Stability limits for the quasi-satellite orbit

An asteroid moving around the Sun having approximately the same mean motion and mean longitude as a planet, but a different eccentricity, circles the planet like a retrograde satellite even when the distance is large enough so that it is not a bound satellite. If the orbits are coplanar, then the motion is stable in the secular approximation. When the orbits are inclined enough, an asteroid can be trapped into such a quasi-satellite (QS) motion for a finite period of time. The conditions under which this can occur are discussed, improved criteria for the recognition of this type of motion are developed, and numerical examples from real QS objects are provided.