# Do we need to go light speed

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This is something I've thought was true for along time- that if you were travelling at 99.9% the speed of light then from your perspective it would take you about 30 years to travel across the entire universe. If this is true then does this mean that travelling at half that speed would take 60 years? Or does it only take effect at a certain speed. Because if this was true wouldn't that mean that travelling to the nearest star at just say 10% the speed of light would take about a week if you were on the ship?

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No. The relationship is nonlinear.  1/sqrt(1-(v^2/c^2))

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Time dilation is not linear.  At 50% c there is very little time dilation.  Look up time dilation on wiki.

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Also, that across the universe in 30 years ship time at 99.9% of c, is quite a bit too optimistic. At that speed the time dilation factor is only about 22.4.   You would only be able to travel ~670 ly in 30 years ship time.  That would barely get you about 0.67% across the Milky way galaxy, let alone across the universe.

Besides, even getting a ship up to 10% of c is a herculean task.

Even with the most efficient propulsion systems we are presently experimenting with, it would take more fuel than there is mass in the galaxy to reach 10% of c for even a Avery small ship.

If we were able to increase that efficiency by 50 times, then you could do it for 74 kg of fuel for every kg of ship( that's just getting the ship up to speed, if you want to slow back down again at the end of the trip it jumps to 500 kg per kg)

Increasing the efficiency of a rocket engine means increasing the exhaust velocity. A 50 times increase in efficiency equates to a 50 times in crease in exhaust velocity, which equates to a 2500 times increase in the energy needed.

And 10% of c isn't going to gain you hardly any advantage in terms of time dilation; the factor is only 1.005 ( a 10 ly trip would take 99.5 yrs ship time rather than 100 yrs)

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In addition to the good answers above, here is a graph showing the nonlinear relationship.