Note that for the 0.285c computation, you're going through the Sun.

And making the necessary turn to go around it at this speed is going to be an adventure in itself.

While that gives you the average speed, in practive you also need to take the acceleration and deceleration (if stopping at Earth) into account, making you reach on the order of 0.5 c at maximum. Furthermore, relativity need be taken into account; if 3 hours on the ship, the time on earth would be something like 3.5 hours.

@bjorn wasn’t one of the problems that the automatically chosen course did not consider to decelerate?

@bjorn as far as I remember, the automatic course to Earth did not contain any deceleration, so still being on a ship with such a course becomes a problem when reaching the destination. So by the time they recognized that they have three hours to solve the problem, it was according to the programmed course, hence there was no deceleration to take into account.

@Nico: Don't wanna go through the Sun? Too hot to handle is it? :-)

@bjorn The ship wasn't going to decelerate - it was going to smash straight into the planet. Of course, that brings up the question of how good of an idea it is to smash a ~3km long space station into a planet at .2c... :)

"Nuke it from [orbit|Jupiter], it's the only way to be sure"

@Luaan thank you, I didn't know it was supposed to crash. This answer is however still wrong, in the sense that it only gives the average speed. The spacecraft must still accelerate, and, once again, relativity is not insignificant here. Check my answer below, which for some strange reason was down-voted... :s

The comments about acceleration time, etc, are not really apposite. The OP is just looking for a ballpark understanding of the speeds involved. Note that - newsflash! - travel at such speeds is 100% handwaving. It is utterly unrealistic with any even vaguely actual-physics. Just giving the "average speed" is all the info that is needed. (Who knows if their drives even "accelerate"? There may be no connection to such concepts. There may be some other totally different concept ( "polar charge!" "twist factor!" "beaglization!) that happens and has no connection to acceleration.

Indeed - note that the needed acceleration (see the other answers), is so high that it would be utterly impossible for life to exist in such acceleration. This means that their physics must be some handwavey thing that plain doesn't involve acceleration. So while it's admirable to point out that it's only an average speed, it's worth noting that the acceleration is simply totally impossible anyway.

Um, everyone knows this is a setting that has artificial gravity, FTL, and acid-blooded xenomorphs, yeah? So worrying about details like the acceleration forces and the like seems a little nit-picky.

FWIW, if you accelerate at 1G, the time it takes you to get to 1 c is 1 year. So the people warning about the acceleration are spot on, even but more so than they think ;-) (365 * 86K * 9.8 ~ 300M)

@Fattie That's what inertial dampeners are for.

@Fattie Am pretty sure they used beaglization.

This assumes a straight-line transit, which (to my understanding) is not how spacecraft usually move between planets. Of course, this does produce a neat minimum value proving it’s at least physically possible, so +1 anyway.

Did this take into consideration that the required acceleration would probably change your sense of time? 3 hours to those on the ship might not be 3 hours to an observer on earth. Not too sure about this though.

@Nico, not if you use the passing lane.

@Lexible The patent on the beaglizerisator has not expired yet, so probably not.

@bjorn At maximum the gamma will be 1/(1 - 0.5^2) = 1.33 but for the average speed 1.04-1.09. Probably at maximum speed it's visible but as far as time dilation goes probably not that important. I'd be more interested how they survived 2829G of acceleration over 3h (assuming speed of 0.5c and constant acceleration).