with a force of 1 g in a space craft, how long would you have to wait before you be gain to reach the speedily

Question

Im trying to figure out how long it takes to get to the speed of light if energy isnt a problem, I read that if you had constant force you could travel around the milky way in a 100 years, becasue of the space dialation in the craft you are ridding in the people on earth would be long gone.

Answer 1

354.06 days at a constant acceleration of 9.8 m/s^2 (1g).

And no it wouldnt take 100 years to get around the Milky Way. the circumference of the Milky Way galaxy is between 250,000 to 300,000 light years. That means that it is the distance that light travels in one year. And since you are traveling at the speed of light it will also take you 250,000 to 300,000 years to do the same.

And on time dilation:

If you were traveling at .99999999999999 of light speed, the factor of time dilation is around 7073895.35. Which means for every year you spent traveling at that speed, 7.07 million years will pass on earth.

So if you traveled at that speed for 20 seconds, 107 years will pass on earth, so you dont even have to travel around for 100 years, just 20 seconds...

Answer 2

The observer at rest would be long gone in the time it took the traveler to sneeze looking at the travelers point of view. As for the rest of the question, I don't know anything about equations.

Answer 3

You would never reach the speed of light.

The Theory of Relativity (whose predictions have been borne out repeatedly with great precision in experiments and in practice) says that your velocity approaches the speed of light closer and closer, but never actually achieves it.

Why not? Well, one way of looking at it is this:
Because of relativistic foreshortening (Lorentz–FitzGerald contraction - see citation #1) the same amount of oomph has less and less effect on your map-based velocity as you go faster and faster. As observed by a map-based observer (in other words, one who is at rest with respect to you), the yardstick on your spacecraft is not 3.00 feet long, but rather 3.00/ý feet long,
where
|--: ý = 1 / √(1-v²/c²)
|--: v = your map-based velocity (as seen by an observer at rest)
|--: c = speed of light == 299,792,458 m/s

Another way of looking at it is this:
At nonzero velocities, relativistic mass (see citation #2) has the following relationship to rest mass:
|--: M = m * ý
where
|--: M = mass as observed by at-rest observer
|--: m = initial rest mass
|--: ý = 1 / √(1-v²/c²)
Thus, when a nonzero rest mass is accelerated to v=c, the observed mass is infinite, requiring an infinite amount of energy.


But your actual question asked if you could ...
> ... travel around the Milky Way in 100 years.
<------ ------ ------ ------ ------ ------ ------ ------ ------

If you are measuring in "map years" as perceived by an observer at rest, then no: nothing can travel 200,000 light-years in any amount of time less than 200,000 years as perceived by an observer at rest.

But we're talking about the viewpoint of the traveler, not the viewpoint of the Milky Way, so let's continue...


When you say "travel around", if you mean "traverse an elliptical path that stays always at the outer margin of the Milky Way," I don't know -- a larger and larger part of the 1-g acceleration you would be feeling would represent the change in direction ("centrifugal force"), not an increase in speed.


But if, instead, you mean "pass from one end of the Milky Way to the other in a straight line," the answer would be yes -- you could do it in less than 13 years (as perceived subjectively by you the traveler).

Here's how it works.

When you travel at a speed very close to light-speed, time passes very slowly for you compared to an observer at rest: see citation #3.

If you were to accelerate in a straight line without any curves, at a an acceleration that you perceived to be a constant 1 g (in other words 9.8 m/s²), over a period of time that you perceived to be 12.889 years, then you would travel 283,000 light-years in less than 13 of your subjective years. However, a "map" observer at rest in the Milky Way would clock your journey as lasting more than 283,000 years.

To double-check the arithmetic, see the calculator in citation #4.