tokens: instability sets in (see Fig. 7 ). As predicted analytically, the main effect of increasing angular momentum ratio j for fixed e b is to monotonically decrease the relative planet-to-binary stationary tilt i s in the prograde case (where i s ≤ 90°) (see Fig. 6 ). In addition, this stationary tilt increases with increasing e b for fixed j in the prograde case. The behaviour of the stationary tilt in the retrograde case is more complicated, but agrees with the analytic predictions given in Martin Lubow ( 2019 ). In this case, the stationary inclination for non-coplanar orbits decreases with increasing j for fixed e b as in the prograde case. But i s changes from increasing with e b to decreasing at . In addition, there are no non-coplanar stationary orbits below a certain j value, denoted by j cr , that depends on e b (see Fig. 10 and equation 4 ). This property does not hold in the prograde case. Another difference between the prograde and retrograde cases is the topology of librating orbits. In the prograde case, the librating orbits are always nested in a i cos φ– i sin φ phase plane about point with i = i s and φ = ±90° (e.g. red and cyan lines in Fig. 1 ). In the retrograde case, for j > j cr described above, librating orbits are not fully nested within each other and do not orbit about the stationary point in the i cos φ– i sin φ phase plane (e.g. magenta lines in Fig. 5 ). In this phase plane, prograde librating orbits have an oval shape, while retrograde librating orbits have a crescent shape. The variation of e b in time is significantly larger for a higher mass planet. In the simulation with initial conditions e b = 0.2, f b = 0.1, and i = 170°, the binary eccentricity can be excited to values very close to 1 (see Fig. 1 ). This behaviour is similar to what occurs with Kozai–Lidov oscillations in which the outer object is a planet (e.g. Naoz 2016 ). The recent release of data from Gaia allowed us to better characterize the kinematics of the eccentric equal mass close binary HD 106906 in the Lower Centaurus Crux group (Bailey et al. 2014 ). This system hosts both a wide asymmetric debris disc and a planetary-mass companion. The formation mechanism of the planet and the stability of its orbit are still under debate (Rodet et al. 2017 ; De Rosa Kalas 2019 ). The binary components have masses and . The orbital period is and the binary eccentricity is e = 0.67 (De Rosa Kalas 2019 ). The planet, HD 106906b, was directly imaged with a projected separation of 738 au and was found to be oriented at 21° from the position angle of the disc mid-plane, suggesting that the planet’s orbit is not coplanar with the system (Kalas et al. 2015 ). The planet mass was inferred to be (Bailey et al. 2014 ). While the orbital properties of the planet are uncertain, if we assume that the semimajor axis is and the eccentricity is zero, the ratio of the angular momentum of the planet to the angular momentum of the binary is j = 1.13. According to our
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