How Large Would a Planet Need to Be to Host a Gas Giant as a Moon?

There's no direct relationship between the sizes of moons and their primaries. For example, if Jupiter were orbited by an Earth-sized world at the same distance as Ganymede, it would still be classified as a moon rather than a binary planet. Most astronomers recognize that a barycentre within one of the bodies indicates a satellite system, while a mutual barycentre outside both bodies classifies as a binary system.

The Relationship Between Planets and Their Moons

You might think that a planet's mass determines the size of its moons, but there's no correlation between a planet and the size of its moons. However, there is a loose correlation between a planet's mass and the number of moons it has. Jupiter, for example, boasts four of the ten largest moons, including the third, fourth, and fifth largest moons in the solar system. Our Moon ranks as the fifth largest in the list.

In our solar system, some moons are already almost as big as Earth and larger than Earth's moon. Ganymede, a moon of Jupiter, is the largest moon in the solar system with a diameter of 5268 kilometers (3273 miles), making it even larger than Mercury and almost the size of Mars. Titan, orbiting Saturn, is the second-largest moon and has a thick atmosphere. Callisto, another Jupiter moon, has a diameter of 4821 kilometers (2995 miles), and Io, another Jupiter moon, is the most volcanically active celestial body in the solar system with a diameter of 3122 kilometers (1940 miles).

Gravitational Forces and Moon Formation

Gas giants like Jupiter and Saturn have immense gravitational fields that allow them to capture and retain large moons. The larger the mass of the planet, the more significant the gravitational influence, potentially enabling it to host moons of considerable size. For a gas giant to host an Earth-sized moon, it would need to be sufficiently massive to provide the necessary gravitational force to keep the moon in a stable orbit. Our solar system provides a model for understanding this relationship: Jupiter, with a mass 318 times that of Earth, hosts Ganymede, larger than Mercury. Saturn, with a mass about 95 times that of Earth, hosts Titan, the second-largest moon in the solar system.

The Formation and Stability of Earth-sized Moons

Moons form in different ways, such as through accretion, the capture of a passing celestial body, or a significant impact event that ejects material into orbit around the planet. For a gas giant to have an Earth-sized moon, the formation process must favor the creation of a large, stable satellite:

The protoplanetary disk around the forming gas giant must contain enough material to coalesce into a large moon. A large planetesimal must be captured by the gas giant's gravity without breaking apart. A significant impact event must result in enough debris to form a large moon.

For an Earth-sized moon to remain in orbit around a gas giant, its orbit must be stable over long periods. This stability depends on several factors:

The distance from the gas giant, avoiding the Roche limit where tidal forces could tear the moon apart. Orbital resonance with other moons, which could either stabilize or destabilize its orbit. Interactions with the gas giant's ring system, if present.

Larger moons experience significant tidal forces from their parent planet, leading to tidal heating. This can profoundly impact the moon's geology and potential habitability. An Earth-sized moon would likely exhibit strong geological activity due to these tidal interactions.

In conclusion, while large moons like Ganymede, Titan, and Callisto indicate that gas giants can support moons significantly larger than Earth's moon, the ability to host an Earth-sized moon would require a gas giant of considerable mass. The stability of such a moon in orbit around a gas giant depends on various factors, including the planet's size and gravitational influence, as well as the moon's distance from the planet and interactions with other celestial bodies. Further study and observations of gas giants and their moons will continue to provide valuable insight into these complex relationships.