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Not sure how to proceed as the "Travel to Asteroid Belt" button does literally nothing.

Maybe the "It will take 4605.1 tons" is the issue as I have just 2912.63 tons, but when I add 100 tons, the requirement is simply increased by 100 tons, so I will never be able to reach it. Am I missing something?

When the station is very heavy, it becomes extremely difficult having enough mass to reach the desired velocity. This is the same reason why there's a total payload limit for rockets and given a technology there is a maximum theoretical limit of payload to orbit.

This is no different.

Unfortunately, once you build to many thrusters, they become too hungry, because now not only your objective is to reach the asteroid belt, but to reach it in 24 days. It should still be possible, but the solution at convergence might require A LOT of matter.

I should implement a way to reduce the thrust and change the parameters of the trip, but I'm not very good with UI.