Traveling at the speed of light

I always wondered about this. I used to be familiar with the equation of how time is shortened as you approach the speed of light. Have you heard that story about the astronaut traveling in a 50-foot-wide spacecraft where he's on one side and a mirror is on the other? As he's traveling at near the speed of light, his image travels to the mirror and reflects back to him not in a straight line but in a longer "V" path.

Anyway, on to my question. I'll simplify it and not take into account any annoying technicalities like huge amounts of fuel which would require an ever-larger spacecraft.

Suppose an astronaut is in a spacecraft at a complete stop, and he started traveling in a straight line at a sustained acceleration of one G, how long would it take to reach the speed of light? (No warped-shrinking time-slowing come back yesterday stuff. Just a straight hypothetical question.)

Quote: Greasyjohn

Suppose an astronaut was in a spacecraft at a complete stop, and he started traveling in a straight line at a sustained acceleration of one G, how long would it take to reach the speed of light? (No warped-shrinking time-slowing come back yesterday stuff. Just a straight hypothetical question.)

This should be simple division.

Suppose you are in a stopped car, and start accelerating in a straight line at 5m/s/s. After 20 seconds, you should be going 100m/s.

We're just using different constants - 299,792,458m/s (c), and 9.81m/s/s (g).

So, I get 30559884 seconds, which would be 8488 hours, or 353 days. So, just shy of a year.


I think you'll find it impractical to actually accelerate like that, however.

Quote: Dieter

This should be simple division.

Suppose you are in a stopped car, and start accelerating in a straight line at 5m/s/s. After 20 seconds, you should be going 100m/s.

We're just using different constants - 299,792,458m/s (c), and 9.81m/s/s (g).

So, I get 30559884 seconds, which would be 8488 hours, or 353 days. So, just shy of a year.


I think you'll find it impractical to actually accelerate like that, however.

Wow. It would take that long? I used 1G because a greater acceleration would make it uncomfortable for the hypothetical astronaut. Thanks for the answer.

Quote: Greasyjohn

Wow. It would take that long? I used 1G because a greater acceleration would make it uncomfortable for the hypothetical astronaut. Thanks for the answer.

If you can attain and sustain 1G acceleration, then yes.. about a year to come up to speed, and about a year to stop again.

You might be able to accelerate faster with some form of intertial damper.

Possibly of interest: Once you've come up to speed (and just "coast"), you cover the same distance in the next 176 days as you did in the previous 353 days. (Half the time, equal distance.)

How far did you travel while accelerating? 4.58*10^15 meters, or about 30620 times the distance from the earth to the sun.

Quote: Greasyjohn

Wow. It would take that long? I used 1G because a greater acceleration would make it uncomfortable for the hypothetical astronaut. Thanks for the answer.

FWIW, RA Heinlein used hard science in writing his fiction stories, and discussed or made this a part of many stories, and based on what we knew at the time (50-odd years ago), this is correct. Until there's a scientific breakthrough that changes the basic laws of acceleration and inertia (such as Star Trek warp drive), this is the time frame.

re the first answer, I am getting years and years, but I did it quickly, stay tuned

no, I am getting the same answer now

Pretty sure the answer is, with 1G linear acceleration, not quite a year and a half, and the same on the other end to decelerate. Could be wrong.

Quote: beachbumbabs

Pretty sure the answer is, with 1G linear acceleration, not quite a year and a half, and the same on the other end to decelerate. Could be wrong.

Math is a curious thing. An arrow fired at exactly a 45 degrees angle from level will land the farthest distance away from the archer. If a spacecraft is traveling in a circular orbit and it is accelerated by a factor of the square root of 2 it will achieve escape velocity. I'm going to go make a möbius strip.

The speed of light is the speed of light, just because. It's not a very good answer, but the best you get. The universe being self-correcting always seemed strange to me, and something like hologram universe or simulation universe are probably going to turn out true.

Quote: Greasyjohn

[something about special relativity...]
Suppose an astronaut is in a spacecraft at a complete stop, and he started traveling in a straight line at a sustained acceleration of one G, how long would it take to reach the speed of light? (No warped-shrinking time-slowing come back yesterday stuff. Just a straight hypothetical question.)

Well, acceleration is the rate of change of velocity.

If you somehow can sustain a constant acceleration (a), then the time to reach a tarvet velocity (v) is v/a.

For special relativity you cannot reach velocity v>c, so the promise that you can always sustain a constant acceleration must be physically impossible at velocities c.

I believe the theory is that in order to maintain an acceleration of one G with even a small object, the amount of energy needed as the speed of light approaches becomes ridiculous, at 99% of C it would be the output of the sun for eons or some such

Quote: Dieter

This should be simple division.

Suppose you are in a stopped car, and start accelerating in a straight line at 5m/s/s. After 20 seconds, you should be going 100m/s.

We're just using different constants - 299,792,458m/s (c), and 9.81m/s/s (g).

