Abstract
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 (Formula presented.) zonal harmonic is included in the analytical formulae. It will be shown that the proposed analytical theory allows for the fast computation of long, multirevolution 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 lowthrust spiral to transfer a spacecraft from an elliptical to a circular orbit around the Earth.
Original language  English 

Pages (fromto)  275300 
Number of pages  26 
Journal  Celestial Mechanics and Dynamical Astronomy 
Volume  121 
Issue number  3 
Early online date  27 Dec 2014 
DOIs  
Publication status  Published  31 Mar 2015 
Keywords
 analytical solutions
 first order expansions
 lowthrust trajectories
 orbit averaging
 orbit circularisation
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Massimiliano Vasile
Person: Academic