How far in space could a person go in a life time if they accelerated at 1 g and decelerated at 1 g?

Question

Assuming they started from a dead stop off the earth and they lived to be about 80 years old.

Answer 1

In a time T, you will travel 1/2 * g * T^2, starting from rest. You spend the first half of your life accelerating at 1g. You cover a total of 825 light years over 40 years. Then, in the second half, you decelerate, covering the same amount of distance. That's a total of 1650 light years.

Notice that this isn't actually possible. You can't cover 1650 light-years in 80 years, because then you would be traveling faster than light. You can't continue accelerating for that long because relativity gets in the way. If you accelerated at 1 g for 40 years, you would reach a maximum speed of 41 times the speed of light.

Edit: Although now that I think about it, 1650 light-years should be right after all. You see, when you move at speeds close to the speed of light, time slows down for you as compared to someone at rest. Even though only 80 years passed for you, the rest of the universe saw you living in super slow motion for more than 1600 years. The effect of the limit on speed from light is exactly opposite of the time dilation effect.

So you still travel 1650 light-years. A side effect will be the passage of 1650 years in the rest of the universe while you only experience 80 years.

Answer 2

I am afraid canopus got it wrong. Relativity does not prevent a body from accelerating constantly. It only transforms a constant acceleration in the "rocket system" into a decreasing acceleration in any proper rest frame. Newtonian mechanics, and there he is right, will lead to a completely nonsensical result.

The problem is called "the relativistic rocket" and you get to calculate it in any course of special relativity. Here is a solution page:

http://math.ucr.edu/home/baez/physics/Relativity/SR/rocket.html

As you can see, the relativistic rocket traveler can go quite far. Indeed, at 1g a man could go all the way to the end of the visible universe (minus expansion and acceleration...)!

The only troublesome thing? Because of time dilation going a billion light years would mean that we couldn't come back for roughly two billion years (plus a few). The traveler who wants to venture further than a couple thousand light years will probably come back to an earth without man... and would find himself wiser but lonely.

Wanna take a ride?