[edna314]

What came to my mind immediately was 'Passengers'. But, reading up the plot on Wikipedia, it is possible that it never actually was mentioned how far away the destination was or how fast they were going. So, maybe it wasn't a misconception on the sci-fi side, but on my side. For sure, any light speed travel shouldn't take any time and infinite amount of time should pass for the rest of the universe.

[eesmith]

From Wikipedia, 60 light years and "a journey lasting 120 years".

It doesn't say if that's 120 ship years or Earth years. I'll assume ship years as that makes the most sense in context.

Assuming constant acceleration to the 1/2-way point, flip, deceleration, and using http://www.projectrho.com/public_html/rocket/slowerlight3.ph... :

  T = (c/a) * ArcCosh[a*d/(c^2) + 1] (given acceleration and distance)

  60 years = (c / a) * arccos(a * 30 ly / (c^2) + 1)
  1893456000.0 = (3E8/a) * arccos(a * 3.15576 + 1)

Using Wolfram Alpha to solve - https://www.wolframalpha.com/input/?i=1893456000.0+%3D+%283E...

  a = 0.14748 m/s^2 or about 1.5% g

Time elapsed on Earth is only a bit longer than ship time:

  t = (c/a) * Sinh[a*T/c] = 1.15 * ship time ("proper time")

Final velocity at flip is:

  v = c * Tanh[a*T/c] = 0.73 * speed of light