1. The Hill Sphere: The Hill sphere is the region around a planet within which its gravity is dominant. Objects within the Hill sphere are more likely to orbit the planet than to be pulled away by the gravity of other objects, such as the Sun. For Earth, the Hill sphere has a radius of about 1.5 million kilometers (0.93 million miles).
2. The Roche Limit: The Roche limit is the distance from a planet at which the gravitational forces acting on an object become greater than the object's own cohesive forces. If an object is too close to the planet, it will be torn apart by tidal forces. For Earth, the Roche limit is about 18,400 kilometers (11,400 miles) for an object with the density of rock.
3. Gravitational Stability: In addition to the Hill sphere and the Roche limit, the gravitational stability of the moons themselves must be considered. If the moons are too close to each other, their gravitational interactions can cause them to destabilize and eventually collide.
Taking these factors into account, it is estimated that Earth could have a maximum of about nine moons. This number could be higher if the moons were small and widely spaced, or if they were located in stable Lagrange points. However, it is unlikely that Earth could have more than nine moons without them becoming gravitationally unstable.
It's worth noting that Earth currently has only one natural moon, which is simply called "the Moon".
