Question on time dilation of a Spaceship near Lightspeed.

[Crossroads Inc.]

IN a story of mine, a Ship is going on a 'small' journey of Two light years, it is travel;ing at .02% of C'
As far as my guess goes, the ship would take about 20miles to reach its target, but taking into account time dilation, how much time would pass on bored?

[Kuroneko]

IN a story of mine, a Ship is going on a 'small' journey of Two light years, it is travel;ing at .02% of C'
As far as my guess goes, the ship would take about 20miles to reach its target, ...

How did you reach that conclusion, and why is it in units of distance?

Ibut taking into account time dilation, how much time would pass on bored?

Two light years at 0.02%c takes (2 c·yr)/(0.0002 c) = 10000 yr. A decent rule of thumb is that for speeds below 10%c, relativistic effects are irrelevant, but if you insist, the ship time is sqrt(1-.0002²) = 1-2E-8 as long, i.e., about two hours shorter.

[Crossroads Inc.]

Oh...um.. first of I meant 20 years.. I don't know why I put miles...
The 2 light years is just the distance to a near by star.

[Kuroneko]

Oh...um.. first of I meant 20 years.. I don't know why I put miles...
The 2 light years is just the distance to a near by star.

If you want it to take 20 yr in the stationary frame, then you should be traveling at (2 c·yr)/(20yr) = 0.10c = 10%c, not 0.02%c. The ship time is sqrt(1-.10²) = 0.9950 as long, or a bit over a month shorter.

[Crossroads Inc.]

Hmmm, well It 20years would be nice, but the race on hand doesn't have tech to travel faster then .02c
How long IS a 2LY trip at that speed going to take?

[Skgoa]

2 LY at 0.02c = 1 LY at 0.01c = 100 LY at 1c => 100 years or am I missing something?

[Kuroneko]

That's right. The speed changed from 0.02%c in the OP to 0.02c in the revised question, so it's a hundred times faster. Due to time dilation, the ship time is about a week shorter.

[Simon_Jester]

Crossroads:

It really is best to ignore relativity at speeds below 10% of light speed, because it just adds mathematical complexity that is mildly irritating if you know what the algebra looks like and very irritating if you don't. Ignoring relativity, the time it takes to travel a light year at a speed expressed as a known fraction of the speed of light is trivial. It's like asking "how many hours does it take to travel 100 miles at 50 miles an hour?"

I have to ask: what are they using for an engine? Orion drives are relatively straightforward and plausible... and have a top speed of considerably more than 0.02c.

[eion]

Crossroads, this may save you some time:

http://home.att.net/~srschmitt/script_starship.html

It's not the most adaptable calculator, but it works quite well for quick calculations. It assumes a torch-ship like journey, accelerate continuously to midpoint, flip over, and decelerate continuously to destination. It provides maximum % of C, Proper (Shipboard) Time, and Independent Time.

If you use it in concert with the engine list at http://www.projectrho.com/rocket/rocket3c2.html you should be able to find a set-up that works for your story. Fuel, of course, is always the biggest issue.