Abstract
The mathematical model used in orbit determination problems must be as close to the actual dynamics as possible. On the contrary, accuracy constraints can be notably relaxed for orbit prediction purposes. For the latter, it is important to determine which is the simplified dynamical model that, while retaining the bulk of the dynamics, allow for faster predictions. Methods for doing that are commonly heuristic. We focus on perturbed Keplerian motion and explore how to ascertain the correct truncation of the dynamical model required in orbit prediction problems by investigating relevant particular solutions of the orbital motion: the so-called frozen orbits.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Notes
- 1.
I do not discuss the case of other frozen orbits that may exist with gā āĀ±āĻ/2.
References
Vallado, D.A.: An analysis of state vector propagation using differing flight dynamics programs (AAS 05ā199). In: Vallado, D.A., Gabor, M.J., Desai, P.N. (eds.) Spaceflight Mechanics 2005. Advances in the Astronautical Sciences, vol. 120, pp. 1563ā1592. American Astronautical Society, Univelt, Inc., Escondido, CA (2006)
Rosborough, G.W., Ocampo, C.: Influence of higher degree zonals on the frozen orbit geometry. In: Kaufman, B., Alfriend, K.T., Roehrich, R.L., Dasenbrock, R.R. (eds.) Astrodynamics 1991. Advances in the Astronautical Sciences, vol. 76, pp. 1291ā1304. American Astronautical Society, Univelt, Inc., Escondido, CA (1992)
Cook, G.E.: Perturbations of near-circular orbits by the Earthās gravitational potential. Planet. Space Sci. 14, 433ā444 (1966)
Kaula, W.M.: Theory of Satellite Geodesy. Applications of Satellites to Geodesy. Blaisdell, Waltham, MA (1966)
Lara, M., de Saedeleer, B., Ferrer, S.: Preliminary design of low lunar orbits. In: Proceedings of the 21st International Symposium on Space Flight Dynamics, Toulouse, pp. 1ā15. ISSFD (2009)
Lara, M.: Fast computation of inclined, frozen, low lunar orbits in a high degree Selenopotential (AAS 10ā220). In: Spaceflight Mechanics 2010. Advances in the Astronautical Sciences, vol. 156, pp. 1769ā1781. American Astronautical Society, Univelt, Inc., Escondido, CA (2010)
Lara, M., Ferrer, S., Saedeleer, B.D.: Lunar analytical theory for polar orbits in a 50-degree zonal model plus third-body effect. J. Astronaut. Sci. 57(3), 561ā577 (2009)
Lara, M.: A Mathematicaāø-based approach to the frozen orbits problem about arbitrary bodies. The case of a Lunar orbiter. In: Astrodynamics Beyond Borders, Proceedings of the 4th International Conference on Astrodynamics Tools and Techniques (ICATT), WPP-308, pp. 1ā8. ESA Publication, Madrid (2010)
Lara, M.: Design of long-lifetime lunar orbits: a hybrid approach. Acta Astronaut. 69(3ā4), 186ā199 (2011)
Coffey, S.L., Deprit, A., Miller, B.R.: The critical inclination in artificial satellite theory. Celest. Mech. 39(4), 365ā406 (1986)
Coffey, S.L., Deprit, A., Deprit, E.: Frozen orbits for satellites close to an earth-like planet. Celest. Mech. Dyn. Astron. 59(1), 37ā72 (1994)
Exertier, A.: Orbitographie des satellites artificiels sur de grandes periodes de temps. Possibilites dāapplications. Ph.D. Thesis. Observatoire de Paris, Paris (1988)
Lara, M., San-Juan, J.F., LĆ³pez-Ochoa, L.M.: Proper averaging via parallax elimination (AAS 13ā722). In: Astrodynamics 2013. Advances in the Astronautical Sciences, vol. 150, pp. 315ā331. American Astronautical Society, Univelt, Inc., Escondido, CA (2014)
Lidov, M.L.: The evolution of orbits of artificial satellites of planets under the action of gravitational perturbations of external bodies. Planet. Space Sci. 9, 719ā759 (1962)
Kozai, Y.: Secular perturbations of asteroids with high inclination and eccentricity. Astron. J. 67, 591ā598 (1962)
Acknowledgements
The author acknowledges partial support by the Spanish State Research Agency and the European Regional Development Fund under Projects ESP2013-41634-P, ESP2014-57071-R and ESP2016-76585-R (AEI/ERDF, EU). Discussions with Hodei Urrutxua, University of Southampton, are acknowledged.
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
Ā© 2018 Springer International Publishing AG
About this paper
Cite this paper
Lara, M. (2018). Exploring Sensitivity of Orbital Dynamics with Respect to Model Truncation: The Frozen Orbits Approach. In: Vasile, M., Minisci, E., Summerer, L., McGinty, P. (eds) Stardust Final Conference. Astrophysics and Space Science Proceedings, vol 52. Springer, Cham. https://doi.org/10.1007/978-3-319-69956-1_4
Download citation
DOI: https://doi.org/10.1007/978-3-319-69956-1_4
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-319-69955-4
Online ISBN: 978-3-319-69956-1
eBook Packages: Physics and AstronomyPhysics and Astronomy (R0)