<p>Terminator orbits are near-circular polar orbits around a small body, which are stabilized by the balance between the body’s gravity and solar radiation pressure. They can be used as temporarily parking orbits for spacecraft around asteroids. In this paper, we consider terminator orbits in binary asteroid systems. First, we study terminator orbits as a family of polar periodic orbits around a single oblate body, and their stability is computed. By adding a smaller asteroid companion, we can proceed by analytic continuation of the periodic orbits to determine terminator orbits for the binary system. In this paper, we consider continuation of orbits in which the period is in 3:1 ratio with the period of the binary. Accounting for the binary’s elliptic motion around the Sun, we also study numerically the effect of inertial forces. We show that suitably chosen initial conditions can maintain quasi-periodic behavior for mission-relevant durations. The physical parameters used correspond to the ESA Hera mission to the Didymos–Dimorphos binary asteroid system.</p>