This is a tough question as it is still being investigated by scientists at NASA. I did not know the answer and did some digging around to find some sources that might be useful.

To start, gravity itself plays a large role in keeping the atmosphere in place, I think much larger than the Earth's magnetic field does to protect against solar wind. There has been some research on Mars about how much of the atmosphere gets taken into space from solar wind. Mars does not have a magnetic field now, but it used to. Researchers and scientists are using this information to determine the rate at which the magnetic field disappeared and how the planet is currently affected by solar winds. Studying the environment on Mars and other planets may help to predict what would happen to Earth if it were to lose its magnetic field.

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Thanks,