Analytic solution to the relative orbital motion around an oblate planet

Analytic solution; Closed-form expression; Initial conditions; Oblateness; Orbital element; Orbital motions; Reference frame; Relative positions; Relative velocity; Satellites formation; Navigation; Satellites

Abstract :

[en] The paper offers a vectorial approach to the J2-perturbed relative orbital motion. The model uses mean orbital elements in order to derive closed form expressions for the relative position and relative velocity with respect to the LVLH frame attached on a main satellite. The advantage of the present approach is that only the motion of one satellite must be known, together with the initial conditions with respect to LVLH of the other satellites. As in the previous works of the authors, a tensorial instrument is used in order to transfer the motion from inertial to non-inertial reference frames and back. In this way, a concise instrument for the study of the satellites formations under the influence of the oblateness factor J2 is offered. Copyright © 2009 by Daniel Condurache and Vladimir Martinusi.

Disciplines :

Aerospace & aeronautics engineering

Author, co-author :

Condurache, D.; Technical University Gheorghe Asachi, Department of Theoretical Mechanics, Iasi, Romania

Martinusi, Vladimir ; Université de Liège - ULiège > Département d'aérospatiale et mécanique > Laboratoire de structures et systèmes spatiaux

Title :

Analytic solution to the relative orbital motion around an oblate planet

Publication date :

2009

Event name :

AIAA Guidance, Navigation, and Control Conference and Exhibit

Event date :

10 August 2009 through 13 August 2009

Audience :

International

Journal title :

AIAA Guidance, Navigation, and Control Conference and Exhibit

Commentary :

81960 9781563479786

Available on ORBi :

since 12 February 2015

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Bibliography

Condurache, D., Martinusi, V., Kepler's Problem in Rotating Reference Frames. Part I: Prime Integrals. Vectorial Regularization, AIAA Journal of Guidance, Control, and Dynamics, Vol. 30, No.1, 2007, pp. 192-200.
Condurache, D., Martinusi, V., Kepler's Problem in Rotating Reference Frames. Part II: Relative Orbital Motion, AIAA Journal of Guidance, Control, and Dynamics, Vol. 30, No.1, 2007, pp.201-213.
Condurache, D., Martinusi, V., Relative Spacecraft Motion in a Central Force Field, AIAA Journal of Guidance, Control and Dynamics, Vol. 30, No.3, 2007, pp. 873-876.
Condurache, D., Martinusi, V., A Quaternionic Exact Solution to the Relative Orbital Motion, AIAA paper 2008-6764, Aug. 2008.
Gurfil, P., Analysis of J2 Perturbed Motion Using Mean Non-Osculating Orbital Elements, AIAA Paper 2004-4853, Aug. 2004.
P. Sengupta, Dynamics and Control of Satellite Relative Motion in a Central Gravitational Field, Ph.D. Thesis, Texas A&M University, 2006.
M. Efroimsky, Long-Term Evolution of Orbits About A Precessing Oblate Planet: 1. The Case of Uniform Precession, Celestial Mechanics and Dynamical Astronomy, Vol. 91, No. 1-2, 2005, pp. 75-108.
Gurfil, P., Analysis of J2-Perturbed Motion using Mean Non-Osculating Orbital Elements, AIAA/AAS Astrodynamics Specialist Conference and Exhibit 16 - 19 August 2004, Providence, Rhode Island, AIAA paper 2004-4853.
Battin, R.H., An Introduction to the Mathematics and Methods of Astrodynamics, AIAA Education Series, 1999.
Gurfil, P., Optimal Fuel-Balanced Impulsive Formationkeeping for Perturbed Spacecraft Orbits, AIAA Journal of Guidance, Control and Dynamics, Vol. 31, No.5, 2007, pp. 1266-1283.
Angeles, J., Fundamentals of Robotic Mechanical Systems: Theory, Methods, and Algorithms, Springer (2006).
Fasano, A. and Marmi, S., Analytical Mechanics, Oxford University Press, 2006.
Condurache, D., New Symbolic Methods in the Study of Dynamic Systems (in Romanian), Ph.D. thesis, Technical University "Gheorghe Asachi" Iasi, 1995.
Condurache, D. and Martinusi, V., Foucault Pendulum-Like Problems: A Tensorial Approach, International Journal of Nonlinear Mechanics, Vol. 43, No. 8, 2008, pp. 743-760.
Condurache, D., Martinusi, V., A complete closed form vectorial solution to the Kepler problem, Meccanica, Vol. 42, No 5, 2007, pp.465-476.