Analytic orbit propagation for transiting circumbinary planets

The herein presented analytical framework fully describes the motion of coplanar systems consisting of a stellar binary and a planet orbiting both stars on orbital as well as secular timescales. Perturbations of the Runge-Lenz vector are used to derive short period evolution of the system, while octupole secular theory is applied to describe its long term behaviour. A post Newtonian correction on the stellar orbit is included. The planetary orbit is initially circular and the theory developed here assumes that the planetary eccentricity remains relatively small (e_2<0.2). Our model is tested against results from numerical integrations of the full equations of motion and is then applied to investigate the dynamical history of some of the circumbinary planetary systems discovered by NASA's Kepler satellite. Our results suggest that the formation history of the systems Kepler-34 and Kepler-413 has most likely been different from the one of Kepler-16, Kepler-35, Kepler-38 and Kepler-64, since the observed planetary eccentricities for those systems are not compatible with the assumption of initially circular orbits.Comment: Accepted for publication in Ap

Effects of variable eccentricity on the climate of an Earth-like world

The Kepler era of exoplanetary discovery has presented the Astronomical community with a cornucopia of planetary systems very different from the one which we inhabit. It has long been known that Jupiter plays a major role in the orbital parameters of Mars and it's climate, but there is also a long-standing belief that Jupiter would play a similar role for Earth if not for its large moon. Using a three dimensional general circulation model (3-D GCM) with a fully-coupled ocean we simulate what would happen to the climate of an Earth-like world if Mars did not exist, but a Jupiter-like planet was much closer to Earth's orbit. We investigate two scenarios that involve evolution of the Earth-like planet's orbital eccentricity from 0--0.283 over 6500 years, and from 0--0.066 on a time scale of 4500 years. In both cases we discover that they would maintain relatively temperate climates over the time-scales simulated. More Earth-like planets in multi-planet systems will be discovered as we continue to survey the skies and the results herein show that the proximity of large gas giant planets may play an important role in the habitability of these worlds. These are the first such 3-D GCM simulations using a fully-coupled ocean with a planetary orbit that evolves over time due to the presence of a giant planet.Comment: 11 pages, 4 figures, 1 table, submitted to ApJ Letters. Updated figures and discussion at referee reques

Improved equations for eccentricity generation in hierarchical triple systems

In a series of papers, we developed a technique for estimating the inner eccentricity in hierarchical triple systems, with the inner orbit being initially circular. However, for certain combinations of the masses and the orbital elements, the secular part of the solution failed. In the present paper, we derive a new solution for the secular part of the inner eccentricity, which corrects the previous weakness. The derivation applies to hierarchical triple systems with coplanar and initially circular orbits. The new formula is tested numerically by integrating the full equations of motion for systems with mass ratios from 10^(-3) to 10^(3). We also present more numerical results for short term eccentricity evolution, in order to get a better picture of the behaviour of the inner eccentricity.Comment: Accepted for publication in MNRA

Long term evolution of planetary systems with a terrestrial planet and a giant planet

We study the long term orbital evolution of a terrestrial planet under the gravitational perturbations of a giant planet. In particular, we are interested in situations where the two planets are in the same plane and are relatively close. We examine both possible configurations: the giant planet orbit being either outside or inside the orbit of the smaller planet. The perturbing potential is expanded to high orders and an analytical solution of the terrestrial planetary orbit is derived. The analytical estimates are then compared against results from the numerical integration of the full equations of motion and we find that the analytical solution works reasonably well. An interesting finding is that the new analytical estimates improve greatly the predictions for the timescales of the orbital evolution of the terrestrial planet compared to an octupole order expansion. Finally, we briefly discuss possible applications of the analytical estimates in astrophysical problems.Comment: Accepted for publication in MNRA