Abstract
In this paper, the Olbers method for the preliminary parabolic orbit determination (in the Lagrange–Subbotin modification) and the method based on systems of algebraic equations for two or three variables proposed by the author are compared. The maximum number of possible solutions is estimated. The problem of selection of the true solution from the set of solutions obtained both using additional equations and by the problem reduction to finding the objective function minimum is considered. The results of orbit determination of the comets 153P/Ikeya-Zhang and 2007 N3 Lulin are cited as examples.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Arnol’d, V.I., Gyuigens i Barrou, N’yuton i Guk (Huygens and Barrow, Newton and Hooke), Moscow: Nauka, 1989.
Bernshtein, D.N., Roots’ number in the equation set, Funkts. Analiz Ego Prilozh., 1975, vol. 9, no. 3, pp. 1–4.
Euler, L., Theoria motuum planetarum et cometarum etc., Berolini, 1744.
Gauss, K.F., Zur parabolischen Bewegung (Nachlass Briefenwechsel), Gottingen, 1906, vol. II, p. 2.
Kuznetsov, V.B., Determination of the parabolic orbit for a body moving in the plane of the ecliptic, by the Laplace method, Solar Syst. Res., 2012a, vol. 46, no. 2, pp. 1–8.
Kuznetsov, V.B., Geometric method for determination of parabolic orbits, Tr. Inst. Prikl. Astron. Russ. Akad. Nauk, 2012b, no. 26, pp. 28–33.
Lagrange, J.L., Sur le probleme de la determination des orbites des cometes, d’apres trois observations, Nouv. Mem. Acad. Roy. Sci. et Belles-Lettres, Berlin, 1778.
Newton, I., Philosophiae Naturalis Principia Mathematica, London, 1687.
Olbers, W., Abhandlung über die leichteste und buquemeste Methode, Weimar, 1797.
Orlov, A.Ya. and Orlov, B.A., Kurs teoreticheskoi astronomii (Course of Theoretical Astronomy), Moscow: Gos. Izd. Tekhniko-Tekhn. Lit., 1940.
Shefer, V.A., A new method of orbit determination from two position vectors based on solving Gauss’s equations, Solar Syst. Res., 2010, vol. 44, no. 2, p. 273.
Subbotin, M.F., Kurs nebesnoi mekhaniki (Course of Celestial Mechanics), Leningrad-Moscow: Gostekhizdat, 1933.
Subbotin, M.F., Vvedenie v teoreticheskuyu astronomiyu (Introduction to Theoretical Astronomy), Moscow: Nauka, 1968.
The International Astronomical Union. Minor Planet Center, 2015a. http://www.minorplanetcenter.net/db_search/show_object?utf8=%E2%9C%93&object_id=153P
The International Astronomical Union. Minor Planet Center, 2015b. http://www.minorplanetcenter.net/db_search/show_object?utf8=%E2%9C%93&object_id=C%2F2007+N3
Author information
Authors and Affiliations
Corresponding author
Additional information
Original Russian Text © V.B. Kuznetsov, 2016, published in Astronomicheskii Vestnik, 2016, Vol. 50, No. 3, pp. 224–232.
Rights and permissions
About this article
Cite this article
Kuznetsov, V.B. Parabolic orbit determination. Comparison of the Olbers method and algebraic equations. Sol Syst Res 50, 211–219 (2016). https://doi.org/10.1134/S0038094616030047
Received:
Published:
Issue Date:
DOI: https://doi.org/10.1134/S0038094616030047