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I'm imagining a moon with a mass of 0.25M (so 10 times larger than Ganymede), in Ganymede's position orbiting a gas giant like Jupiter. Maybe the atmosphere is anywhere from 0.1 - 1 bar. Would the surface of this alternate Ganymede be protected by it's atmosphere against the charged particles coming from the planet's radiation belts? Could the surface be hospitable to life, or would the radiation belt's particles still make it to the surface in large quantities and/or erode the moon's atmosphere? Do you think a moon could be habitable in this radiation environment?

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Initially it would give protection, but because of the very protection it offered, it would end up being kicked away and leave the moon atmosphereless.

Charged particles can get accelerated by magnetic field, and when they hit another molecule they would transfer part of their momentum and kinetic energy to the other one. Statistically this will result in a fraction of the atmosphere reaching escape velocity and leaving the moon over geological times.

Considering that the moon would have a lower gravity, also lower would be its escape velocity, therefore the above process would happen even faster.

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