Ok…not light speed since that’s impossible but let’s say 99.9% light speed. For the sake of simplicity assume a constant 1g acceleration throughout the process with instant on/off acceleration. If you’re up to it I’d like an answer for how long it’d take to reach 99.9% light speed under a 3g acceleration (I’m curious if it is a straight three times faster than 1g or if relativistic effects complicate the issue)?
On a related note I know that mass increases as you get close to light speed so the assumption is it gets harder to push your spaceship the faster it goes. However, doesn’t your reaction mass increase in mass as well thus providing you with more thrust? Assume we have an antimatter propulsion system (for 100% coversion of mass to energy) does gaining mass have any effect on acceleration at all (since the antimatter is gaining mass too thus providing more energy)?
The formula to calculate acceleration is a = (v[sub]2[/sub] - v[sub]1[/sub]) [sup].[/sup] t, where a is acceleration, v[sub]2[/sub] and v[sub]1[/sub] are the final and starting velocities, respectively, and t is time. Thus, given a and needing to calculate t, we use t = (v[sub]2[/sub] - v[sub]1[/sub]) / a. Using your values, I get 118.02 days to reach c at 3 g of acceleration.
Q.E.D. I am pretty sure that is not right because that formula only works for small speeds. You can’t just add speed like that or you could exceed C after 118 days.
Good point…stationary observer I think as that would be the longer time. As perceived aboard the spaceship it’d be shorter but I don’t think it’d be all that much. IIRC time dilation only really becomes serious above .85 or .9 c. It exists before that but the dilation is so small that I think it can be safely ignored.
This is assuming constant acceleration, per the OP. In reality as you approach C. the energy needed to accelerate also increases, approaching infinity as V approaches c.
Clearly we can never exceed light speed no matter how hard we try but your point stands and is the reason for my question. I am assuming the acceleration to relativistic velocities isn’t as simple as doing the same thing at more sedate speeds. I know you can’t simply add two relativistic velocities together (such that two ships going in opposite directions at .9c does not equate to a closure rate of 1.8c). I figure you have to adjust something for acceleration as well (but I’m just guessing).
The formula for relativistic acceleration can be found on Scienceworld. I’m too lazy to do the actual calculation. I’ll just point out that there is indeed an adjustment for “relativistic gamma”. This doesn’t really come into play, however, until you reach velocities exceeding 0.8c.
X = (0.9687) [cosh (1.032313T) - 1]
Capital T is shipboard time elapsed.
small t is Earth time elapsed
X is distance in light years
V is velocity as a percentage of C
For V = 0.9999, I get T = 4.797, and t = 68.5 years. 99.99% C is a fantastically huge velocity.
Yipes! Not being an expert (essentially no clue) I hate to a call into question your answer but 68 years? I have a super dim recollection from somewhere that the acceleration was on the order of weeks/months…not decades.
Are you sure we’re talking about the same thing (1g constant acceleration througout the process)?
Also, any comments on the issue of your reaction mass gaining mass along with the mass of your ship to counteract how hard it is to push the thing?
68 years is the time elapsed on Earth, which is much longer than the time elapsed on the ship … which is more like 4.8 years.
Slight hijack here, but I have a question somewhat related to this: a few years ago, I calculated (using the non-relativistic formula for velocity from acceleration) that you would reach light speed in under a year at a constant 1g of acceleration. Obviously it doesn’t quite work out that way, but it got me thinking.
The reason you would accelerate at 1g would be to provide a normal environment for the people on the ship. But obviously, using the standard nonrelativistic v=at formula, there’s a fundamental limit on how long you can accelerate at 1g – once you accelerate to within 9.8m/s of c, you can’t keep accelerating at 9.8m/s[sup]2[/sup].
So what I wondered was, once you get beyond (c-9.8m/s), can you still produce a 1g gravitational field by acceleration alone? Or would the gravity the crew of the ship experiences grow smaller and smaller as the ship velocity asymptotically approaches c?
Yes you can still produce a 1g gravitational field. Remember velocity is relative. If you are going c-9.8m/s relative to me, you are going 0 relative to you.
mm, i’m no genius, but i was under the impression that the timedifferences would only be appearing to differ?
i mean, it’s not like you are actually doing timetravel, sure the light takes <insert time period> from the ship to earth, so you are looking at the past, but it still happened earlier.
or did i miss something vital in my understanding of the world?
so, how can you at less than lightspeed reach 68 years difference from only 4.8 years of acceleration?
At relativistic speeds, time dilation occurs. The people on the ship would experience 4.79 years, and during the same period 68 years would go by on earth.
so if i had a couple of kids and left for some ten year journey out in space my kids could be 120 years old when i came home, but i’d have aged 10 years(or somesuch, based on the speed and whatnot of course)?
i’m not being sarcastic, i’m really curious, it seems like theres some accepted truth about it, i just cant see what speed would have to do with time. if i travel at 0.9999 times the speed of light from london to new york i would expect a fraction of a second to pass both on my clock and in new york
That’s exactly right. If you want to read more about it, do a google for “twin paradox” and you’ll find a whole lot of information. And there’s plenty of fiction where this time dilation effect comes into play as well. One of my favorites is Larry Niven’s A World Out of Time, where the protagonist travels to the galactic core and back, starting as a young man and returning as an old man, but over two million years have passed on earth.
yea i’ve read some books which include time dilation, but they havent given a satisfying exlpanations
looked up some stuff about it, i found alot of, “this is how it is”, but nothing about the whys or hows.
if i understood it correctly, it isnt the speed difference, but rather the acceleration that causes the effect?
i just cant get my head around the fact that a trip to alpha centauri(4.8 light years or so?) at 99.9% the speed of light would take more than 5 years earth time(conviently accelerating from 0 to max speed in 2 sec of course) hmm, i’m repeating myself!
bah, i hate not understanding things, i dont wanna get a degree to get it, but if i have to, i will!