So, I get 30559884 seconds, which would be 8488 hours, or 353 days. So, just shy of a year.


I think you'll find it impractical to actually accelerate like that, however.

Wait a minute. When you say 353 days are you talking about earth days?









(Sorry, I couldn't resist.)

Quote: Greasyjohn

Wait a minute. When you say 353 days are you talking about earth days?

... as measured by an outside observer...

I believe the answer I gave was in seconds, and then convenient approximations in more familiar terms with manageable numbers followed.

Quote: Dieter

Quote: Greasyjohn

Wait a minute. When you say 353 days are you talking about earth days?

... as measured by an outside observer...

I believe the answer I gave was in seconds, and then convenient approximations in more familiar terms with manageable numbers followed.

You did see my "Sorry, I couldn't resist." I hope.

Quote: Greasyjohn

You did see my "Sorry, I couldn't resist." I hope.

Yep! No problem.

Hehe ... I can't add to Dieter's answer, which appears to be correct, but I will say the answer is as simple as spelling "cat":

Not accounting for the relativistic effect and using a newtonian kinematic equation:

vf = vi + at
vf = c
vi = 0
c = 0 + at
c/a=t

Cat!

NB - Yeah, I guess I could've substituted g for a, but "cgt" doesn't spell anything.

The "V" thing, though, is an interesting thing, and it always served me in better understanding time dilation.

If you're standing still and you flash a light F at a mirror M and it reflects back, its path through space is like this (not accounting for earth's rotation, revolution, solar system's revolution, procession, etc., etc., etc.):

F >-----------------------------------------------------------> M
F <-----------------------------------------------------------< M

Ideally, those would be on top of each other, but the graphic capability of ASCII just isn't there. Anyway, now imagine the source F moving slowly and the path through time looks like:

F >--------------------
--------------------
------------------> M
------------------< M
--------------------
F <--------------------

Same distance. Same speed of light. If you're moving with the source, it looks like the top graphic. If you're standing still (not accounting yada yada yada) observing it, it looks like the bottom graphic.

But they still take the exact same amount of time. The only explanation is that time-still (t) is not the same as time-moving (t'). This happens at every speed, even those close to zero. The Lorentz transformations tell us how fast F must be moving relative to still to see how different t is from t'. As it happens, it isn't really perceptible until you get to about .90c, I think. But GPS systems have to account for it, so while we wouldn't perceive it, it's clearly detectable and meaningful long before our perception thresholds.

NB - I know that many of you understand this and don't need/want to have it explained. This is just the way I first understood it, so I'm passing it on. If you understand it, and don't need/want this, that's fine. If you learned it using a different mental picture, share it, that would be interesting!

Quote: Dieter

...as measured by an outside observer.

Because there's relativistic effects here, it's actually one year based on the inertial frame of reference of the TRAVELLER, not the observer on earth.

Quote: UP84

Because there's relativistic effects here, it's actually one year based on the inertial frame of reference of the TRAVELLER, not the observer on earth.

I'll gladly admit that relativity isn't my strong suit, but this one doesn't make sense to me.

Pretty sure the final answer is:

Quote: Dieter

I'll gladly admit that relativity isn't my strong suit, but this one doesn't make sense to me.

I doubt that the question as posed makes any sense.

Like approaching infinity, the quality of the speed of light is another undefined. Who said anything about going faster, or becoming bigger?

http://news.harvard.edu/gazette/1999/02.18/light.html

People say that if you say you understand quantum physics, then you're wrong.

So, in the mean time, who figured out what is light? Other than a bunch of rest mass of zero which can't ever stop completely, ie.

Quote: Dieter

I'll gladly admit that relativity isn't my strong suit, but this one doesn't make sense to me.

Supposedly as velocity increases, time decreases, or something to that effect. I remember doing some thought experiment in school where there was a pair of twins - one lived his life as normal, the other traveled near the speed of light for 30-40 (Earth) years. The "normal" one aged as expected, while the other only aged a few months/years. (I don't remember the specifics, just that the time frame of reference is decreased as observed by an outsider.)

Quote: wudged

The "normal" one aged as expected, while the other only aged a few months/years. (I don't remember the specifics, just that the time frame of reference is decreased as observed by an outsider.)

Right... so an outsider will see it take them about a year to come up to speed.

A passenger on the ship won't think it takes that long.

Quote: UP84

Because there's relativistic effects here, it's actually one year based on the inertial frame of reference of the TRAVELLER, not the observer on earth.

... This is saying something different, which I don't follow.

Quote: Dieter

Right... so an outsider will see it take them about a year to come up to speed.

A passenger on the ship won't think it takes that long.

I thought it was the reverse (I'm not a specialist). It takes one year for the passenger but much longer for the reference frame. Like in the Planet of the Apes or the Forever War or the Queen song '39.

Another problem is that the relativity effects will distort the ship, which leads to an impossibility of defining 'constant acceleration' between the bow and the sprit of the ship.