He said 2 months, so about 2 turns worth. And our ship is more a transport than a war ship, we'd have to retro-fit the thing. And grav force dont work like that, its travelling to fast to be affected. I think nukes the best option
The speed it is traveling would really just make it more difficult for us to get to the asteroid in time and keep up with it, which isn't really a problem if we can go FTL or at least considerably high STL. The idea is to shift the forward momentum of the asteroid slightly in another direction so it misses the planet, and even if the gravitational force applied is small and the object is traveling fast then the trajectory will still change greatly over time because we will be able to redirect the momentum.
What is crucial is the size of the object and the size of the ship, as that controls the level of gravitational force you will be able to exercise on the object and the diffuculty of redirecting it's momentum, the GM has stated our ship is large enough, and if it two months away that is plenty of time for a large ship to subtly influence a large asteroid, but he also said it could fail so we should do the below instead.
Let's nuke it. We can make a better nuke building plant later and any fallout would be to far strewn to cause any real harm. Plus it is sure fire.
Well the problem with the nuke is that it could just break the asteroid into smaller chunks that could still maintain the forward momentum of larger asteroid. Position the ship so that we can launch the nuke in such a way that it hits the asteroid head on, hopefully negating most its forward momentum. Then to make sure it doesn't hit the planet move the ship to side of the asteroid chunks and use gravity to nudge them off course.
This would be considerably easier than the larger asteroid due to the reduced mass of the chunks.
What would the irradiated pieces do? Most radioactive materiel has a half life of 7 seconds or significantly shorter. Plus it will burn in atmosphere and be spread veeerrry thinly in ocean that we don't use. Our problems will be absolutely completely no doubt gone in 4 or 6 months if there are any.
No it ussually blows up into other smaller asteriods that could still make it through the atmosphere, if it where a asteroid that could destroy a planet. Even if they were small enoung to burn up in the atmosphere, if the fragments weren't knocked off couse, we would face a scenerio of the smaller asteroids lighting the atmospehre around their combined impact area on fire, obviously destroying much of the wildlife.
The mining is just impractical, the asteroid is most likely useless space junk and it would take too long.
The nuke, ship, combo is best because it avoids all the negatives of using a nuke and would insure that the asteroid doesn't imapct the planet, if we fail one roll we have another chance.