According To Relativity
Imagine you are on a ship that is capable of accelerating at g, the acceleration of gravity on Earth (9.8 m/s2). That would make it a comfortable journey since it would feel just like being on Earth, as far as the force of gravity is concerned. (Remember the Equivalence Principle?) Since you want to explore once you reach your destination, you would spend half the journey speeding up and the other half slowing down.
You would be traveling near the speed of light after accelerating at this rate for a year or so. That means you must account for time dilation and length contraction. Distances to other stars or galaxies would appear shorter to you than to your Earth-bound colleagues. On the other hand, time would appear to pass more slowly for you as far as they were concerned.
The result is that you could travel vast distances without aging much. The graph shows how far you can travel (in light years) as a function of the amount of time (in years) that elapsed for the traveler.
Note that the vertical scale is logarithmic; this means that each division is a factor of one hundred. (Look at the math page for an explanation of how large numbers are written.) So, while in ten years you can get just over 100 light-years away from Earth, in 20 years you can travel about 30,000 light years! Of course, everyone you knew on Earth would be long dead by then. You probably wouldn't want to return.
According to the graph, how long would it take to get to the edge of the observable universe, about 20 billion (2x1010) light years away?
For further details, consult the books by Taylor & Wheeler and by Kip Thorne mentioned in the reading list.
Light years and years
The terminology can be a bit confusing. Light years are a measure of length: the distance a beam of light can travel in one year, about 6x1012 miles or 9x1012 kilometers. Of course, years just measure time.
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