The shared magnetic field situation, with Earth and Moon's magnetospheres joined, could have persisted from 4.1 to 3.5 billion years ago, according to the NASA-led study published in the journal Science Advances.
"The Moon seems to have presented a substantial protective barrier against the solar wind for the Earth, which was critical to Earth's ability to maintain its atmosphere during this time," said Jim Green, NASA's chief scientist and lead author of the new study.
"We look forward to following up on these findings when NASA sends astronauts to the Moon through the Artemis programme, which will return critical samples of the lunar South Pole."
Scientists have long known about Earth's magnetic field, which causes the beautifully coloured aurorae in the Arctic and Antarctic regions.
Thanks to studies of samples of the lunar surface from the Apollo missions, scientists figured out that the Moon once had a magnetosphere, too.
The new study simulated how the magnetic fields of the Earth and Moon behaved about four billion years ago.
Scientists created a computer model to look at the behaviour of the magnetic fields at two positions in their respective orbits.
At certain times, the Moon's magnetosphere would have served as a barrier to the harsh solar radiation raining down on the Earth-Moon system, the scientists wrote.
That is because, according to the model, the magnetospheres of the Moon and Earth would have been magnetically connected in the polar regions of each object.
Importantly for the evolution of Earth, the high-energy solar wind particles could not completely penetrate the coupled magnetic field and strip away the atmosphere.
But there was some atmospheric exchange, too. The extreme ultraviolet light from the Sun would have stripped electrons from neutral particles in Earth's uppermost atmosphere, making those particles charged and enabling them to travel to the Moon along the lunar magnetic field lines.
This may have contributed to the Moon maintaining a thin atmosphere at that time, too. The discovery of nitrogen in lunar rock samples support the idea that Earth's atmosphere, which is dominated by nitrogen, contributed to the Moon's ancient atmosphere and its crust.
"Understanding the history of the Moon's magnetic field helps us understand not only possible early atmospheres, but how the lunar interior evolved," said David Draper, NASA's deputy chief scientist and study co-author.
"It tells us about what the Moon's core could have been like -- probably a combination of both liquid and solid metal at some point in its history -- and that is a very important piece of the puzzle for how the Moon works on the inside."
Over time, as the Moon's interior cooled, our nearest neighbour lost its magnetosphere, and eventually its atmosphere.
The field must have diminished significantly 3.2 billion years ago, and vanished by about 1.5 billion years ago, said the study.
Without a magnetic field, the solar wind stripped the atmosphere away. This is also why Mars lost its atmosphere: Solar radiation stripped it away.
If our Moon played a role in shielding our planet from harmful radiation during a critical early time, then in a similar way, there may be other moons around terrestrial exoplanets in the galaxy that help preserve atmospheres for their host planets, and even contribute to habitable conditions, the scientists said.
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