Displaced non-Keplerian orbits using impulsive thrust

Abstract

This paper investigates new families of displaced, highly non-Keplerian orbits in the two-body problem and artificial equilibria in the circular restricted three-body problem. The families of orbits presented extend prior work by using periodic impulses to generate displaced orbits rather than continuous thrust. The new displaced orbits comprise a sequence of individual Keplerian arcs whose intersection is continuous in position, with discontinuities in velocity removed using impulses. For frequent impulses the new families of orbits approximate continuous thrust non-Keplerian orbits found in previous studies. To generate approximations to artificial equilibria in the circular restricted three-body problem, periodic impulses are used to generate a sequence of connected three-body arcs which begin and terminate at a fixed position in the rotating frame of reference. Again, these families of orbits reduce to the families of artificial equilibria found using continuous thrust.

Elliptic Displaced Orbit Approximation with Equally Spaced Impulses

“…The aim of this Note is to extend the results of Ref. [13] to the case of two-body elliptic DNKOs, by obtaining a general method to calculate the propulsive performance of a spacecraft that covers the corresponding CPOs. In particular, the proposed approach gives the analytical expression of the total velocity variation per revolution around the primary body, required to approximate an assigned DNKO with a sequence of (azimuthally) equally spaced impulsive maneuvers.…”

“…In principle, a DNKO can be approximated with a sequence of Keplerian arcs patched by impulsive maneuvers, so that the points where the impulses are applied coincide with points belonging to the original DNKO [11,12]. Such a trajectory type, which will be referred to as closed patched orbit (CPO), has been thoroughly investigated by McInnes [13], who proposed an elegant mathematical model useful for approximating DNKOs of circular shape.…”

Distributed situational observer in a displaced orbit: relative dynamics and control

“…Large families of displaced orbits have been identified by solar sail or electric propulsion thrusters in the context of the non-Keplerian two-body problem including three types of circular orbits by propulsive acceleration, [1][2][3] quasiperiodic displaced trajectories by a fixed thrust along the rotation axis of a planet, 4 body-fixed hovering orbits by open-loop control, 5 elliptic displaced orbits with an advanced thrust model, 6 a sequence of individual Keplerian arcs connected by slight impulse propulsion, 7 and a displaced geostationary orbit (GEO) using hybrid sail propulsion. 8 A large catalog of these orbits was provided by McKay et al 9 for motions around planetary bodies.…”

“…14 gave a linear analytical solution and dealt with the practical applications of solar-sail formations. McInnes 7 linearized the relative motion in a rotating frame of reference and obtained analytical solutions, but no propulsive acceleration was included. Wang et al 15 worked on the relative motions between the two heliocentric circular displaced orbits by defining a set of displaced orbital elements and obtained a semianalytical approximation of bounds of relative distance.…”

New families of Sun-centered non-Keplerian orbits over cylinders and spheres

“…A particular subset of non-Keplerian orbits in the two-body problem are the so-called displaced NKOs where the continuous acceleration is applied perpendicular to the orbit plane to displace the orbit away from the natural Keplerian orbit (McInnes, 1998(McInnes, , 2011Mengali and Quarta, 2009). The dynamics of such two-body displaced NKOs have been investigated before by considering the spacecraft's equations of motion in a rotating frame of reference to make the problem autonomous (McInnes, 1997).…”