The Solar System is finely balanced, with the gravitational pull of each body almost perfectly keeping all the planets in a stable orbit. Thus, if we were magically able to instantly switch the places of Earth and Mars, the results would be catastrophic due to their differing masses.
From a climate point of view, Martians would enjoy a noticeable increase in habitability. In Earth’s position, at a closer point to the Sun, ice at the planet’s poles would melt, bathing the Red Planet in water. The temperature would increase and gas would be released from the soil, thickening the atmosphere and making it nearly as warm as Earth is now.
On the flip side, Earth would receive half as much sunlight, and thus the planet would freeze over. Our days would be up to an hour longer, and we’d likely lose some of our atmosphere into space as well. It wouldn’t be good news for us.
In terms of the motion of the planets, however, the results would be chaotic. The outer planets would likely remain the same, but Mercury’s orbit would vary wildly in a giant ellipse. Likewise, the orbit of Mars in Earth’s position would fluctuate greatly from near to far from the Sun. Out of the inner planets, only Earth and Venus would be able to retain a somewhat stable orbit in their positions.
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Image courtesy of NASA