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Assume spoilers about Passengers from here, but really this has nothing to do with the plot so...

There are a number of tiny points to criticize in the film, but what I'm really coming up empty on is the math concerning where they are and how.

I think we know these things:

  • The ship has been on course from Earth for 30 years
  • The ship when we meet the cast is moving at ~50% lightspeed
  • At 31 years the ship passes Arcturus
  • Arcturus is a red giant star ~37 lightyears from Earth and will not be much closer than that ever before it finally completes its trip across the plane of our galaxy and goes away.

So did they travel around ~37 lightyears in thirty years? Did I miss something?

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    Just FYI, questions asking for real-world explanations or real-world physics or science are very off-topic here. However, it definitely looks like this is on-topic to me, assuming these are all facts in-universe, it looks like a potential in-universe inconsistency. Just thought I'd flag it up, though, given your question title
    – Au101
    Commented Dec 31, 2016 at 4:43
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    I'm enjoying all the maths-based answers. They don't answer the question but they're fun.
    – Valorum
    Commented Dec 31, 2016 at 19:08
  • Small correction to earlier responses. Gus mentions the speed as 0.5c, but that is after the slingshot maneouvre so the speed before and approaching "Arcturus" was somewhat less.
    – John
    Commented Jan 3, 2017 at 3:32
  • Well, in truth we don't know anything concrete about the velocity except for what was said by Gus. It's speculation to assume that because they were going .5c at that moment in time that .5c was their average velocity for the whole trip. For all we know, they accelerated to .9c and stayed there for 25 years, then started slowing down to be at .5c for the duration of the movie.
    – Paul
    Commented Apr 12, 2017 at 12:01
  • I felt my answer was pretty comprehensive. Is there anything you think I should add before you consider an acceptance?
    – Valorum
    Commented Dec 5, 2018 at 11:48

4 Answers 4

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In the 'Passengers' universe Arcturus is only (approximately) 20 light years from Earth.

We can be certain of the ship's flight time because the map room tells us

Jim: Wait. How long ago did we leave Earth?

Maproom computer: Approximately 30 years ago.

and we can be certain of the ship's location because when Jim uses the (laser-based) Comms Terminal to contact Earth, it tells us

Computer terminal: Message will arrive in 19 years.

and we know that the ship is traveling at approx .5 of lightspeed because the ship's Flight Engineer tells us

Gus: We're doing 50% of lightspeed.

Given that Jim is awake for approximately one year before waking Aurora and Aurora is awake for approximately one year before Gus wakes up, at most they could have traveled a further 1-2 light years before the ship slingshots around Arcturus.

That being said, it's possible that the ship accelerated dramatically (see below) after they fixed the onboard computers. This would have have allowed them to reach the real Arcturus in a shorter period.

The ship must have been traveling at a higher speed before Jim woke up.

We know that the ship must have been traveling at a speed greater than 75% of light speed for the first leg of its journey (in order to have traveled 19 light years in just 30 years) and that the Avalon is presumably slowing down, possibly due to the magnetic ramscoop encountering space dust to feed the engines or possibly as a result of the accident that woke Jim. This would also explain the need for a mid-course slingshot to increase their speed.

Real world

Obviously none of the above tallies with what the film's writer, Jon Spaihts said about the accuracy of the physics of the film.

Q: There was one reference to a star that the spaceship was making a slingshot maneuver around – Arcturus, I think? Filmgoers might be thinking to themselves, ‘Now, how far away is that?’

A: “It’s about the right distance away. [36.7 light-years from Earth.] I think the dodgiest thing about the slingshot maneuver is, I don’t know how much velocity you can steal from a body you’re passing that does not have substantial proper motion with respect to a transit perpendicular to your direction of travel.

“If it’s pretty stationary with respect to you, I don’t think you can steal a lot of velocity from it, especially if you’re traveling 0.5 c before you get there. So it’s more of a showy move. It might be a way of changing your trajectory.”

How screenwriter Jon Spaihts worked the physics of starship travel into ‘Passengers’

At the very least this implies that the ship's speed is highly inconsistent but more likely it's just a straight up goof by the writer.

He did admit to having taken some liberties with our "local neighbourhood". Perhaps this is one of those changes.

"I did investigate our general galactic neighborhood. Traveling at a fraction of the speed of light for 120 years can't actually get [a ship] very far; there's really just a basket of stars that they could be going to," Spaights said. "I had a general notion of where they might have found the habitable planet, and maybe stretched a little bit how far they might have gone [to get there]."

Real Science Inspires Voyage to the Stars in 'Passengers'

You might wish to note that in the original script the star was simply described as "a Red Giant", rather than being named as Arcturus.

A STAR looms ahead of the ship: a RED GIANT. The Excelsior rockets toward the star. The passage takes less than a minute. The Red Giant swells in the windows. The ship shudders. The engines howl. Aurora falls into Jim’s arms. The ship bathed in red light.

and the ship's position was far more explicitly confirmed.

COMMUNICATIONS BOOTH: We are nineteen light years from Earth. By the time your message arrives, we will be thirty-six lightyears from Earth. We apologize for the delay."

