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Revista mexicana de astronomía y astrofísica
Print version ISSN 0185-1101
Abstract
SHARAF, M. A. and SAAD, A. S.. Analysis of Hansen’s Inferior and Superior Partial Anomalies and the Division of the Elliptic Orbit Into Two Segments. Rev. mex. astron. astrofis [online]. 2017, vol.53, n.2, 00004. Epub Oct 21, 2019. ISSN 0185-1101.
In this paper, a novel analysis was established to prove how Hansen’s inferior and superior partial anomalies k and k 1 can divide the elliptic orbit into two segments. The analysis depends on the departures of r (for k) and 1/r (for k 1) from their minima. By these departures, we can find: (i) Transformations relating the eccentric anomaly to k and the true anomaly to k 1. (ii) Expressions for k and k 1 in terms of the orbital elements. (iii) The interpretation and the intervals of definition of two moduli (X, S) related to k and k 1. (iv) The extreme values of r and the elliptic equations in terms of k and k 1. (v) For r ' and r '', the modulus X as a measure of the asymmetry of r ' (or r '') from r '' (or r '), and the modulus S 12 as a measure of the asymmetry of r ' and r '' from the minimum value of r. (vi) A description of the segments represented by k and k 1. (vii) The relative position of the radius vector at k = 0o and k 1 = 180o.
Keywords : celestial mechanics; comets; general; methods; analytical.