So, I came here from the thread where this show (Ascension on Syfy) is being bashed over in Café Society. In the show, the whole ship is shown to be arranged vertically, not radially, with everyone being subjected to 1g of gravity. (No need to talk about the plot twist here). The only way for this to happen is if the ship is under a constant 1g acceleration. So my question is: how long would it take to get to Proxima Centauri (distance 4.243 LY or 4.01410220012 x 10^16 meters) under a constant acceleration of 9.8 m/s/s. Assume traveling in 1 direction for half of the trip, then taking 1 day to swing the ship around, then decelerating at 1g all the way there. Using standard Newtonian physics you pass the speed of light in just under 1 year. I am not good with relativity, so I came here for help. This is not homework, I am just a geek who wonders these kind of things.
Thanks in advance.
P.S the trip is supposed to take 100 years. I think that that is way to long, but I have no idea how to find out.
My understanding is that they were headed toward a habitable planet (ignoring the plot twist), so they could populate it as an alternative to Earth. Nobody, least of all the current occupants, had any idea where they could be . . . probably not Proxima Centauri. And they had no idea where or how to look for one. Just getting to Proxima Centauri, and turn around back to Earth would defeat the ostensible purpose. Ginormous fail.
At 9.8 m/s[sup]2[/sup] you’ll be hitting a significant fraction of c in no time.
Even using Newtonian mechanics, 1 year at 9.8 m/s[sup]2[/sup] from a dead stop gets you up to 1.03c -> which is impossible I know but it shows just how quickly the velocity can increase.
So assuming they’d actually like to stop at their destination instead of screaming past it, you could simply flip your craft around and decelerate at 1 g once you get half way there.
So 1 g acceleration over 2 light years gives you 3.6 observer years of travel time with a max velocity of 0.8c
Long story short, Newtonian acceleration will work pretty well until you get to near light speed, so your quick calculation is about right. From the link it looks like with 1g acceleration you can go about 2.9 ly in 3.75 years (2 years personal time), so if you accelerate turn around and decelerate on the way back, you can go 5.8 ly in 7.5 years. If you did plan a 100 (earth time) year journey, most of it would be at near light speed, so you would travel almost 100ly, (and age about 6 years).
However unless you are really set on maximizing internal time dilation so that you don’t age on your journey, you can save massive amounts of fuel if you stop accelerating once you get past about 90% the speed of light. That final 10% just aint worth it.
ETA: Nijnja’d a few times. I should learn that I can’t take the time write long explanations for straight forward physics questions on the dope, or someone will beat me to the punch.
What I wondered about was this : there’s a shot of the ship’s library. I can bring it up on my DVR and take a screenshot if you want. Anyways, on the shelves, there’s clearly a whole section of paper books with a tag over them that says “physics”.
So, uh, do any of the crew every read these books or are they too busy screwing everyone else in the crew, literally and figuratively, to bother? If they bothered to crack one open, they’d maybe wonder :
Why is the star field not at all blue shifted or red shifted?
Where is the gravity coming from?
If their orion drive is somehow still running, why don’t they see flashes from the nukes going off behind them?
How does the transparent glass/plastic in the “radiation pods” not allow through radiation?
How do they know they will find a planet at all where they are going?
And, probably many other things. Guess whoever built the Ascension project must have spent a whole bunch of time and effort creating fake physics books with theories that would explain all of this within the constraints of any experiment the crew could potentially run.
From the viewpoint of observers on the ship, the time and distance appear to be much less. From the viewpoint of observers back on Earth, the time and distance appear to be normal. Each set of measurements is consistent with a speed less than the speed of light.
Combining the time measured by the accelerating ship and the distance measured from the surrounding universe is convenient for answering the sort of question posed in the OP (how much time would the crew measure on an interstellar flight), but it doesn’t yield a physically meaningful speed value.
Well, it yields something called the “proper velocity”, which is really convenient in a whole bunch of formulas. I’ll leave it to the philosophers to argue about the distinction between “convenient in a whole bunch of formulas” and “physically meaningful”.
For what it’s worth, a precise answer would also have to account for matching velocity with Proxima when you arrive. It’s not quite as simple as starting from “stop” and ending at “stop.” This is one reason why so many interplanetary missions look like spirals rather than straight lines. If you’re moving on a curved path, it also means a longer total travel distance than a straight line.
Of course, at 1 G continuous acceleration, this isn’t a big issue. Maybe it would add a couple months to the journey - it’s certainly not going to explain the missing 90 years.
More like a couple of hours, at most. One hour at 1g provides 35.2 km/s delta vee, which is in the general ballpark for matching velocities from one star to another in the same general galactic neighborhood. (For instance, the Alpha Centauri system is moving at about 30 km/s relative to the Solar System.)
Apparently, watching several hours of poorly written story is the penalty for not being honest enough to just look up pr0n on the Internet.