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

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

Mar 2005

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=2005cemda..91..239d&link_type=abstract

Celestial Mechanics and Dynamical Astronomy, Volume 91, Issue 3-4, pp. 239-268

Astronomy and Astrophysics

Astronomy

2

Artificial Satellite Theory, Lie, Hamiltonian, Zonal Harmonic, First Order, Closed Form

Scientific paper

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 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 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 2 to J 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.

Affiliated with

Also associated with

No associations

Rating

Complete Zonal Problem of the Artificial Satellite: Generic Compact Analytic First Order in Closed Form does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Complete Zonal Problem of the Artificial Satellite: Generic Compact Analytic First Order in Closed Form, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Complete Zonal Problem of the Artificial Satellite: Generic Compact Analytic First Order in Closed Form will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-1214577