Physicists/Astronomers, question about traveling to Pandora, the location of the movie “Avatar”?
Question by Variable 46: Physicists/Astronomers, question about traveling to Pandora, the location of the movie “Avatar”?
Somewhere I read that “Avatar” takes place on the hypothetical moon of Pandora, orbiting the equally hypothetical gas giant Polyphemus, which in turn is orbiting Alpha Centauri A. Somewhere early in the movie it is mentioned that our travelers from Earth took 5 years to get there. To travel the approximate distance of 4.37 light years to Alpha Centauri in only 5 years means our guys must have been really hauling the mail, and must have also experienced considerable time dilation due to their relative velocity.
So my question is: In the 5 years it took for them to make this trip, how much time passed back on Earth? I imagine the answer can be complicated by the question of acceleration, i.e., how long did it take to accelerate to their maximum velocity, and how long did it take to decelerate to a full stop, and if you’re inclined, feel free to incorporate that into your answer.
Thanks!
(And no, you’re not doing my Physics 101 homework for me!)
Interesting, yes, I’ve seen the formula and calculated similar numbers, but I wasn’t sure of my math; actually, I was intuitively expecting a much longer of period of time had passed on earth, say on the order of 20 to 30 years. Also, I wasn’t sure what would be a reasonable assumption for an acceleration that wouldn’t leave the passengers as a very thin layer of molecular paste on the aft bulkhead, or vice-versa for slowing down upon arrival. I guess the movie only said they’d been asleep 5 years; this could allow for them to be awake during a much more extended acceleration period, arguably a period of aclimating to extended zero-g. Or this could have been merely the final period of several periods of sleep, to which the narrative was referring. Anyway, thanks for the answers!
Best answer:
Answer by bw022
If it took them 5 years to travel 4.37 light years, then they were travelling at (4.37/5) 0.874 the speed of light.
The formula for time dilation is:
t(d) = t / sqrt( 1 – v^2 / c^2)
Plugging in the numbers:
t(d) = 5 / sqrt( 1 – 0.874*0.874 / 1*1 )
t(d) = 10.29 years
However… any vehicle needs to both accellerate to reach that speed and decellerate upon reaching the planet. Assuming a 1g (9.8m/s/s) accelleration and decelleration, it would take nearly a year to get to the speed of light and a year to slow down from it — making the trip impossible within five years. Even if they only took six months (total) accellerating/decellerating (and didn’t kill themselves doing so), then the trip was made in about 4.5 years and the numbers quickly go to (4.37 / 4.5) 0.97 the speed of light and you get over 18.5 years passes on Earth.
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