Study of orbital transfers with time constraint and fuel optimization

Abstract

Over the decades, with the advance in computational power and the development of new optimization techniques, a new opportunity arose for a reviewed approach and analysis of already existing solutions to orbital transfer problems. With that in mind, a study was proposed over Lambert’s problem of bi-impulsive orbital transfers with time constraint for the execution of minimum fuel maneuvers between coplanar and non coplanar elliptical orbits. In order to achieve this goal, a genetic search algorithm was developed to determine the minimum fuel trajectory with an iterative variation of two Keplerian elements of the final orbit, one of them being the mean anomaly and the other a choice between the eccentricity, the inclination or the argument of periapsis. A number of six simulations were performed under these conditions, using different values - on each simulation - for the Keplerian elements of the final orbits not being iteratively varied. Remarkable sections were noted regarding the behaviour of fuel consumption values of the minimum fuel trajectories. One of which was a noted relation between the lowest cost minimum fuel transfers and the ratio of the semi-major axis and eccentricity of these transfers’ initial and final orbits, considering both the orbits have the same value of argument of periapsis. Amongst all simulations, it was important to identify the choice between short or long way for the determination of the minimum fuel transfer, analysing the implications of that choice on the transfer time.