The equations of motion of a secularly precessing elliptical orbit

The equations of motion of a secularly precessing ellipse are developed using time as the independent variable. The equations are useful when integrating numerically the perturbations about a reference trajectory which is subject to secular perturbations in the node, the argument of pericentre and t...

Full description

Saved in:
Bibliographic Details
Published inMonthly notices of the Royal Astronomical Society Vol. 428; no. 3; pp. 2605 - 2616
Main Authors Casotto, S., Bardella, M.
Format Journal Article
LanguageEnglish
Published London Oxford University Press 01.01.2013
Subjects
Astrophysics
Frequencies
Numerical analysis
Orbits
methods: analytical
celestial mechanics
Online AccessGet full text

Cover

More Information
Summary:The equations of motion of a secularly precessing ellipse are developed using time as the independent variable. The equations are useful when integrating numerically the perturbations about a reference trajectory which is subject to secular perturbations in the node, the argument of pericentre and the mean motion. Usually this is done in connection with Encke's method to ensure minimal rectification frequency. Similar equations are already available in the literature, but they are either given based on the true anomaly as the independent variable or in mixed mode with respect to time through the use of a supporting equation to track the anomaly. The equations developed here form a complete and independent set of six equations in time. Reformulations both of Escobal's and Kyner and Bennett's equations are also provided which lead to a more concise form.
Bibliography:SourceType-Scholarly Journals-1
ObjectType-Feature-1
content type line 14
ISSN:0035-8711
1365-2966
DOI:10.1093/mnras/sts239