Analytic formulation for J2 perturbed orbits

Analytic formulation for J2 perturbed orbits

Silvano Sgubini, Giovanni B. Palmerini

Abstract. The paper deals with a technique developed along the years at the Scuola di Ingegneria Aerospaziale to provide an exact solution for J2 perturbed orbits, here applied to spacecraft formations. Analytic solutions are useful in the design phase and can help in operations to identify and to efficiently maintain a suitable configuration. The approach is based on the elaboration, conveniently performed by means of a symbolic software tool, of a set of equations analogous to the Lagrange planetary relations. Resulting parameters are expressed through Fourier series depending only on the initial conditions. Comparison with standard, longer to obtain and less accurate numerical propagation clarify the advantage of the technique, which is limited only by the number of terms taken into account in the expansion.

Keywords
Orbit Propagation, Orbit Perturbations, J2 Effects, Formation Flying

Published online 11/1/2023, 4 pages
Copyright © 2023 by the author(s)
Published under license by Materials Research Forum LLC., Millersville PA, USA

Citation: Silvano Sgubini, Giovanni B. Palmerini, Analytic formulation for J2 perturbed orbits, Materials Research Proceedings, Vol. 37, pp 621-624, 2023

DOI: https://doi.org/10.21741/9781644902813-135

The article was published as article 135 of the book Aeronautics and Astronautics

Content from this work may be used under the terms of the Creative Commons Attribution 3.0 license. Any further distribution of this work must maintain attribution to the author(s) and the title of the work, journal citation and DOI.

References
[1] R.F. Moulton. Introduction to Celestial Mechanics. McMillian, New York, 1914.
[2] S.A. Klioner. Lecture Notes on Basic Celestial Mechanics, Technische Universitaet Dresden, 2016. https://doi.org/10.48550/arXiv.1609.00915
[3] L. Broglio. Lezioni di Meccanica del Volo Spaziale (a cura di S. Sgubini), Scuola di Ingegneria Aerospaziale, Università di Roma “La Sapienza”, 1973.
[4] S. Sgubini, G.B. Palmerini. A fast approach for relative orbital determination in spacecraft formations, in “IEEE Aerospace Conference Proceedings”, Big Sky (MT, USA), 2012.
[5] S. Sgubini, G.B. Palmerini. Efficient Techniques for Relative Motion Analysis between Eccentric Orbits under J2 Effect, in “IEEE Aerospace Conference Proceedings”, Big Sky (MT, USA), 2013.
[6] S. Sgubini, G.B. Palmerini. Fast Analytical Evaluation of Near-Keplerian Orbit Evolution in Multiple Launch Release. Congresso Nazionale AIDAA, Roma, 2019.
[7] M. Sabatini, D. Izzo, G.B. Palmerini. Analysis and control of convenient orbital configuration for formation flying missions. Adv. Astronaut. Sci. 124, (2006) 313–330.
[8] S.R. Vadali, P. Sengupta, H. Yan, K.T. Alfriend. On the fundamental frequencies of relative motion and the control of satellite formations. Adv. Astronaut. Sci. 129 (2008) 2747–2766.
[9] M. Sabatini, D. Izzo, G.B. Palmerini. Minimum control for spacecraft formations in a J2 perturbed environment, Celest. Mech. Dyn. Astron. 105 (2009) 141-157. https://doi.org/10.1007/s10569-009-9214-5
[10] Symbolic Math Toolbox™ User’s Guide, The MathWorks Inc., 2023.