Optimal solar sail transfers to circular Earth-synchronous displaced orbits

The aim of this paper is to evaluate the minimum flight time of a solar sail-based spacecraft towards Earth-synchronous(heliocentric)circular displaced orbits.These are special displaced non-Keplerian orbits characterized by a period of one year,which makes them suitable for the observation of Earth’s polar regions.The solar sail is modeled as a flat and purely reflective film with medium-low performance,that is,with a characteristic acceleration less than one millimeter per second squared.Starting from a circular parking orbit of radius equal to one astronomical unit,the optimal steering law is sought by considering the characteristic acceleration that is required for the maintenance of the target Earth-synchronous displaced orbit.The indirect approach used for the calculation of the optimal transfer trajectory allows the minimum flight time to be correlated with several Earth-synchronous displaced orbits,each one being characterized by given values of Earth-spacecraft distance and displacement over the ecliptic.The proposed mathematical model is validated by comparison with results available in the literature,in which a piecewise-constant steering law is used to find the optimal flight time for a transfer towards a one-year Type I non-Keplerian orbit.