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In Alien Resurrection, the science ship was parked in "unregulated space" while they did experiments. Then, when the aliens get loose, the ship starts an autopilot trip program to fly back to Earth. When Ripley asks how long until they get to Earth, a soldier says 3 hours. The next shot is of the ship passing by Jupiter on its way. The ship does not look to be traveling at the speed of light! So how fast would the ship need to travel to go from, we'll say, slightly beyond Jupiter to Earth in only 3 hours?

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    Maybe they slowed down on the way past? – Valorum Feb 21 '18 at 7:01
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    According to Space.com, the distance between Earth and Jupiter varies between 365 million and 600 million miles. So, you're talking tens of thousands of miles per second in the best case scenario, and substantially more if you're going to factor in real world physics of deceleration at the halfway point, etc. 3 hours seems a bit unrealistic, in that light. But then again, this is Alien Resurrection we're talking about. :) – Helbent IV Feb 21 '18 at 7:23
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    They are going at the speed of the plot! – Rebel-Scum Feb 21 '18 at 7:32
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    Bear in mind that in the Alien universe, humanity does have ships capable of FTL travel. They may still need to cold-sleep for long journeys, but they are travelling between star systems in reasonable time frames. There's no reason to suggest that they couldn't/wouldn't use that tech within a star system as well. Although given that, I'm not sure why they would have to be going so slowly as they go past Jupiter. (nor even why they would want to go that close to Jupiter at all - it's a really deep gravity well; you don't go near it unless you actually need to) – Simba Feb 21 '18 at 14:18
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    Enlighten me, what does it look like when you travel at the speed of light? :-) – Maarten Feb 21 '18 at 16:18
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Jupiter averages about 43 light-minutes from the Sun, Earth is about 8.3 light-minutes. That means, at most, it's 51.3 light-minutes from Earth to Jupiter, and at a minimum 34.7 light-minutes.

So, simple math. The ship would be traveling at between 0.193 and 0.285 c to take three hours to cover the distance, depending on the distance between Earth and Jupiter at the time.

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    Note that for the 0.285c computation, you're going through the Sun. – Nico Feb 21 '18 at 11:17
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    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 Feb 21 '18 at 11:39
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    @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... :) – Luaan Feb 21 '18 at 13:58
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    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. – Fattie Feb 21 '18 at 15:44
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    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. – Fattie Feb 21 '18 at 15:47
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Depends where Earth and Jupiter are in their orbits.

If Jupiter is in opposition, it is abt 390 million miles from Earth, so the ship would need to travel at 130 million mph - just under 0.2c.

If they are on opposite sides of the Sun (superior conjunction) they are a bit over 570 million miles apart, so a speed of 190 million mph would be required - just over 0.28c.

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    Well, if they are on opposite sides of the Sun, you'd certainly have to make a big detour! – Law29 Feb 21 '18 at 11:11
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    Depends how heat resistant the ship is. The Sun's radius is less that half a million miles, so you wouldn't have to detour by much to miss it. Even if you decided that Mercury's orbital radius was your safe limit, that would be less than one-fifteenth of the distance traveled, so you'd still be going in almost a straight line. – Mike Stone Feb 21 '18 at 11:38
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    For a ship that can handle accelerating between 0 and 0.2 c in a matter of minutes, the heat radiation you get at Mercury's orbital radius should hardly be a problem. If anything, the higher solar-wind density would. – leftaroundabout Feb 21 '18 at 15:12
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    Or indeed the higher density of just about anything. At a substantial fraction of c, hitting even a dust grain might generate enough energy to wreck the ship, unless it was built with materials unknown today. And there are a lot of dust grains floating around in interplanetary (or even interstellar) space. – Mike Stone Feb 21 '18 at 16:03
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    @Octopus feigned ignorance is not endearing. – hobbs Feb 22 '18 at 7:31
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Here is a nice app here for calculating exactly this kind of thing: http://convertalot.com/relativistic_star_ship_calculator.html

First the space ship must accelerate with full power, and when it has reached half-way, it has to decelerate with full power in order to stop at earth.

What the other comments fail to take into account is relativity. Time will move slower on the spaceship than on Earth, so if it takes 3 hours on the spaceship, the time passed on earth would have been ~3 hours 10 minutes.

The acceleration would also have to be insanely high, at ~3150 g (1 g ~=9.82 m/s)

Traveling the 6.168 AU (if opposite sides of the Sun, otherwise use 4.172 AU if they are closest to each other), the following values apply:

Acceleration: 3150 g

Time on spaceship: 3 hours

Time on Earth: 3 hours 10 min

Maximum speed relative to Earth: 0.5 c (1 c = 299792458 m/s, speed of light)

Rule of thumb gives that when speed is above ~0.1 c, you need to take relativity into account.

EDIT

The above was under assumption that the spaceship will stop at Earth, but in the movie the spaceship was supposed to crash. In that case, just increase the distance, 6.168 AU, by a factor two, and adjust the acceleration such that the time on the ship becomes 6 hours. Earth would then be reached after 3 hours on the ship, and the maximum speed indicated is the speed it would impact Earth with.

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    Forget relativity, the acceleration would crush all humans on the ship. Possibly even pulverize them. – einpoklum Feb 21 '18 at 22:40
  • @einpoklum: Nonsense, the ship doesn't accelerate, the drive just shifts the universe around the ship. The forces involved are distributed among all the mass in the universe, which is basically unnoticeable. – TMN Feb 22 '18 at 14:48
  • @TMN I think you are thinking of the Farnsworth engine from Futurama now ;) – bjorn Feb 22 '18 at 14:55
  • @TMN: If the ship shifts the universe around, then we can't use special relativity / Newtonian mechanics for a rule-of-thumb and the question becomes kind of meaningless . – einpoklum Feb 22 '18 at 14:59
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As has been answered by others, the average speed would have to be at least 0.2c (or 60,000 km/s) over a distance of 624,000,000 km (in round numbers). With even acceleration all the way, the end speed would have to be 0.4c, which means that the acceleration would have to be 1,154 gees. That's a pretty hefty acceleration. It gets worse if the ship accelerates to the midpoint and then decelerates. Then the speed of 0.4c would have to be reached at the midpoint, which means double the acceleration.

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    Better assume that they are using a spindizzy. – Mike Stone Feb 21 '18 at 11:40

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