In this study, new analytical solutions to the equations of motion of a propelled spacecraft are investigated using a shape-based approach. There is an assumption that the spacecraft travels a two-dimensional spiral trajectory in which the orbital radius is proportional to an assigned power of the spacecraft angular coordinate. The exact solution to the equations of motion is obtained as a function of time in the case of a purely radial thrust, and the propulsive acceleration magnitude necessary for the spacecraft to track the prescribed spiral trajectory is found in a closed form. The analytical results are then specialized to the case of a generalized sail, that is, a propulsion system capable of providing an outward radial propulsive acceleration, the magnitude of which depends on a given power of the Sun-spacecraft distance. In particular, the conditions for an outward radial thrust and the required sail performance are quantified and thoroughly discussed. It is worth noting that these propulsion systems provide a purely radial thrust when their orientation is Sun-facing. This is an important advantage from an engineering point of view because, depending on the particular propulsion system, a Sun-facing attitude can be stable or obtainable in a passive way. A case study is finally presented, where the generalized sail is assumed to start the spiral trajectory from the Earth’s heliocentric orbit. The main outcome is that the required sail performance is in principle achievable on the basis of many results available in the literature.


    Access

    Download


    Export, share and cite



    Title :

    Spiral trajectories induced by radial thrust with applications to generalized sails



    Publication date :

    2021-01-01



    Type of media :

    Article (Journal)


    Type of material :

    Electronic Resource


    Language :

    English



    Classification :

    DDC:    621



    Logarithmic spiral trajectories generated by Solar sails

    Bassetto M / Niccolai L / Quarta A et al. | BASE | 2018

    Free access


    Optimization of Low-Thrust Spiral Trajectories by Collocation

    Falck, Robert / Dankanich, John | AIAA | 2012


    Near Minimum-Time Trajectories for Solar Sails

    Michiel Otten / Colin R. McInnes | AIAA | 2001


    Interplanetary trajectories under low thrust radial acceleration

    Copeland, J. | Engineering Index Backfile | 1959