Whether one considers asteroid collisions or alien invaders, obviously, I need to get instances of myself and my kids off planet Earth and looking for new solar systems to colonize. The alien invasion scenario presents more challenges because I need to worry about outrunning them and leaving no tracks or hints for them to follow. The technical problems are enormous, but the first question is, how much head start do I need? For the analysis I am going to assume that there the rules of relativity apply—no warp drives or worm holes or any other go-faster-than-the-speed-of-light physics. One of the fascinating results is that given a modest head start, even if the bad guys can follow at the speed of light, they can never catch us if we keep accelerating. You can check out our calculations here. Of course, the volume of space that the aliens must search grows as the cube of time. To put real numbers on it, even if we only accelerate at one g, we can never be caught if we have a one-year head start. Special relativity is very cool. I can probably build computers that will be able to withstand over 200 g, and that drives the head start needed to a few days. On the other hand, if the aliens are coming here at the speed of light, we may have no notice.
If we wanted to take humans with us, then there are three scenarios for getting people to the stars. The first is the stuff of movies with men and women either in hibernation or living out lives and having children in space. Even though it is possible to make a clean getaway with one g, these scenarios are highly impractical. Almost as impractical is doing this only with women and a large bucket of sperm. This saves half the payload, and it is the ultimate feminist plan, but still crazy hard. The only conceivable solution is sending eggs and sperm, perhaps frozen, plus as-yet-undeveloped artificial womb technology. At least that is plausible given advances in IVF and robotics and also allows for higher than one g acceleration until one starts incubation.