Resumo

SHARAF, M. A.  e  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 21-Out-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.

Palavras-chave : celestial mechanics; comets; general; methods; analytical.

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