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    That sentence in and of itself is inconsistent with a 0.5c velocity. :-)
    – Harry Johnston
    Commented Dec 31, 2016 at 22:49
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    @HarryJohnston - The earlier script is filled with inconsistencies.
    – Valorum
    Commented Dec 31, 2016 at 22:55
  • Your calculations assume the ship is moving at constant velocity, but is it possible the engine is running continuously, perhaps making use of the ramscoop for fuel? If the ship is accelerating it's possible the writers were assuming the relativistic rocket equations, in which it is quite possible to travel large distances in short amounts of onboard time (for example, the chart at that page shows a rocket with 1G acceleration would travel 82.7 light-years in 5 years of onboard time).
    – Hypnosifl
    Commented Jan 11, 2017 at 22:25
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    @Hypnosifl - It's certainly possible (see edit). We know that they've gone an impossible distance at .5 of c which means that they must (at some point) have gone faster. Who's to say that the ship didn't start picking up speed again after they fixed it.
    – Valorum
    Commented Jan 11, 2017 at 22:30
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The combination of velocity, travel time and travel distance is impossible.

At 0.5 c (lightspeed), from the perspective of people on Earth, the trip to Arcturus would take 74 years. At 0.5 c there is a relativistic time dilation of 0.866 (0.5 SQR(3)). This would reduce the ship's time to 64 years.

To achieve a ship's travel time the velocity would have to be 0.76652 c. From Earth's perspective the trip would take 48.27 years. The time dilation is 0.64222 and that results in a ship's travel time of 31 years.

Calculations:

enter image description here

NOTE: I have assumed that the travel velocity is maintained throughout the trip, and reached after a negligible amount of time after departure. If this is not the case then the average/maximum velocity should be higher.

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    I know that SQR means square root, but other people may not. try to use less funny looking formulas and more explaining.
    – Gallifreyan
    Commented Dec 31, 2016 at 17:31
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    Why not format some of this in word or LaTeX, and then put it in as a picture? It would look much neater, and you could get the square root signs and everything.
    – Adamant
    Commented Dec 31, 2016 at 17:41
  • @Adamant - did my best, though the font is off. The site I used didn't have much to offer.
    – Gallifreyan
    Commented Jan 11, 2017 at 22:15
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I think you are missing time dilation. At 0.5c, time is moving 15% slower on the ship. https://en.wikibooks.org/wiki/A_Roller_Coaster_Ride_through_Relativity/Time_Dilation

So it is possible to cover larger distances in less time (our view). Or distance is compressed from people on the ship's point of view.

However the number don't line up so well. 32 years (ship time) would be better for 37 light years.... but that does not factor in time to accelerate to 0.5c. Which does not seem plausible with the ship design.

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    You've overlooked that the ship is only traveling at .5c so it would take 74 years Earth time. (So did I.) So it isn't even close.
    – Harry Johnston
    Commented Dec 31, 2016 at 22:46
  • I thought it was 120 years ship time, wasn't it? So it would be more years on Earth.
    – Scott Whitlock
    Commented May 23, 2017 at 14:50
  • 120 years to reach Homestead II
    – mike
    Commented Nov 4, 2019 at 2:28
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I believe that another thing should be taken into account: in my opinion the ship is not flying at constant 0,5c velocity. During the movie we see that the ship's engine is constantly in operation, therefore I believe that we should assume the speed of 0,0c at the beginning of the journey (relative to Earth, I believe that we can forget about orbital velocity oraund Earth, is it would be negligible) and the velocity of 0,5c after 30 years (probably ship's time). The relativistic factor calculation would then become much more difficult as it would change constantly (I am unable to make them, but I am certain that someone here could).

I believe that it should be assumed that the ship would accelerate until reaching speed closer to 1c, then turn around and apply break until reaching the orbit of Homestead II. As to the exact figures, I do not know enough math to answer. Corrcect me if I am wrong.

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  • Are you suggesting that they were traveling FTL for some of their journey? Because although that would be an answer to the question asked, it's not a correct answer.
    – Valorum
    Commented Jan 1, 2017 at 19:27
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    This reads like a reply to some of the other answers, and as such should be posted as a comment rather than an answer. Regardless, do you have any specific evidence from the movie to suggest a constant acceleration? (In real life, we'd be at least as likely to use, for example, a launching laser, or a rocket booster of some sort. The engineering problems are simpler.)
    – Harry Johnston
    Commented Jan 1, 2017 at 23:32
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    "During the movie we see that the ship's engine is constantly in operation" do we?
    – Christopher Peterson
    Commented Jan 2, 2017 at 5:08
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    I am not suggesting that the ship is going to fly FTL, I just want to say that it started on Earth's orbit at 0,0c and started to accelerate slowly. After 30 years of travel it had reached 0,5c and it would continue to slowly accelerate until it reached the speed close to but slower than 1c. Roughly in the middle of the journey the ship would turn around and decelerate using the thrust from the main engine.
    – Michal Kurek
    Commented Jan 2, 2017 at 7:48
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    That makes the discrepancy worse, not better. But out of curiosity, can you point out what specific part of the movie makes you think that the engines are actually in operation, and not just, e.g., providing the ship with power? (It's hard to imagine that the ship has sufficient propellant for decades of continuous operation, and if it uses a Bussard ramjet or similar there should be evidence of that in the ship design.)
    – Harry Johnston
    Commented Jan 3, 2017 at 1:33

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