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Let's say humankind terraforms Mars aggressively, increasing the planet's mass (and gravity) to Earth-like levels and causes its core to produce a significant magnetosphere. For example, perhaps they could use Jupiter's moons (from the smallest to the largest) and even Mercury, and crash them in a manner that wouldn't split apart the planet. Disregarding the feasibility of this endeavour, how much time would Mars take to cool down enough to be habitable for humans?

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    $\begingroup$ What do you mean by a "galactic" impact? Be careful when using astronomical hyperbole. $\endgroup$
    – HDE 226868
    Commented Oct 20, 2015 at 0:49

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Assuming you have the technology to maneuver moons or small planets at the required speed, and that the impact creates a core similar to that of Earth, Mars would need almost as long as Earth did to cool down.

The Hadean lasted 600 million years.

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    $\begingroup$ That's because of repeated impacts $\endgroup$ Commented Oct 20, 2015 at 13:36
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After a major impact, there would be a vaporized silicate atmosphere that would persist for about 1000 years, and the crust would cool sufficiently for a water ocean to condense again within 1 million years.

The Hadean age lasted for a longer time than that (hundreds of millions of years), but that's partially due to repeated impacts remelting the crust again and again, and also due to the high content of radioactive materials in the early Earth. These materials have decayed so would not be an issue in your case.

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