The aim of this study is to explore an enigmatic finding about the ν Octantis binary system that indicates the possible existence of a Jupiter-type planet even though the planet seems to be located outside the zone of orbital stability. We perform a detailed analysis of orbital stability based on previous studies that carefully considers the ν Octantis system parameters including their observationally deduced uncertainties. In our analysis, we confront the probability distribution of the parameter space of the system with the requirements of planetary orbital stability. Our results indicate that the suggested planet, if in a prograde orbit with respect to the motion of the binary components, is virtually impossible. However, the estimated probability of existence for a planet in a retrograde orbit is nearly 60%, an estimate that encapsulates the probability distribution of the mass ratio of the stellar components. This estimate increases if a relatively low stellar mass ratio (within the error bars) is assumed. The principal possibility of a planet in a retrograde orbit is also consistent with long-term orbital stability simulations pursued as part of our study. Thus, the existence of the suggested planet in the ν Octantis system constitutes a realistic possibility.

Aims. We study the onset of orbital instability for a small object, identified as a planet, that is part of a stellar binary system with properties equivalent to the restricted three body problem. Methods. Our study is based on both analytical and numerical means and makes use of a rotating (synodic) coordinate system keeping both binary stars at rest. This allows us to define a constant of motion (Jacobi's constant), which is used to describe the permissible region of motion for the planet. We illustrate the transition to instability by depicting sets of time-dependent simulations with starplanet systems of different mass and distance ratios. Results. Our method utilizes the existence of an absolute stability limit. As the system parameters are varied, the permissible region of motion passes through the three collinear equilibrium points, which significantly changes the type of planetary orbit. Our simulations feature various illustrative examples of instability transitions. Conclusions. Our study allows us to identify systems of absolute stability, where the stability limit does not depend on the specifics or duration of time-dependent simulations. We also find evidence of a quasi-stability region, superimposed on the region of instability, where the planetary orbits show quasi-periodic behavior. The analytically deduced onset of instability is found to be consistent with the behavior of the depicted time-dependent models, although the manifestation of long-term orbital stability will require more detailed studies.

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.

Aims. We establish a criterion for the stability of planetary orbits in stellar binary systems by using Lyapunov exponents and power spectra for the special case of the circular restricted 3-body problem (CR3BP). The criterion augments our earlier results given in the two previous papers of this series where stability criteria have been developed based on the Jacobi constant and the hodograph method.Methods. The centerpiece of our method is the concept of Lyapunov exponents, which are incorporated into the analysis of orbital stability by integrating the Jacobian of the CR3BP and orthogonalizing the tangent vectors via a well-established algorithm originally developed by Wolf et al. The criterion for orbital stability based on the Lyapunov exponents is independently verified by using power spectra. The obtained results are compared to results presented in the two previous papers of this series. Results. It is shown that the maximum Lyapunov exponent can be used as an indicator for chaotic behaviour of planetary orbits, which is consistent with previous applications of this method, particularly studies for the Solar System. The chaotic behaviour corresponds to either orbital stability or instability, and it depends solely on the mass ratio μ of the binary components and the initial distance ratio ρ 0 of the planet relative to the stellar separation distance. Detailed case studies are presented for μ = 0.3 and 0.5. The stability limits are characterized based on the value of the maximum Lyapunov exponent. However, chaos theory as well as the concept of Lyapunov time prevents us from predicting exactly when the planet is ejected. Our method is also able to indicate evidence of quasi-periodicity. Conclusions. For different mass ratios of the stellar components, we are able to characterize stability limits for the CR3BP based on the value of the maximum Lyapunov exponent. This theoretical result allows us to link the study of planetary orbital stability to chaos theory noting that there is a large array of literature on the properties and significance of Lyapunov exponents. Although our results are given for the special case of the CR3BP, we expect that it may be possible to augment the proposed Lyapunov exponent criterion to studies of planets in generalized stellar binary systems, which is strongly motivated by existing observational results as well as results expected from ongoing and future planet search missions.

The aim of our study is to investigate the possibility of habitable moons orbiting the giant planet HD 23079b, a Jupitermass planet, which follows a low-eccentricity orbit in the outer region of HD 23079's habitable zone. We show that HD 23079b is able to host habitable moons in prograde and retrograde orbits, as expected, noting that the outer stability limit for retrograde orbits is increased by nearly 90% compared with that of prograde orbits, a result consistent with previous generalised studies. For the targeted parameter space, it was found that the outer stability limit for habitable moons varies between 0.05236 and 0.06955 AU (prograde orbits) and between 0.1023 and 0.1190 AU (retrograde orbits), depending on the orbital parameters of the Jupiter-type planet if a minimum mass is assumed. These intervals correspond to 0.306 and 0.345 (prograde orbits) and 0.583 and 0.611 (retrograde orbits) of the planet's Hill radius. Larger stability limits are obtained if an increased value for the planetary mass m p is considered; they are consistent with the theoretically deduced relationship of m 1/3 p . Finally, we compare our results with the statistical formulae of Domingos, Winter, & Yokoyama, indicating both concurrence and limitations.