How long does terraforming take if you have to build the planet from asteroids?

I'd like to set a story in our solar system with Earth and the inner planets becoming uninhabitable and a new planet being required. If human beings decided to build a world by making slight deviations to asteroids in the main asteroid belt, trojan asteroids, and Kuiper belt until they start to coalesce, and continue adding asteroids to this until they have an Earth sized planet, and then terraform the resulting world, how would I estimate how long this is likely to take?

I think it's clear it would take too long if the reason was an imminent comet impact with Earth, but what about planning for the expansion of the sun making Earth uninhabitable? Would a few hundred thousand years be long enough for a new planet to be prepared and made ready for life?

I'm interested in what different factors would affect how long this would take:

• How much can be provided by the three asteroid sources mentioned - are there any elements that would need to be obtained from elsewhere and increase the expected time?
• In particular would the asteroids release enough gas while coalescing to provide an atmosphere, or would this need to be redirected from elsewhere?
• Would the planet need to start off molten or could the time required be reduced by choosing glancing approach angles for the incoming asteroids so they spiral in and create less heat on impact?

posted over 9 years ago

trichoplax‭

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