# Relativistic Time dilation and travel to exoplanets

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?

• Should the word revengeful in the first line be recently? Apr 30, 2014 at 6:59
• 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. Apr 30, 2014 at 8:31

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 $517$.