What if I stacked 26,571 rocket ships end to end in space, each capable of about 25,000 mph (7 mps), and fired each of their engines in sequence as the one before it attained top speed? By my quick calculations the last rocket should approach c. If my numbers are off, please ignore that and adjust.
I know such a thing is impossible, because of the acceleration’s effect on mass, but what exactly would happen with the last few rockets? Nothing? Would the engines just burn with no effect? That’s what I think, but at what speed would this happen? Does each rocket become more massive than the last?
This is an infinity question, isn’t it?
Peace,
mangeorge
Speeds don’t add like that as you approach the speed of light. So that’s not what should happen, it’s just what would happen if we lived in a universe where Gallilean relitivity was universally applicable. Which we don’t.
As far as what would happen . . . the ship would get heavier as its speed increased, but so would the weight of the fuel. I’m no expert on rocket engines, but my understanding it that the basic concept is the fuel ignites, causing a pressure increase that drives the exhaust products out the back of the rocket and propels the rocket forward. But as the mass increased, the energy produced by burning the fuel would no longer be enough to propel the exhaust out the back of the rocket – at least not at such great velocities. And moreover, the force produced would not have as much an effect on the now more massive rocket. So the fuel would burn, but not much else would happen.
Also, just to clarify, relativistic effects don’t just happen right before you reach the speed of light. It’s just that that’s when they’re most noticable. But even if you’re travelling at a fraction of the speed of light, they can still be significant. So it’s not just the last few rockets that would be affected. I haven’t tried to calculate it, but I doubt this many rockets would get you anywhere near the speed of light. Just taking 186,000 mps and dividing by 7 mps isn’t going to give you an accurate answer for how many rockets you’d need.
It all depends on where you are observing it from. So, where is your observer?
Ignoring the relativistic effects. Rockets provide a roughly constant force. The acceleration they provide depends on the mass they’re moving. At the beginning when you have all these rocket engines and all the fule you’d be carrying, you’d get very little acceleration. This is one thing that makes travel to the stars so difficult. If you want to stop and visit and come back, you have to burn enough fuel to accelerate all that fuel thats going to stop you. And thast has to be enough to stop all the fuel you’ll use on the return trip.
Whoa, you got me there!
I’m not sure. On, or alongside the final rocket. Wherever one need be to observe the speed relative to it’s starting point. I personally don’t want to become infinitely massive, though. 
The observer on the final rocket will see his rocket pull away from the penultimate rocket at 7 fps. From his vantage point, he will be at a normal mass, length, and time will be passing at a normal rate. But the starting point, from his vantage point, will not be at the same mass, length, and time rate as when he left. The starting point, from the last rocket’s observation, will be more massive, contracted, and time will be moving more slowly than when the rockets left.
Good point – I was going to mention this when I first saw the question, then got caught up in talking about relativity and forgot about it.
To set up the situation mangeorge wanted, where relativity was the limiting factor, he’d have to have the second to last rocket able to give a 7 mps speed to itself and another rocket before exhausting all its fuel, meaning it would have to be larger than the last rocket. And the third to last rocket would have to be able to give that acceleration to itself and two more rockets, meaning it would have to be larger still. And since the second to last rocket was larger than the last one, this is more than just a linear increase we’re talking about. The initial rockets would have to be absurdly large, even ignoring relativity completely.
**tim314 **, each rocket is capable of accelerating itself and all the rockets ahead of it to the 25k from stop. Fuel and all that are no problem. My confusion is in what happens to the rockets as they approach c. Does the mass increase (logarithmically) as it nears c? Or does mass double at c/2? Do the rockets actually become heavier? If the latter is true, we’ve got a problem.
I think it’s coming to me. I need a cheeseburger.
I’ll be back.
As the rockets go faster their mass asymptotically approaches infinity as their velocity asymptotically approaches c (from the starting point’s vantage point).
