Extended analytical formulas for the perturbed Keplerian motion under a constant control acceleration

This paper presents a set of analytical formulae for the perturbed Keplerian motion of a spacecraft under the effect of a constant control acceleration. The proposed set of formulae can treat control accelerations that are fixed in either a rotating or inertial reference frame. Moreover, the contrib...

Full description

Saved in:
Bibliographic Details
Published in:Celestial mechanics and dynamical astronomy 2015-03, Vol.121 (3), p.275-300
Main Authors: Zuiani, Federico, Vasile, Massimiliano
Format: Article
Language:English
Subjects:
Acceleration
Accuracy
Aerospace Technology and Astronautics
Astrophysics and Astroparticles
Circular orbits
Classical Mechanics
Constants
Dynamical Systems and Ergodic Theory
Geophysics/Geodesy
Inertial
Mathematical analysis
Numerical analysis
Orbits
Original Article
Physics
Physics and Astronomy
Solar eclipses
Spacecraft
Spirals
Citations: Items that this one cites
Items that cite this one
Online Access:Get full text
Tags: Add Tag
No Tags, Be the first to tag this record!
Description
Summary:This paper presents a set of analytical formulae for the perturbed Keplerian motion of a spacecraft under the effect of a constant control acceleration. The proposed set of formulae can treat control accelerations that are fixed in either a rotating or inertial reference frame. Moreover, the contribution of the J 2 zonal harmonic is included in the analytical formulae. It will be shown that the proposed analytical theory allows for the fast computation of long, multi-revolution spirals while maintaining good accuracy. The combined effect of different perturbations and of the shadow regions due to solar eclipse is also included. Furthermore, a simplified control parameterisation is introduced to optimise thrusting patterns with two thrust arcs and two cost arcs per revolution. This simple parameterisation is shown to ensure enough flexibility to describe complex low thrust spirals. The accuracy and speed of the proposed analytical formulae are compared against a full numerical integration with different integration schemes. An averaging technique is then proposed as an application of the analytical formulae. Finally, the paper presents an example of design of an optimal low-thrust spiral to transfer a spacecraft from an elliptical to a circular orbit around the Earth.
ISSN:0923-2958
1572-9478
DOI:10.1007/s10569-014-9600-5