Its the other way around. Mars revolves around the Sun, with a period of 687 Earth days.
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Mars period of revoultion around the sun, its orbit, is 686.971 Earth days long. Earth takes 365.25 days.
It takes Mars approximately 1.88 Earth years to orbit the sun once. This is equal to about 17,569 hours.
It takes mars 687 days for mars to travel around the sun once
Mars does not rotate around the Earth. It rotates on its axis, and it revolves around the Sun, just as all the other planets do.
About another 4 billion years. Then the sun will explode and destroy the solar system, including mars. Until then it will have to orbit the sun. If you mean, "How long does it take for Mars to make a full orbit around the sun" (or something similar to that) , its 687 days