Second-order semi-analytical solution of the J2-problem in satellite theory
Author
Martin Lara
Title
Second-order semi-analytical solution of the J2-problem in satellite theory
Description
Solution of the J2 problem by exact decomposition into mean variations and short-period corrections
Category
Academic Articles & Supplements
Keywords
Perturbed Kepler motion, Semianalytical methods, Mean elements, Lie transforms, Noncanonical perturbation theory
URL
http://www.notebookarchive.org/2025-05-0yxr1iu/
DOI
https://notebookarchive.org/2025-05-0yxr1iu
Date Added
2025-05-02
Date Last Modified
2025-05-02
File Size
3.77 megabytes
Supplements
Rights
CC BY 4.0



Accompanying file for: Martin Lara, "Purely periodic, second-order terms of the -problem in closed form and arbitrary variables," The Journal of the Astronautical Sciences submitted 2025 .
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2nd order semi-analytical solution of the J2-problem
2nd order semi-analytical solution of the -problem
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Martin Lara
Scientific Computation Research Institute at the University of La Rioja (SCRIUR)
C/ Madre de Dios, 53
ES-26006 Logrono, Spain
<mlara0@gmail.com>
C/ Madre de Dios, 53
ES-26006 Logrono, Spain
<mlara0@gmail.com>
Semi-analytical solution to the problem given in the form of a mean-to-osculating transformation that is purely periodic in the mean distance to the ascending node, and the mean variations of the semi-equinoctial elements (to be integrated numerically). The former are truncated to the second order of , yet allow for a calibration of the semimajor axis to O[], whereas the mean variations are accurate up to .
Please, report bugs to <mlara0@gmail.com>
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3
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3
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Please, report bugs to <mlara0@gmail.com>
Semi-analytical solution and needed functions (initialize!)
Semi-analytical solution and needed functions (initialize!)
Sample orbit propagation: 1 week
Sample orbit propagation: 1 week
Change the orbital elements below to simulate a different orbit. The accuracy of the semianalytical propagation may change from orbit to orbit, but it should remain always within the accuracy expected from the truncation of the perturbation solution.
The time interval may be changed too. However, care must be taken for longer time intervals in order to guarantee that the numerically integrated reference orbit is accurate enough
Labels (I,M,D) of the different simulations identify the order truncation of the Inverse (osculating to mean) periodic corrections, of the Mean elements, and the Direct (mean to osculating) periodic corrections. The plus sign in labels (I+,M,D) signifies that the mean semimajor axis–and hence the mean Delaunay action–is calibrated in Brekwell and Vagners’ style (Celestial Mechanics 2, 1970, 253-264)
The time interval may be changed too. However, care must be taken for longer time intervals in order to guarantee that the numerically integrated reference orbit is accurate enough
Labels (I,M,D) of the different simulations identify the order truncation of the Inverse (osculating to mean) periodic corrections, of the Mean elements, and the Direct (mean to osculating) periodic corrections. The plus sign in labels (I+,M,D) signifies that the mean semimajor axis–and hence the mean Delaunay action–is calibrated in Brekwell and Vagners’ style (Celestial Mechanics 2, 1970, 253-264)
True (numerical) solution
True (numerical) solution
2nd order mean orbit from numerical integration
2nd order mean orbit from numerical integration
3rd order s/a orbit from numerical integration
3rd order s/a orbit from numerical integration
RSS position errors all together
RSS position errors all together


Cite this as: Martin Lara, "Second-order semi-analytical solution of the J2-problem in satellite theory" from the Notebook Archive (2025), https://notebookarchive.org/2025-05-0yxr1iu

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