A universal, singularity-free determination of an orbit for two positions and time interval
- Paper ID
IAF-69-31
- author
- company
University of California
- country
U.S.A.
- year
1969
- abstract
Given the problem of finding an orbit satisfying two position-vectors ri and r3, and the time interval t3 — t1} the Gaussian ratio-of-sector-to- triangle solution, the Lambert-Euler solution, and my proposed Universal solution all start with the calculation of quantities selected from the following: x = 2}/ r1r3cos f 2/= w3-®i T = }//! (t3 — ti) a = 2]/rlr3 sin/ G+G G—G «=Ig-gI (1) where v3 and v, are true anomalies and 5 is the chord, related to x and a by s2 = (rs+rrf-x2 = (>3-ri)2+cr2. (2) Formulae for x and a may be found in many texts; I give new singularity- free formulae for them, develop formulae stated below, and discuss calculation-examples in Vol. 1, Chap. 8 of my “Astrodynamics” (N.Y., Van Nostrand Reinhold, 1971).