A comprehensive approach is provided for the study of both S-type and P-type habitability in stellar binary systems, which in principle can also be expanded to systems of higher order. P-type orbits occur when the planet orbits both binary components, whereas in the case of S-type orbits, the planet orbits only one of the binary components with the second component considered a perturbator. The selected approach encapsulates a variety of different aspects, which include: (1) the consideration of a joint constraint, including orbital stability and a habitable region for a putative system planet through the stellar radiative energy fluxes ("radiative habitable zone"; RHZ), needs to be met; (2) the treatment of conservative, general, and extended zones of habitability for the various systems as defined for the solar system and beyond; (3) the provision of a combined formalism for the assessment of both S-type and P-type habitability; in particular, mathematical criteria are presented for the kind of system in which S-type and P-type habitability is realized; (4) applications of the attained theoretical approach to standard (theoretical) main-sequence stars. In principle, five different cases of habitability are identified, which are S-type and P-type habitability provided by the full extent of the RHZs; habitability, where the RHZs are truncated by the additional constraint of planetary orbital stability (referred to as ST- and PT-type, respectively); and cases of no habitability at all. Regarding the treatment of planetary orbital stability, we utilize the formulae of Holman & Wiegert as also used in previous studies. In this work, we focus on binary systems in circular orbits. Future applications will also consider binary systems in elliptical orbits and provide thorough comparisons to other methods and results given in the literature.
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