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Long Term Evolution of Planetary Systems with a Terrestrial Planet and a Giant PlanetWe 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.
Document ID
Document Type
Reprint (Version printed in journal)
Nikolaos Georgakarakos ORCID
(New York University Abu Dhabi Abu Dhabi, United Arab Emirates)
Ian Dobbs-Dixon ORCID
(New York University Abu Dhabi Abu Dhabi, United Arab Emirates)
Michael J Way ORCID
(Goddard Institute for Space Studies New York, New York, United States)
Date Acquired
September 16, 2016
Publication Date
June 8, 2016
Publication Information
Publication: Monthly Notices of the Royal Astronomical Society
Volume: 461
Issue: 2
ISSN: 0035-8711
Subject Category
Report/Patent Number
Funding Number(s)
WBS: 811073.
Distribution Limits
Public Use Permitted.
Technical Review
Professional Review
Dynamical evolution
Terrestrial planets
Planets and satellites
Celestial mechanics
Celestial mechanics

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