Sterotypical argument at work… Person at work states that, given enough fuel, the Ion engine on deep space-1 could conceivably push itself faster than the particles leaving the engine (68000 mph, per an article on http://www.space.com, if anyone knows the thrust, it would be appreciated)due to the fact that, in space, it would always be as if the craft were at 0 velocity and the particles would just keep accelerating the craft indefinitely, until of course, realtivity took over and it began to gain mass close to the speed of light. I say bullshit, the terminal velocity would be whatever the thrust of the particles propelling the craft is. Need some SDMB wisdom here.
Also, if anyone knows the speed (not pounds of thrust) of the propellent coming out our current shuttle rockets, it would also be appreciated…
I could be wrong about this (I’m sure the physics gurus will correct me if I am), but I don’t think propellant speed is a limiting factor. The fact that the drive is operating in space seems irrelevant (except for the practical problems of generating enough thrust to overcome gravity and friction with an ion drive). This appears to be basic Newtonian mechanics: as long as you’re accelerating propellant out of the drive, you’re accelerating everything attached to the drive in the opposite direction. The action/reaction pair is the accelerated particle and the ion drive.
I think your pal is right. Newton’s third still applies. Whether you’re a mile-wide tank full of xenon that’s doing twenty percent of the speed of light, or a lowly astronaut emptying the urine catch during an EVA, if you toss something away from you, you are going experience an equal and opposite reaction, however trivial it may be.
OK, gedanken experiment time. You’re on a sled, on level ice, moving at 10 mph forward. Friction is negligible. Now, you throw your little brother off the back of the sled, at a velocity of five mph backwards, relative to the sled. The sled will accelerate some, as a result.
Another way to look at it: If the probe has a maximum speed, then what is that speed relative to? The propellant speed is relative to the probe, but the probe doesn’t have a convenient reference frame. Of course, it’ll eventually run out of fuel, but that won’t necessarily happen before it reaches any given speed.
However, the speed of the propellant is important. The faster you throw stuff out the back, the less stuff you need to acheive a given acceleration. What this means is that although DS1’s thrust is miniscule, it can keep it up for a very long time. It’s been firing for hundreds of days now, and has only used a fraction of its fuel. By the time that it uses up all its fuel, it’ll have changed its velocity much more than a chemical rocket with the same amount of fuel would have.
Exhaust velocity of the shuttle rockets (the hydrogen rockets, not the solid fuel boosters) is about 4.5 km/s in vacuum, lower in the atmosphere.
low orbital velocity is about 8 km/s, which should demonstrate that a reaction engine can exceed the velocity of its reaction mass, and is in fact required to in the case of chemical rockets reaching orbit.
So I’m afraid your pal is right! Even if you’re travelling forward at the exhaust velocity of your rocket, you still get a “push” from slowing your reaction mass down to stationary.
As long as we’re answering rocket thrust questions, I’ve been wondering:
How do you calculate the thrust of a photon drive? Let’s say you react half a gram of matter with half a gram of antimatter, and can safely shoot all the resulting gamma ray photons out the back of your rocket. What is the resulting thrust? Is it one gram moving at the speed of light, calculated Newtonian? Or do you have to use relativistic calculation?
With a light drive, you absolutely must use the relativistic calculations. Specifically, you need the momentum of a photon, which is hf/c (h is Planck’s constant, f is frequency, and c is the speed of light). Your rocket will probably also eventually reach some pretty impressive speeds, so you’ll need relativity for that, too.
Objects do not gain physical mass when they go near relativistic speeds. They only behave as if they had (ie:needing more energy to get an acceleration).
Ranma, the same can be said about acceleration and gravity. For all intents and purposes, the craft has gained mass. It’s all about your frame of reference.
Not really. This is off topic, but the “gaining mass” thing bugs me.
Imagine a pair of objects traveling parallel to each other at relativistic speeds (relative to something else, to each other, they are stationary). If they were to actually gain mass, then an outside observer could detect that by the increased gravitational attraction between the objects. They’d accelerate toward each other faster than they normally would. This just strikes me as very wrong.
