This is a schematic showing how atmospheres form.
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The Origin of an Atmosphere
There are four ideas for where the atmosphere comes from.
Those four ideas are 1. that the planet-elements which made the planets made the atmosphere too, 2. that the atmosphere was drawn to the planet from the cloud out of which everything came, 3. that comets hit the planet and brought molecules of air with them, 4. that volcanos erupted and made an atmosphere.
The one that applies to Jupiter is hypothesis #2, in which the original molecules, which Jupiter drew out of the primitive gas cloud stayed, and form the atmosphere today.
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