The Milky Way is attracted to (and we could say orbits around) the center of the Laniakea Supercluster, the Sun orbits the center of the Milky Way, the Earth orbits the Sun, and the Moon orbits the Earth. But, is there something that forces us to stop there? Could we go one step further and have the Moon have a satellite of its own? The theory tells us that, without a doubt, yes. Although practice, or at least the current state of the solar system, tells us otherwise.
Currently we do not know of any satellite of any planet that in turn has a subsatellite (or submoon, as these bodies would be called) orbiting it. In 2008 it was believed that a ring was detected around the moon Rhea, which orbits Saturn, although later more detailed observations by the Cassini probe have ruled out the presence of objects larger than a few centimeters orbiting around it. Although it is true that there could be small submoons, a few kilometers in diameter, orbiting some less studied system, such as those of Uranus and Neptune, the reality is that they have not been observed to date .
Knowing this, what does the theory think? The most important concept to take into account in all this discussion is that of the Hill sphere , described by the American astronomer George William Hill , based on works by the Frenchman Roche . This sphere would be the volume around a body in which said body has gravitational dominance over the orbits of any possible satellite . That is, in the case of the Earth, there will be a region around it in which the gravity of the Earth itself is stronger than that of the Sun. If an object has its orbit entirely contained in this sphere, it will be able to orbit in a stable way , while if part of its orbit is outside the Hill sphere, in that region the satellite will be more attracted to the Sun and will no longer orbit the Earth.
The size of this sphere depends of course on the mass of the planet for which it is calculated, but also on its distance from the Sun. For example, for Venus and Earth, which are very similar in size and mass, their Hill spheres are of considerably different sizes . For Venus this region has a radius of approximately one million kilometers, while for Earth it reaches almost one and a half million kilometers. This also has the consequence that the radius of the Hill sphere is more than twice as large for Neptune as for Jupiter, despite the latter being 18 times as massive as the former . Also, the Hill sphere of Pluto or Eris is more than four times that of the Earth, despite the fact that these bodies have a mass of approximately 0.3% of the Earth’s mass.
The Hill sphere can not only be calculated for a planet, but also for its satellites. In this way we can calculate it for the Moon, thereby obtaining the region around the satellite that could host sub-satellites with stable orbits . For our Moon it would have a size of approximately one sixth of the distance between Earth and Moon, about 60,000 kilometers. Thus any object orbiting between this distance and the Moon’s Roche limit , and not so large that its gravity would require it to be entered into the calculations, could have a stable orbit .
Of course, the closer to the boundary of the Hill sphere that potential satellite was, the more susceptible it would be to any disturbance (introduced by collision with another smaller body or by the influence of Jupiter or Saturn itself) knocking it out of the sphere and from the stable orbit. Therefore the best distance for a submoon from our Moon would be between 10,000 and 20,000 kilometers . This may seem too close, but the reality is that the satellites of Mars, Phobos and Deimos, orbit at these distances from the red planet . Furthermore, Uranus and Neptune both have satellites tens of kilometers in size orbiting less than 50,000 kilometers from their surface, a relatively small distance given their sizes.
Therefore, the answer to the question that gives title to this article is yes, that the Moon could perfectly well have a satellite and that if it does not, it is because there are too many variables involved and many coincidences that must be accumulated for this to happen. As for natural subsatellites, at least, because the Moon has had an artificial subsatellite for almost 13 years, NASA’s Lunar Reconnaissance Orbiter , which orbits just a few tens of kilometers above the surface of our satellite.
All the discussion made here for our Moon can be extended to other satellites of the Solar System. The larger it is and the farther it orbits from its planet, the larger its Hill sphere will be and the easier it will be to house stable orbits around it. Satellites such as Callisto or Himalia (Jupiter), Titan or Iapetus (Saturn) and Nereida (Neptune) could fulfill both characteristics. However, whether they ultimately have some lesser body orbiting around them will largely depend on luck.
REFERENCES:MS Tiscareno et al, 2010, Cassini imaging search rules out rings around Rhea, Geophys. Res. Lett., 37, L14205, doi:10.1029/2010GL043663
