Mirror Trajectories in Space Mission Analysis

Aerotecnica Missili & Spazio

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Title Mirror Trajectories in Space Mission Analysis
Creator Pontani, Mauro

Description The theorem of mirror trajectories was proven almost six decades ago by Miele, and states that for a given path inthe restricted problem of three bodies (with primaries in mutual circular orbits) there exists a mirror trajectory (intwo dimensions) and three mirror paths (in three dimensions). This theorem regards feasible trajectories and provedextremely useful for investigating the natural spacecraft dynamics in the circular restricted problem of three bodies.Several trajectories of crucial importance for mission analysis and design can be identied by using the theorem of mirrortrajectories, i.e. (a) free return paths, (b) periodic orbits, and (c) homoclinic connections. Free return paths have beendesigned and own in the Apollo missions, because they allow safe ballistic return toward the Earth in case of failure ofthe main propulsive system. These trajectories belong to the class of mirror paths with a single orthogonal crossing of theaxis that connects the Earth and the Moon in the synodic reference system. Instead, if two orthogonal crossings of thesame axis exist, then the resulting path is a periodic orbit. A variety of such orbits can be found, encircling either bothprimaries, a single celestial body, or a collinear libration point. In all cases, periodic orbits represent repeating trajectoriesthat can be traveled indenitely, (ideally) without any propellant expenditure. Homoclinic connections are special pathsthat belong to both the stable and the unstable manifold associated with a periodic orbit. These trajectories departasymptotically from a periodic orbit and can encircle both primaries (even with close approaches) before convergingasymptotically toward the initial periodic orbit. After almost six decades, the theorem of mirror trajectories, whichclaried the fundamental symmetry properties related to the motion of a third body (or, more concretely, a spacevehicle), still excerpts a considerable inuence in space mission analysis and design.
Publisher Associazione Italiana di Aeronautica e Astronautica (AIDAA)
Date 2018-02-11
Type info:eu-repo/semantics/article
Peer-reviewed Article

Format application/pdf
Source Aerotecnica Missili & Spazio; Vol 96, No 4 (2017); 195-203
Language eng
Rights Copyright (c) 2018 Aerotecnica Missili & Spazio

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