As the speed of the rockets approach the speed of light with respect to their starting inertial reference frame, each rocket’s power is affected more and more by the Lorentz equation for adding velocities. Call the velocity before rocket i accelerates v[sub]i[/sub], and the additional velocity a given rocket adds u.
v[sub]i + 1[/sub] = (u + v[sub]i[/sub])/(1 + u * v[sub]i[/sub]/c[sup]2[/sup])
u = 7 mi/s =~ 11265.408 m/s
v[sub]26571[/sub] = 228202462.1 m/s, a bit more than 2/3 c.
don’t forget that as the rockets approach the speed of light their length wil shrink until they become two dimensional.
E=mc^2 the change in mass will increase with the amount of energy you put into the rockets according to this equation (no c/2 does not double the mass, mass does not depend on c it depends on energy)
correct me if i’m wrong but i believe einsteins famous formula is just a form of the formula for kinetic energy Ke=mv^2
Yes. And the energy required to accelerate aproaches infinity as the speed nears c, right. Can’t have that, can we? as energy goes infinite, mass goes to zero. Can’t have any mass with only two dimensions.
So moving at the speed of light is, in layman’s terms, impossible.
And 2/3c is way too slow for interstellar travel. Kinda slow, actually, even for practical interplanetary travel.
We’re going to have to cheat.
They won’t ever get two dimensional. They will asymptotically approach zero length (along the velocity vector) as they approach the speed of light (from the perspective of the starting point).
Well, it is the energy of a object at rest. At velocity v an object’s energy is E = mc^2 / (1 – v^2/c^2)^1/2
actually mass increase with energy. because c is a constant if we increase E m must increase. it’s also been demonstrated (i won’t say proven) in the labratory. they use particle accelerators to bring a particle up to the speed of light and collide it into a block of aluminum, the particle has momentum, it makes a tiny crater. they then repeat the experiment, bring the particle up speed of light, and then add more energy, and when it hits the block, it makes a bigger crater. the particle is still traveling at the speed of light, so in order to have more momentum to create a bigger crater, the mass must have increased. sorry i don’t have a cite for this experiment, just something i remember from physics class.
I understand that. I thought that mass would require infinite energy to attain the speed of light, then mass would become infinite, which is impossible because it becomes two dimensional. And mass cannot exist in two dimensions, and neither mass nor energy can become infinite. You can’t accelerate that particle to c. You can get close because you have little mass and a lot of energy available.
I think I got these ideas from reading some Steven Hawking’s stuff.
I’ll have to go to his website and see how I got such ideas. :eek: As good as an excuse as any, IMO.
IIRC, the Super Collider (sorry, Texas :)) was supposed to do what you speak of. Accelerate a particle to near light, then really near light speed that is.
That’s what all accelerators do, and have been doing for at least fifty years. The SSC would just do it a bit better.
Whaaat? How can you ignore relativistic effects? That’s like asking what does chocolate syrup taste like without chocolate! I mean, the question is a question about relativity! How can you ignore it? I mean, it’s a moot question, isn’t it, if one ignores relativity? …Is this the Zen of relativity?
Am I missing something here?
- Jinx
Better as in faster, correct? As I understand it, it takes a lot more accelerator to move a particle just a little bit faster.
What is the limit, anyway? .999c, .9999c? Does anybody know?
Here we go, from Wired;
I calculate that to be 14,500 m/s, or .078c. Wait a minnit, when I do it in mph, I get .78c. That sounds better. Which is closer to correct?
I’m gettimg sleepy.
0.078c is correct, which sounds awfully slow for a collider. I think your original numbers are wrong. The LHC website describes two of the design parameters as:
Machine Circumference: 26658.883 m
Revolution frequency: 11.2455 (*) kHz
(*) The exact value of the revolution frequency depends on the particle velocity and changes on the level of 0.1 Hz between the Pb beam at injection and the proton beam at 7 TeV. [i.e. blah blah blah]
If a particle can cover a distance of 26,658.883 meters 11,245.5 times a second, it’s velocity is 299,792,468.7765 m/s, or a very large fraction of the speed of light (actually, it’s 10 m/s faster than light, so I assume there’s a rounding error somewhere).