Abstract
We propose two algorithms to provide a full preliminary orbit of an Earth-orbiting object with a number of observations lower than the classical methods, such as those by Laplace and Gauss. The first one is the Virtual debris algorithm, based upon the admissible region, that is the set of the unknown quantities corresponding to possible orbits for a given observation for objects in Earth orbit (as opposed to both interplanetary orbits and ballistic ones). A similar method has already been successfully used in recent years for the asteroidal case. The second algorithm uses the integrals of the geocentric 2-body motion, which must have the same values at the times of the different observations for a common orbit to exist. We also discuss how to account for the perturbations of the 2-body motion, e.g., the J 2 effect.
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Bini D.A.: Numerical computation of polynomial zeros by means of Aberth’s method. Numer. Algorithms 13, 179–200 (1996)
Cox D.A., Little J.B., O’Shea D.: Ideals, varieties and algorithms. Springer, London (1996)
Fujimoto K., Maruskin J.D., Scheeres D.J.: Circular and zero-inclination solutions for optical observations of Earth-orbiting objects. Celest. Mech. Dyn. Astron. 106, 157–182 (2010)
Gronchi, G.F., Dimare, L., Milani, A.: Orbit determination with the two-body integrals. Celest. Mech. Dyn. Astron. (2010). doi:10.1007/s10569-010-9271-9
Maruskin, J.M., Scheeres, D.J.: Metrics on the space of bounded Keplerian orbits and space situational awareness. In: Proceedings of the 48th IEEE Conference and Decision Control, pp. 5912–5917 (2009)
Maruskin J.M., Scheeres D.J., Alfriend K.T.: Correlation of optical observations of objects in earth orbit. J. Guid. Control Dyn. 32, 194–209 (2009)
Milani A.: The asteroid identification problem I: recovery of lost asteroids. Icarus 137, 269–292 (1999)
Milani A., Sansaturio M.E., Chesley S.R.: The asteroid identification problem IV: Attributions. Icarus 151, 150–159 (2001)
Milani A., Gronchi G.F., de’Michieli Vitturi M., Knežević Z.: Orbit determination with very short arcs. I admissible regions. Celest. Mech. Dyn. Astron. 90, 59–87 (2004)
Milani A., Gronchi G.F., Knežević Z., Sansaturio M.E., Arratia O.: Orbit determination with very short arcs. II identifications. Icarus 79, 350–374 (2005)
Milani A., Knežević Z.: From Astrometry to Celestial Mechanics: Orbit determination with bery short arcs. Celest. Mech. Dyn. Astron. 92, 1–18 (2005)
Milani A., Gronchi G.F.: Theory of orbit determination. Cambridge University Press, Cambridge (2010)
Milani, A., Gronchi, G.F., Farnocchia, D., Tommei, G., Dimare, L.: Optimization of space surveillance resources by innovative preliminary orbit methods. In: Proceedings of the Fifth European Conference on Space Debris. 30 March–2 April 2009, Darmstadt, Germany, SP-672 on CD-Rom
Roy A.E.: Orbital motion. Institute of Physics Publishing, London (2005)
Taff L.G., Hall D.L.: The use of angles and angular rates. I - Initial orbit determination. Celest. Mech. 16, 481–488 (1977)
Tommei G., Milani A., Rossi A.: Orbit determination of space debris: Admissibl regions. Celest. Mech. Dyn. Astron. 97, 289–304 (2007)
Tommei, G., Milani, A., Farnocchia, D., Rossi, A.: Correlation of space debris observations by the virtual debris algorithm. In: Proceedings of the Fifth European Conference on Space Debris. 30 March–2 April 2009, Darmstadt, Germany, SP-672 on CD-Rom
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Farnocchia, D., Tommei, G., Milani, A. et al. Innovative methods of correlation and orbit determination for space debris. Celest Mech Dyn Astr 107, 169–185 (2010). https://doi.org/10.1007/s10569-010-9274-6
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DOI: https://doi.org/10.1007/s10569-010-9274-6