this analytical solution much better describes the simulated Nbody behavior of highα planet pairs; at α ≈ 0.5, the higherorder solution, on average, reduces the median analytical error by a factor of 7.5 from linear theory and 6.2 from a similar expansion assuming low α. We set limits on eccentricity and inclination where the theory is precisely validated by Nbody integrations, which can be useful in future secular treatments of planetary systems.
 Publication:

The Astronomical Journal
 Pub Date:
 May 2020
 DOI:
 10.3847/15383881/ab83f0
 arXiv:
 arXiv:2003.07835
 Bibcode:
 2020AJ....159..217B
 Keywords:

 Analytical mathematics;
 Ascending node;
 Celestial mechanics;
 Exoplanet systems;
 Exoplanet dynamics;
 Nbody simulations;
 Orbits;
 Threebody problem;
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 Astrophysics  Earth and Planetary Astrophysics
 EPrint:
 18 pages, 11 figures, submitted to AJ