We review the orbital stability of the planar circular restricted three-body problem, in the case of massless particles initially located between both massive bodies. We present new estimates of the resonance overlap criterion and the Hill stability limit, and compare their predictions with detailed dynamical maps constructed with N-body simulations. We show that the boundary between (Hill) stable and unstable orbits is not smooth but characterized by a rich structure generated by the superposition of different mean-motion resonances which does not allow for a simple global expression for stability.We propose that, for a given perturbing mass m 1 and initial eccentricity e, there are actually two critical values of the semimajor axis. All values a < a Hill are Hill-stable, while all values a > a unstable are unstable in the Hill sense. The first limit is given by the Hill-stability criterion and is a function of the eccentricity. The second limit is virtually insensitive to the initial eccentricity, and closely resembles a new resonance overlap condition (for circular orbits) developed in terms of the intersection between first and second-order mean-motion resonances.

Context. The secular dynamics of small planetesimals in tight binary systems play a fundamental role in establishing the possibility of accretional collisions in such extreme cases. The most important secular parameters are the forced eccentricity and secular frequency, which depend on the initial conditions of the particles, as well as on the mass and orbital parameters of the secondary star. Aims. We construct a second-order theory (with respect to the masses) for the planar secular motion of small planetasimals and deduce new expressions for the forced eccentricity and secular frequency. We also reanalyze the radial velocity data available for γ-Cephei and present a series of orbital solutions leading to residuals compatible with the best fits. Finally, we discuss how different orbital configurations for γ-Cephei may affect the dynamics of small bodies in circumstellar motion. Methods. The secular theory is constructed using a Lie series perturbation scheme restricted to second order in the small parameter. The orbital fits were analyzed with a minimization code that employs a genetic algorithm for a preliminary solution plus a simulated annealing for the fine tuning. Results. For γ-Cephei, we find that the classical first-order expressions for the secular frequency and forced eccentricity lead to large inaccuracies ∼50% for semimajor axes larger than one tenth the orbital separation between the stellar components. Low eccentricities and/or masses reduce the importance of the second-order terms. The dynamics of small planetesimals only show a weak dependence with the orbital fits of the stellar components, and the same result is found including the effects of a nonlinear gas drag. Thus, the possibility of planetary formation in this binary system largely appears insensitive to the orbital fits adopted for the stellar components, and any future alterations in the system parameters (due to new observations) should not change this picture. Finally, we show that planetesimals migrating because of gas drag may be trapped in mean-motion resonances with the binary, even though the migration is divergent.

We analyse the dynamics of individual kilometre‐size planetesimals in circumstellar orbits of a tight binary system. We include both the gravitational perturbations of the secondary star and a non‐linear gas drag stemming from an eccentric gas disc with a finite precession rate. We consider several precession rates and eccentricities for the gas, and compare the results with a static disc in circular orbit. The disc precession introduces three main differences with respect to the classical static case. (i) The equilibrium secular solutions generated by the gas drag are no longer fixed points in the averaged system but limit cycles with frequency equal to the precession rate of the gas. The amplitude of the cycle is inversely dependent on the body size, reaching negligible values for ∼50‐km‐size planetesimals. (ii) The maximum final eccentricity attainable by small bodies is restricted to the interval between the gas eccentricity and the forced eccentricity, and apsidal alignment is no longer guaranteed for planetesimals strongly coupled with the gas. (iii) The characteristic time‐scales of orbital decay and secular evolution decrease significantly with increasing precession rates, with values up to two orders of magnitude smaller than for static discs. Finally, we apply this analysis to the γ‐Cephei system and estimate impact velocities for different‐size bodies and values of the gas eccentricity. For high disc eccentricities, we find that the disc precession decreases the velocity dispersion between different‐size planetesimals, thus contributing to accretional collisions in the outer parts of the disc. The opposite occurs for almost circular gas discs, where precession generates an increase in the relative velocities.