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NASA recently discovered the first habitable exoplanet with the Kepler space telescope.

Recently I was on this site: http://www.cthreepo.com/lab/math1/

With the Long Relativistic Journeys calculator on that page, I calculated the amount of time it would take according to the traveler to travel 500 light years with half of the journey at a constant acceleration of 2g and the second half with equal deceleration.

The result was under 7 years.

Does this require going near the speed of light? Or does it only require acceleration? If, say, we were to accelerate the space ship up to a certain speed and then decelerate periodically, could the same result be achieved? Or would no significant time dilation occur?

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  • $\begingroup$ Should the word revengeful in the first line be recently? $\endgroup$
    – John Rennie
    Apr 30, 2014 at 6:59
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    $\begingroup$ Why the downvote? The question is basically whether it's acceleration or velocity that causes the time dilation, and this is a more subtle question that it appears. I challenge the downvoter to justify the downvote by giving an answer. $\endgroup$
    – John Rennie
    Apr 30, 2014 at 8:31

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You might be interested to look at How long would it take me to travel to a distant star? as this discusses the physics behind the calculation.

Acceleration does not cause time dilation, so repeatedly accelerating at 2g then decelerating at 2g, but never allowing the speed to get near $c$ will not cause significant time dilation. The travel times at constant acceleration then deceleration are only short because the prolonged acceleration allows the ship to get very, very close to $c$ (as measured in the Earth rest frame). The equation for the velocity measured in the Earth rest frame is:

$$ v = c \tanh \left( \frac{a\tau}{c} \right) $$

where $\tau$ is the time measured on the ship. So for your $2g$ acceleration at the halfway point of $3.36$ years $v = 0.999998c$ and the Lorentz factor is $517$.

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