Exact solution to the relative orbital motion in eccentric orbits

• Published in: Solar system research Vol. 43; no. 1; pp. 41 - 52
• Main Authors: Condurache, D., Martinuşi, V.
• Format: Journal Article Web Resource
• Language: English
• Published: Dordrecht SP MAIK Nauka/Interperiodica 01.02.2009; Springer Nature B.V; Springer
• Subjects: Aerospace & aeronautics engineering; Approximation; Astronomy; Astrophysics; Astrophysics and Astroparticles; Astrophysics and Cosmology; Engineering, computing & technology; Exact solutions; Ingénierie aérospatiale; Ingénierie, informatique & technologie; Initial value problems; Mathematical analysis; Mathematical models; Observations and Techniques; Orbitals; Parametrization; Physics; Physics and Astronomy; Planetology; Solar system; Trajectories; 95.10.Eg; 91.10.Sp
• ISSN: 0038-0946; 1608-3423; 1608-3423
• DOI: 10.1134/S0038094609010043

This paper studies the relative orbital motion between arbitrary Keplerian trajectories. A closed-form vectorial solution to the nonlinear initial value problem that models this type of motion with respect to a noninertial reference frame is offered. Without imposing any particular conditions on the leader or the deputy satellites trajectories, exact expressions for the relative law of motion and relative velocity are obtained in a closed form. This solution allows the parameterization of the relative motion manifold and offers new methods to study its geometrical and topological properties. The result presented in this paper opens the way to obtain new classes of approximate solutions to the equations of relative motion with time, an eccentric or true anomaly as independent variables.