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Stringent Criteria for Stable and Unstable Planetary Orbits in Stellar Binary Systems

The existence of planets in stellar binary (and higher order) systems has now been confirmed by many observations. The stability of planetary orbits in these systems has been extensively studied, but no precise stability criteria have so far been introduced. Therefore, there is an urgent need for developing stringent mathematical criteria that allow us to precisely determine whether a planetary orbit in a binary system is stable or unstable. In this Letter, such criteria are defined using the concept of Jacobi's integral and Jacobi's constant. These criteria are used to contest previous results on planetary orbital stability in binary systems.