Complete Zonal Problem of the Artificial Satellite: Generic Compact Analytic First Order in Closed Form

This paper is a contribution to the Theory of the Artificial Satellite, within the frame of the Lie Transform as canonical perturbation technique (elimination of the short period terms). We consider the perturbation by any zonal harmonic J sub(n) (n . 2) of the primary on the satellite, what we call...

Full description

Saved in:
Bibliographic Details
Published in:Celestial mechanics and dynamical astronomy 2005-12, Vol.91 (3-4), p.239-268
Main Author: Saedeleer, Bernard De
Format: Article
Language:English
Subjects:
Artificial satellites
Asymptotic properties
Computer programs
Eccentricity
Exact solutions
Mathematical analysis
Perturbation methods
Studies
Zonal harmonics
Citations: Items that this one cites
Items that cite this one
Online Access:Get full text
Tags: Add Tag
No Tags, Be the first to tag this record!
Description
Summary:This paper is a contribution to the Theory of the Artificial Satellite, within the frame of the Lie Transform as canonical perturbation technique (elimination of the short period terms). We consider the perturbation by any zonal harmonic J sub(n) (n . 2) of the primary on the satellite, what we call here the complete zonal problem of the artificial satellite. This is quite useful for primaries with symmetry of revolution. We give an analytical formula to compute directly the first order averaged Hamiltonian. The computation is carried out in closed form for all terms, avoiding therefore tedious expansions in the eccentricity or in any anomaly; this feature makes the averaging process, not only valid for all kind of elliptic trajectories but at the same time it yields the averaged Hamiltonian in a very short and compact way. The formula allows us to now skip the averaging process, which means an asymptotic gain of a factor 3n/2 regarding the computational cost of the n super(th) zonal. Our analytical formulae have been widely checked, by comparison on one hand with published works (Brouwer, 1959) (which contained results for particular zonal harmonics, let's say typically from J sub(2) to J sub(8)), and on the other hand with the results of 3 symbolic manipulation software, among which the MM (standing for 'Moon's series Manipulator'), which has already been used and described in (De Saedeleer B., 2004). Additionally, the first order generator associated with this transformation is given into the same closed form, and has also been validated.
ISSN:0923-2958
1572-9478
DOI:10.1007/s10569-004-1813-6