# How long would it take for a person to accelerate up to the speed of light...?

...within a tolerable acceleration threshold?

I mean, if you were to send spacemen to the far reaches of the universe, and you wanted them to eventually reach the speed of light (or almost) without killing them... how long would it take for them to reach it safely?

(I'm supposing that it is a high acceleration what may kill you, not a high speed)

Relevance
• RickB
Lv 7

Great question!

The answer depends on how close "almost" is. If reaching 99% lightspeed takes a certain amount of time, then reaching 99.9% takes about 3.2 times as long; and reaching 99.99% takes about 10 times as long. As you add more "9"'s to that target speed, the required time stretches out to infinity.

Here are some actual numbers, assuming an acceleration of "1g". The first colum is your target speed as a fraction of the speed of light; the 2nd column is how long it takes to reach that speed (from mission control's point of view).

99%............6.8 years

99.9%..........21.66 years

99.99%.........68.5 years

99.999%........216.76 years

You can cut those times in half by going at "2g" instead of "1g"...but you still have the same problem of the times stretching out to infinity.

This has to do with the way time and space are related in relativity theory. Because time and space are perceived differently for the pilot as compared to "mission control" on earth, the two observers have different conceptions of how quickly the ship is gaining speed.

Let's say we engineer the ship so that it has an essentially infinite amount of fuel and can provide enough thrust to generate "1g" of acceleration for an indefinitely long time. That means, from the pilot's point of view, the ship is continually picking up speed at the rate of 1g (about 22 mph faster each second).

But there's a problem. Because of time dilation, the ship's clock (as observed from mission control) ticks slower and slower as the ship picks up speed. So let's consider the time it takes for the ship to add an extra 22 mph to its speed. From the pilot's point of view, that timespan is "1 second". But back at mission control, they may measure it as "30 seconds". So from mission control's point of view, it's taking an ever longer time for the ship to pick up an extra 22 mph. As the speed approaches lightspeed, it may take YEARS to get an extra 1 mph out of it.

This has the effect of making the ship seem more "sluggish" as it gets close to lightspeed. When doing energy and momentum equations, it's convenient to treat this "sluggishness" as though the ship has gained extra inertia, or mass. You'll often hear people say that you can't reach lightspeed "because" your ship becomes infinitely massive. But this sort of confuses cause and effect: it's better to say that the ship behaves as though it's infinitely massive _because_ the relationships between time and space prevent it from reaching lightspeed.

Source(s): Physics degree. Relevant equations here: (http://math.ucr.edu/home/baez/physics/Relativity/S... )
• Gary B
Lv 7

forever.

Due to Einsteins Theory of Relativity and its corollary the Mass Dilation Effect, as an object WITH MASS approaches the speed of light, its mass approached infinity.

We ALSO know that the more massive an object is, the more energy it take to maintain acceleration. Therefore, as the mass of the object approaches infinity, the energy necessary to accelerate it ALSO approaches infinity.

but the universe is FINITE. There is NOT "infinite energy" contained in the universe!

it is therefore impossible to accelerate a person, or a space ship at , or even near, the speed of light.

Ignoring relativity, at 1G acceleration, call it 10m/s², and speed of light 3e8 m/s, 3e8/10 = 3e7 seconds or 8000 hours or 1 year.

But relativity will not let that happen, your acceleration tapers off as you get close to the speed of light. However, to the observer on the spaceship, that would not be noticeable, as time compresses also.

.

• Anonymous

If you're ask how long a PERSON would take, i'd say never... but if you ever find out if anyone can run that fast, tell me. But if we ever found a way to move that fast, without leaving our guts behind us, I'd say since a the fastest acceleration in the world of a human is 0-30,000 m/s in 3 secs, and you wanted to reach 299,792,458 metres/sec it would take you a little bit less than three hours to reach... but you would've run into a house or pole or something by then. (I'm not sure if I did the math right... could a really good mathematician correct me if I'm wrong?)

Source(s): en.wikipedia.org/wiki/Speed_of_light