# Size of a gas giant with an Earth-sized moon

I am working on a world that is an Earth-sized planet that was captured by a gas giant planet moving inward in the solar system, then becoming a moon. Through magic and hand-waving mechanisms, the planet remains habitable following mass extinctions during its capture.

The question, then, is what would be the necessary size of a gas giant to have an Earth-sized moon in a stable orbit? Would a Jupiter-sized planet be sufficient, or would it need to be a super-Jupiter?

In case it matters, I'm intending the orbit of the moon to be far enough away to avoid catastrophic radiation and tidal forces. However, unless that makes a difference for how big the planet would be I'm saving questions of orbital distance for the next post.

Your question cannot be answered without further information on the whole system.

You want to keep an Earth-sized body orbiting around a gas giant while being far away from it enough to be safe from dangerous radiations.

This is not a problem of the mass of the gas giant, but more a problem of the neighborhood: the body will stably orbit the gas giant as long as it is deep enough into its Hill sphere.

The Hill sphere of an astronomical body is the region in which it dominates the attraction of satellites. To be retained by a planet, a moon must have an orbit that lies within the planet's Hill sphere. That moon would, in turn, have a Hill sphere of its own.

The extension of the Hill sphere depends on the mass of the planet and the masses and distances of its neighbor: if there is another gas giant nearby the range of predominant gravitation influence will be much closer to the planet than if there were no other large bodies around.

• Thanks! So if I understand correctly a Jupiter-sized planet could have an Earth-size moon, as long as there were no other gas giant planets nearby to perturb the orbit of the moon? Commented Apr 15, 2023 at 22:38
• @Tiluchi The moon has to be within the inner half or third of he HIll sphere for long term stability. . And if other giant planets are far away, the planet the Earth sized moon orbits can be much smaller than Jupiter. Commented Apr 16, 2023 at 5:17

The dwarf planet Pluto has several satellites, the largest being Charon.

Pluto has a mean radius of 1,188.3 kilometers and a mass of 0.00218 Earth mass.

Charon has a mean radius of 606.0 kilometers and a mass of 0.000266 Earth mass.

So Charon has about one eighth the mass of Pluto.

Based on mass updates from observations made by New Horizons[12] the mass ratio of Charon to Pluto is 0.1218:1. This is much larger than the Moon to the Earth: 0.0123:1. Because of the high mass ratio, the barycenter is outside of the radius of Pluto, and the Pluto–Charon system has been referred to as a dwarf double planet. With four smaller satellites in orbit about the two larger worlds, the Pluto–Charon system has been considered in studies of the orbital stability of circumbinary planets.[40]

[https://en.wikipedia.org/wiki/Charon_(moon)#Physical_characteristics][1]

So the example of Pluto and Charon indicates that an Earth mass moon might have a stable orbit around a planet with a mass of only eight Earth masses for billions of years.

So basically any gas giant planet should be massive enough to have an Earth mass moon in orbit around it.

https://en.wikipedia.org/wiki/Charon_(moon)#Physical_characteristics