If a spaceship accelerates at a constant one g, how long would it take it to get to light speed?

Question

In addition, how many miles or kilometers would that same spaceship have to travel at one g before it achieves light speed?

Answer 1

A spaceship can never achieve light speed.
Have a look at special relativity.

Ignoring relativity (which you really shouldn't), we get:
v = at
3 x 10^8 = (~10)t
t ~ 3 x 10^7 s = almost 1 year.

Answer 2

You can look at that from both the spaceship's passenger's and the outsider's (i.e. the guy on Earth) viewpoints.

1. Should you be in the spaceship, the 1st answer would probably apply, although I haven't worked out the calculations to check that up,

2. For the Earth observer focused on observing the spaceship, that would be an infinite duration.

It's right that you should go on yourself to study Special Relativity to get the gist of that answer. It would also show you that according to this model, the ship's clock would appear to elongate more and more with respect to an identical clock ticking on Earth. Also, as the ship's velocity gets closer to that of light, the ship's mass would tend to increase to reach infinity at exactly the speed of light, which is somewhat perplexing, right?

Answer 3

Forever. In classical mechanics, zener_drake_42 would have gotten the right answer, but relativity says that time, distance and mass change with speed, so that you can accelerate at 1G for 10 years and still be going at only 99% the speed of light, and then accelerate at 1G for another 10 years (or 100 or 1 million years) and SILL not gain that last 1% of speed you need to reach the speed of light. That is because time slows down, length gets shorter and mass increases until, in theory, at the speed of light time stops, distance shrinks to zero and mass becomes infinite. So you cannot even calculate speed by dividing distance by time because you would be dividing zero by infinity, or would it be infinity by zero? Mathematically, it is forbidden to even do the calculation. It has nothing to do with technology or engine power. It is extremely hard for most people to comprehend since it is so alien to every day experience.

Answer 4

This becomes a tricky question as one gets close to the speed of light.

Viewed from the outside (a "stationary" frame of reference):

At an acceleration of 1 g ( 9.80665 m/s^2), from speed 0, you'd think that it would take 30,570,323 seconds to reach the speed of light (299,792,458 m/s).

At 86,400 seconds per day, that would be 353 days, 19 hours, 45 minutes, 23 seconds.

However, as the ship appears to approach the speed of light, its mass, relative to us, would increase. So, if the ship uses a constant force (F = m a), then the acceleration diminishes as the mass increases.

OK, you tell yourself, Let's tell the ship to increase the force of the engines. As the speed approaches the speed of light, the "gravitational mass" (that is what Einstein calls it) of the ship grows without bound (others would say: it approaches infinity), so that, at some point, maintaining a constant acceleration would require more energy that there exists in the universe.

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From the point of view of the accelerating frame of reference (the ship), time flows more slowly (Lorentz compression). It just so happens that the rate at which time flow varies is the same as the rate at which, from the other frame of reference, the mass appears to increase. Coincidence? I think not!

Therefore, same conclusion (using different words): the ship (literally) runs out of time before reaching the speed of light.

Lorentz time dilation: Gamma = 1/ SQRT(1 - (v^2 / c^2) )

Mass increase: M = Mo / SQRT(1 - (v^2 / c^2) )
Mo being the "rest-mass"

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PS: finger problems on the calculator. I've corrected the numbers. Thanks to Bugman.

Answer 5

So since this question is purely hypothetical, let's suppose it is possible to attain the speed of light- or at least to attain a value just below the speed of light.
The Earth's gravitational acceleration constant is 9.8 m/s^2. By "meters per second squared," we mean "meters per second per second." So in one second, the spaceship would have accelerated to 9.8 m/s. In two seconds it would have a speed of (2s × 9.8m/s) 19.6 m/s.
Notice that the acceleration is constant, so by Calculus, the change in speed will be linear.

The speed of light is approximately 3×10^8 m/s (three hundred million meters per second). Simply divide this by 9.8 and you'll get 30.61 million seconds, which is about 354 days.

Answer 6

It will not. As the speed approaches the speed of light the mass will start to increase and at the speed of light it mass would be infinite and require that much fuel to get there .

Answer 7

In round figures, it will take one year, and it will have travelled half a light year - over a thousand times as far as Neptune.

There are relativistic arguments about how much energy this would take, or how the occupants would perceive their progress.

Answer 8

He replaced into suited in that the "mass of the deliver could bypass up exponentially, attaining infinity". for that reason vacationing close to the cost of sunshine is inconceivable b/c we've yet to discover a achievable thank you to strengthen up the deliver to this velocity. particularly bearing directly to "mass", this refers to relativistic mass, which will strengthen with velocity. It reaches infinity by using fact the cost of the deliver procedures that of sunshine.

Answer 9

g=9.8m/s^2
c=299,792,458 m/s

t=v/a

so t=30,591,067 seconds, or about 354 days, little less then a year.

d=0.5at^2 I believe

d=4,585,485,562,972,596.1 meters or about 0.48 lys.