Mean longitude

Mean longitude

Canonical Equations of Celestial Mechanics

Published in G.A. Gurzadyan, Theory of Interplanetary Flights, 2020

One of the Jacobi elements, α1, enters into the perturbation function R explicitly, through α, as well as indirectly, through the mean longitude λ. To remove this defect, Delaunay introduced new elements slightly differing from Eq.(116), namely () L=kMa1/2,l=n(t−T),G=kM(1−e2)1/2a1/2g=π−Ω,H=kM(1−e2)1/2a1/2cosih=Ω.

A multiscaling-based semi-analytic orbit propagation method for the catalogue maintenance of space debris

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Journal Information

Published in Journal of Spatial Science, 2020

Bin Li, Jizhang Sang, Jinsheng Ning

A well-known SST technique, Draper Semi-analytic Satellite Theory (DSST), uses the variation of parameters (VOP) to convert three second-order differential equations of motion into a system of six first-order differential equations (Danielson et al. 1995). Then, the averaging technique (Nayfeh 1977) is applied to the VOP equations of motion to give a system of first-order differential equations for the slowly varying mean element rates and a short-periodic variation that is 2-periodic in the fast variable, the mean anomaly for the Keplerian elements or the mean longitude for the equinoctial elements. A numerical propagator with a large step of one day or a half is applied to solve the equations of mean elements, whereas the short-periodic equations are solved analytically. The DSST has achieved great improvements in computation accuracy since its invention (Cefola 1972, Green 1979, Fonte et al. 1995, San-Juan et al. 2012, Setty et al. 2016).

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Canonical Equations of Celestial Mechanics

A multiscaling-based semi-analytic orbit propagation method for the catalogue maintenance of space debris