The concept of a spacecraft for collecting space debris assumes that its orbit continuously changes in relation to the location of space debris in various orbits. The highest density of space debris, which is 10–6 t/km3, is observed at orbital altitudes of 800–1000 and 1400–1500 km with an inclination of 60°–80°. To this end, stable trajectories in the sense of Zhukovskii should be determined. We propose a method for selecting the orbit of a space debris collector, including a robotic spacecraft, using the theorem on the stability of trajectories in the sense of Zhukovskii.