Simplified existence and uniqueness conditions for the zeros and the concavity of the F and G functions of improved Gauss orbit determination from two position vectors

Roy Danchick

Applied Mathematics and Computation, 2015, vol. 269, issue C, 279-287

Abstract: In our first paper we showed how Gauss's method for determining the initial position and velocity vectors from two inertial position vectors at two times in an idealized Keplerian two-body elliptical orbit can be made more robust and efficient by replacing functional iteration with Newton–Raphson iteration. To do this we split the orbit determination algorithm into two sub-algorithms, the x-iteration to find the zero of the fixed-point function F(x) when the true anomaly angular difference between the two vectors is large and the y-iteration to find the zero of the fixed-point function G(y) when the angular difference is small.

Keywords: Classical two-body problem; Gauss orbit determination; Newton–Raphson iteration; Functions of a real variable; Polynomials; Roots of polynomials (search for similar items in EconPapers)
Date: 2015
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Persistent link: https://EconPapers.repec.org/RePEc:eee:apmaco:v:269:y:2015:i:c:p:279-287

DOI: 10.1016/j.amc.2015.07.008

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