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## Space Travel

The velocity addition law 11.11 implies that no object can be accelerated to speeds greater than the speed of light. At first glance this seems to put a damper on the prospects for space travel beyond our solar system. The nearest star to our Sun is four light years away, and to get to a potentially more interesting star, say one with planets, you would have to travel hundreds of light years. A light year is the unit of distance corresponding to the distance light travels in a year. It is a terribly long distance, about 1012kilometers. More importantly, the speed limit imposed by Special Relativity forbids us from getting anywhere in less time than it would take light to get there, so that trips to even nearby stars would take many years, and perhaps even hundreds of years. If this were true it would make travel between the stars undesirable at best for a species whose life span is only about one hundred years. Luckily, what Special Relativity takes away with one hand, it gives back with the other.

A trip to the nearest star would take approximately four years for a spaceship traveling at 99% of the speed of light. However, this is the time as measure by observers stationary with respect to the Earth and the star (we assume that the relative motion between them is nowhere near light speed). According to the time dilation effect, the time required for the same journey would be shorter to those on the spaceship. For example, if the spaceship is moving at 0.99c, the time dilation factor is seven, so that to the astronauts, the journey takes only 4/7 of a year, or about seven months. If the spaceship were able to reach 0.999c, the time dilation factor would be twenty, and the trip would take only about one month. Space travel, and the colonization of space are therefore possible despite the relativistic speed limit. The only downside is that the taxpayers on Earth who funded the mission would still have to wait at least eight years before the astronauts returned, even though the astronauts themselves would have only aged two months.

Next: The Twin Paradox Up: Other Implications of Special Previous: E = mc
modtech@theory.uwinnipeg.ca
1999-09-29