Yes, some of the largest satellites in our solar system, such as Ganymede, Titan, and Callisto, have their own satellites or moons. These moons are referred to as "moonlets" or "satellites of satellites." There are a few reasons why these large satellites can have their own smaller moons:
Gravitational Influence: The primary reason for the existence of moonlets around these large satellites is their strong gravitational influence. As massive objects, Ganymede, Titan, and Callisto exert significant gravitational forces on nearby objects. If a smaller object, such as an asteroid or comet, gets close enough, it can be captured by the gravitational pull of the larger moon and become a moonlet.
Stability of Orbital Resonances: Orbital resonances occur when the orbital periods of two bodies have a simple numerical relationship. For example, the moons of Jupiter, including Ganymede and Callisto, are in a 1:2:4 resonance, meaning that for every orbit Ganymede completes, Callisto completes two and the innermost moon completes four orbits. This resonance creates stable orbital configurations that can allow smaller moons to exist within the gravitational influence of the larger satellite.
Formation during Accretion: The formation of moonlets around large satellites can occur during the accretion process, where the satellite itself is forming. As the parent satellite is accreting material, smaller chunks can coalesce and form moons in orbit around the growing satellite. This process is thought to be responsible for the formation of some moonlets, such as Saturn's moons around Titan.
It's important to note that not all large satellites have moonlets, and the presence of moonlets around a satellite depends on various factors, including the satellite's mass, proximity to other objects, and its history of gravitational interactions. Each moon system in our solar system is unique and exhibits different characteristics and dynamics.