2017MNRAS.468.2672V

Although conjunctions and oppositions frequently occur in planetary systems, eclipse-related phenomena are usually described from an Earth-centric perspective. Space missions to different parts of the Solar system, as well as the mounting number of known exo-planets in habitable zones and the possibility of sending featherweight robot spacecraft to them, prompt broader considerations. Here, we derive the geometry of eclipses, transits and occultations from a primarily exo-Earth viewpoint, and apply the formulation to the Solar system and three types of three-body extrasolar planetary systems: with one star and two planets (Case I), with two stars and one planet (Case II) and with one planet, one star and one moon (Case III). We derive the general conditions for total, partial and annular eclipses to occur at exo-syzygy, and implement them in each case in concert with stability criteria. We then apply the formalism to the TRAPPIST-1, Kepler-444 and Kepler-77 systems - the first of which contains multiple potentially habitable planets - and provide reference tables of both Solar system and TRAPPIST-1 syzygy properties. We conclude by detailing a basic algebraic algorithm that can be used to quickly characterize eclipse properties in any three-body system.