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Explicit evolution relations with orbital elements for eccentric, inclined, elliptic and hyperbolic restricted few-body problems
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Veras, Dimitri (2014) Explicit evolution relations with orbital elements for eccentric, inclined, elliptic and hyperbolic restricted few-body problems. Celestial Mechanics and Dynamical Astronomy, Volume 118 (Number 4). pp. 315-353. doi:10.1007/s10569-014-9537-8 ISSN 0923-2958.
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Official URL: http://dx.doi.org/10.1007/s10569-014-9537-8
Abstract
Planetary, stellar and galactic physics often rely on the general restricted gravitational N-body problem to model the motion of a small-mass object under the influence of much more massive objects. Here, I formulate the general restricted problem entirely and specifically in terms of the commonly used orbital elements of semimajor axis, eccentricity, inclination, longitude of ascending node, argument of pericentre, and true anomaly, without any assumptions about their magnitudes. I derive the equations of motion in the general, unaveraged case, as well as specific cases, with respect to both a bodycentric and barycentric origin. I then reduce the equations to three-body systems, and present compact singly- and doubly-averaged expressions which can be readily applied to systems of interest. This method recovers classic Lidov–Kozai and Laplace–Lagrange theory in the test particle limit to any order, but with fewer assumptions, and reveals a complete analytic solution for the averaged planetary pericentre precession in coplanar circular circumbinary systems to at least the first three nonzero orders in semimajor axis ratio. Finally, I show how the unaveraged equations may be used to express resonant angle evolution in an explicit manner that is not subject to expansions of eccentricity and inclination about small nor any other values.
Item Type: | Journal Article | ||||||
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Divisions: | Faculty of Science, Engineering and Medicine > Science > Physics | ||||||
Journal or Publication Title: | Celestial Mechanics and Dynamical Astronomy | ||||||
Publisher: | Springer Verlag | ||||||
ISSN: | 0923-2958 | ||||||
Official Date: | April 2014 | ||||||
Dates: |
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Volume: | Volume 118 | ||||||
Number: | Number 4 | ||||||
Page Range: | pp. 315-353 | ||||||
DOI: | 10.1007/s10569-014-9537-8 | ||||||
Status: | Peer Reviewed | ||||||
Publication Status: | Published | ||||||
Access rights to Published version: | Restricted or Subscription Access |
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