Abstract
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 = 0 degrees and k(1) = 180 degrees.