Abstract Analysis and design of low-energy transfers to the Moon has been a subject of great interest for decades. Exterior and interior transfers, based on the transit through the regions where the collinear libration points are located, have been studied for a long time and some space missions have already taken advantage of the results of these studies. This paper is concerned with a geometrical approach for low-energy Earth-to-Moon mission analysis, based on isomorphic mapping. The isomorphic mapping of trajectories allows a visual, intuitive representation of periodic orbits and of the related invariant manifolds, which correspond to tubes that emanate from the curve associated with the periodic orbit. Two types of Earth-to-Moon missions are considered. The first mission is composed of the following arcs: (i) transfer trajectory from a circular low Earth orbit to the stable invariant manifold associated with the Lyapunov orbit at L 1 (corresponding to a specified energy level) and (ii) transfer trajectory along the unstable manifold associated with the Lyapunov orbit at L 1, with final injection in a periodic orbit around the Moon. The second mission is composed of the following arcs: (i) transfer trajectory from a circular low Earth orbit to the stable invariant manifold associated with the Lyapunov orbit at L 1 (corresponding to a specified energy level) and (ii) transfer trajectory along the unstable manifold associated with the Lyapunov orbit at L 1, with final injection in a capture (non-periodic) orbit around the Moon. In both cases three velocity impulses are needed to perform the transfer: the first at an unknown initial point along the low Earth orbit, the second at injection on the stable manifold, the third at injection in the final (periodic or capture) orbit. The final goal is in finding the optimization parameters, which are represented by the locations, directions, and magnitudes of the velocity impulses such that the overall delta-v of the transfer is minimized. This work proves how isomorphic mapping (in two distinct forms) can be profitably employed to optimize such transfers, by determining in a geometrical fashion the desired optimization parameters that minimize the delta-v budget required to perform the transfer.

    Highlights Two different missions from low Earth orbit to lunar orbit are described. Manifold dynamics associated with the Lyapunov orbit at L1 is investigated. Two distinct isomorphic mappings are introduced for mission analysis. Two near optimal three-impulse missions are determined through isomorphic mapping. The theorem of image trajectories is employed to find the returning path for Mission 1.


    Zugriff

    Zugriff prüfen

    Verfügbarkeit in meiner Bibliothek prüfen

    Bestellung bei Subito €


    Exportieren, teilen und zitieren



    Titel :

    Low-energy Earth–Moon transfers involving manifolds through isomorphic mapping


    Beteiligte:

    Erschienen in:

    Acta Astronautica ; 91 ; 96-106


    Erscheinungsdatum :

    2013-05-14


    Format / Umfang :

    11 pages




    Medientyp :

    Aufsatz (Zeitschrift)


    Format :

    Elektronische Ressource


    Sprache :

    Englisch





    Earth-Moon Transfers Involving Periodic Orbits and Invariant Manifolds through Isomorphic Mapping (AAS 12-542)

    Giancotti, M. / Pontani, M. / Teofilatto, P. | British Library Conference Proceedings | 2013



    Transfers from Earth to Earth–Moon L3 halo orbits using accelerated manifolds

    Davis, Kathryn / Parker, Jeffrey / Butcher, Eric | Elsevier | 2015