Can the moon have its own satellite, because it also has mass

Most planets in the solar system have satellites, and some of them are quite impressive in size. In this regard, the question arises: can they have their own companions? After all, they also have significant mass and are able to attract other bodies.

According to scientists, such a situation is impossible or extremely short time is possible for a number of reasons. Even if the satellite manages to capture any celestial body, its orbit will not be stable. The newly made satellite will have a gravitational effect not only of the satellite, but also of its planet, as well as the Sun. As a result of the influence of these external factors, the celestial body will not be able to stay in orbit around the satellite for a short time and will either be pulled to the satellite and "fall" onto it, or leave the orbit. Theoretically, options are possible when the new system will be in equilibrium with all centers of attraction, but similar objects have not yet been identified. For example, studies of the moon showed that our satellite cannot possess its natural satellites with stable orbits. Those celestial bodies that were captured and began to rotate in low orbits close to the Moon, after a short time are attracted to it, and those that were able to overcome the lunar attraction, ultimately fall under the influence of gravitational perturbations of the Earth and the Sun and leave the Moon . But a number of theorists do not exclude the existence of stable orbits around the moon, although he admits that this is possible only in exceptional cases and under a very unlikely set of circumstances.