Because all objects exert gravity, the motion of the primary object is also affected by the satellite. If two objects are sufficiently close in mass, they are generally referred to as a binary system rather than a primary object and satellite. The general criterion for an object to be a satellite is if the [center of mass]? of the two objects is inside one of the objects.
All masses in the solar system, including the earth, are satellites of the sun, or satellites of those objects, such as the moon.