From 27 March 2012 - 05:16 PM:

No, it would be not be too much more than 88 years.

At 1/22 the speed of light it would take 88 years to cover 4 light years. The Alpha Centauri system is a little further than that, 4.24 ly for Proxima and 4.37 ly for Alpha Centauri A & B. This gives use journey times at 1/22 c of 93 and 96 years respectively. I give these figures not to show off, but to justify a step in the calculation I will do below.

pallidin, on 29 March 2012 - 02:56 AM, said:

So, how much time dilation would there be with an object traveling only 1/22th light speed?

The short answer is not a lot. Time dilation is an exponential function and really only becomes significant above about 10% of the speed of light.

For fun (because I had nothing else to do) I decided to do the calculation.

The formula for time dilation is:

**t = t**_{0}/√(1-v^{2}/c^{2})

Where:

t = time observed in the other reference frame

t

_{0} = time in observers own frame of reference (rest time)

v = the speed of the moving object

c = the speed of light in a vacuum

I am going to round up the journey time to 100 years to make the maths easier (that is why I give the figures to Alpha Centauri above).

We do not need to use the absolute value of c. If we say c=1 then we can use 1/22 (or 0.04545 as a decimal) as the value for v.

This gives us:

t = 100/√(1-0.4545

^{2}/1

^{2})

= 100/√(1-2.060x10

^{-3}/1)

= **100.1 years**
In other words, from the point of view of an observer on Earth, a traveller on our hypothetical planet would only be a little bitt over one month younger than he would have been.