Or, for that matter, consider a mass just larger than it’s swartzchild radius. At rest, it’s just a big mass, but accelerate it to near C, and if it gains actual mass, it would become a black hole. Again, this strikes me as wrong.
If either of these scenarios are actually predicted by theory, I’d really like to hear someone knowledgeable explain it.
Didn’t Chronos post an example in another thread about rest mass vs. relativistic mass? I think he talked about a closed box with photons bouncing inside (the walls are lined with perfect mirrors of course :)). The gravitional pull of objects to the box would also be affected by the relativistic mass of the photons (which have zero rest mass). If I’m remembering it correctly, this would imply that TheNerd’s objects travelling next to each other would have an increased attraction. Maybe from one frame of reference they would seem to move to each other faster, but from another frame they wouldn’t.
OK, the trouble is not the velocity of the ion rocket, the trouble is the amount of reaction mass you can carry with you on your ion-rocket ship. Even if you postulate total conversion, you can still only accelerate your ship by the amount of delta-v you are carrying. Even if your ship is 90% fuel tanks with a total conversion engine, you’re going to run out of fuel very quickly. The higher the exhaust speed the more effective each gram of reaction mass is at increasing your speed, but you still have to keep throwing stuff out the back to accelerate.
Okay, the parallel objects scenario I can see being resolved due to relativistic time dilation. But the relativistic maybe-black-hole is more problematic. At least in my mind.
A photon emitted from the surface of the object either will or won’t escape. Ah screw it. I can tell I’m missing something fundamental here.
If your rocket (when empty) has more mass than its fuel, then there is no way to accelerate it faster than its exhaust. If it weighs less than its fuel, it must be moving faster than its fuel once all the fuel is exhausted.
Chronos
But the energy is hf/c[sup]2[/sup]. Since energy of photon= relativistic mass of photon, energy=hf/c[sup]2[/sup]=1 gram. So multiplying both sides by c, we get hf/c=(1gram)c which, as you said, is equal to the momentum. So momentum=(1gram)c, which the same as what you’d get with Newtonian physics.
The increase in mass is independent of frame of reference–the key thing here is to understand that relativistic mass is energy. When you accelerate something, you put more energy into it–therefore it has more “relativistic mass”. The tricky bit is that energy and mass are fundamentally the same thing. Thus, adding energy to something increases its gravitation.
Acceleration has a time component, which would be subject to dilation assuming that the objects involved are in different frames of reference. Maybe one of the physics gurus can explain what that effect would be, exactly.
As always, subject to correction or elaboration by those patently more knowledgable than myself.
OK, I’m thinking of the train-car thought-experiments that are classically used to teach about frames of reference.
From the experiments, if the train is going at a constant velocity (ie not accelerating) it is not possible for the passengers in the compartment to tell whether they are moving.
However, if what you say about increased mass is true, I would be able to tell, from within the car travelling at constant velocity, that something was up with the masses of objects in the compartment, thus contradicting the conclusion of the original experiment.
I just knew I was making trouble with that last post. Well, I’ll try to fix it. Maybe someone will come to my rescue if I screw it up.
Everything within the compartment gains mass in the same proportion, which provides an illusion of changelessness. The interactions within the compartment don’t appear to change, although more force is involved. Remember, F=ma, so if two masses increase in the same proportion, the acting force will increase without changing the acceleration. The objects in the compartment are exerting stronger gravitation on each other, but the increased mass of the objects balances the extra force. The mass of the accelerated system has increased, and this will affect the interactions of the accelerated objects with outside objects–regardless of relative velocity.
Umm…, I don’t think so. Movement is relative. If you are moving relative to, say, Earth. Your increase in mass is relative to Earth. In your frame there is no increase in mass. If the mass increased relative to you, where would the necessary increase in force come from that would keep the acceleration constant? In order to have an increase in mass in a moving frame relative to the frame, you need to suppose that there some absolute frame to measure the velocity. Relativity says that all motion is relative.