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## Rocket physics question

Ok, I should probably know the answer to this, but I can't convince myself that I do. Anyways, when a rocket is in space, will it accelerate as long as the engine is firing, or will it reach a terminal velocity.

For example. Lets assume that the thrust leaves the engine at 1000 m/s. Is the rocket's top speed 1000 m/s, or will it continue to accelerate as long as the engine is running?

2. It will keep accelerating as long as the engine is running. (Unless you get close to the speed of light when relitivity makes things more complex)

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thx, that's what I thought initially, but then I was trying to convince myself otherwise.

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## Re: Rocket physics question

Originally Posted by jgravatt
For example. Lets assume that the thrust leaves the engine at 1000 m/s. Is the rocket's top speed 1000 m/s, or will it continue to accelerate as long as the engine is running?
Let me explain more, because this is a tricky one. You are wondering if when the rocket gets to 1000 m/s the exhaust stream now going at 0 m/s (relative to whatever you measured the speed of the rocket against) still does anything. If its not moving, how can it propel the rocket? Easy: Relative to the ROCKET, the fuel is still moving backwards and has the same momentum (and force required to accelerate it to that speed) as it always did. The force generated by the engine is independent of the speed of the rocket. The acceleration force is constant.

5. Originally Posted by zebo-the-fat
It will keep accelerating as long as the engine is running. (Unless you get close to the speed of light when relitivity makes things more complex)
well, not that complex really. IT Will keep accelerating, but as you get closer to the speed of light it will take it longer and longer to gain more speed.

6. Well, fuel tank limitations (really the ratio of the mass of the rocket+payload to the mass of the fuel) and the specific impulse of the fuel/rocket engine will get you long before you approach the speed of light - at least with our current technology. Given the the ratio of the mass of the rocket+payload to the mass of the fuel and the specific impulse, that defines the maximum delta-V you get with a vehicle, so yes, there really is a terminal velocity, but it's not quite like the terminal velocity you would get falling out of the sky or if you have a magic rocket with unlimited fuel and no penalty for the mass of the fuel.....

Jim.

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I was reading in Pop Sci's special issue on the future of spaceflight (yeah, yeah, I know they're not a particularly... um... credible source), wherein they quoted a physicist that the maximum speed for a rocket is about twice the speed of the exhaust exiting the nozzle. I understand the whole constant acceleration thing, so I was wondering where the guy came up with this idea.

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Originally Posted by Betenoire
I was reading in Pop Sci's special issue on the future of spaceflight (yeah, yeah, I know they're not a particularly... um... credible source), wherein they quoted a physicist that the maximum speed for a rocket is about twice the speed of the exhaust exiting the nozzle. I understand the whole constant acceleration thing, so I was wondering where the guy came up with this idea.
It's the rocket equation. V/Ve = ln(Mr), where V is the final velocity of the rocket, Ve the effective velocity of the exhaust, and Mr the ratio of the initial weight of the rocket to the final weight ((payload+structure+fuel)/(payload+structure)). It's a bit more complicated for multi-stage rockets, but that's a detail. Mass ratios of 20 are doable, but that's pushing fairly hard. That gives a final velocity of about 3x your exhaust velocity. A mass ratio of 10 puts your final velocity at about 2.3x your exhaust velocity.

9. Originally Posted by jscotti
Well, fuel tank limitations (really the ratio of the mass of the rocket+payload to the mass of the fuel) and the specific impulse of the fuel/rocket engine will get you long before you approach the speed of light - at least with our current technology. Given the the ratio of the mass of the rocket+payload to the mass of the fuel and the specific impulse, that defines the maximum delta-V you get with a vehicle, so yes, there really is a terminal velocity, but it's not quite like the terminal velocity you would get falling out of the sky or if you have a magic rocket with unlimited fuel and no penalty for the mass of the fuel.....

Jim.
very true. I was just addressing the speed of light statement. Let say there was an infinite fuel sourse the rocket was using that never changed in amount of thrust it provided, nor did the mass of the rocket ever change.

The my earlier post would would be correct. ( I just kinda lept ahead of myself earlier and forgot to mention what i just did...oops)

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Originally Posted by kenneth rodman
Let say there was an infinite fuel sourse the rocket was using that never changed in amount of thrust it provided, nor did the mass of the rocket ever change.
Though, isn't the reason that it takes the rocket longer and longer to gain velocity as it approaches the speed of light due to the fact that the added energy from the acceleration has added mass to the rocket?

(From my limited understanding, someone please correct if necessary!) If a rocket were hypothetically able to accelerate without gaining mass, would there actually be anything stopping it from reaching and surpassing the speed of light?

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Originally Posted by WorseAstronomer
(From my limited understanding, someone please correct if necessary!) If a rocket were hypothetically able to accelerate without gaining mass, would there actually be anything stopping it from reaching and surpassing the speed of light?
I'm not sure how to answer this. The people aboard the rocket don't think they've gotten any heavier, and don't think the rocket is any heavier. They also don't think they've gotten any closer to the speed of light. If the rocket had some sort of space drive that allowed it to go faster but not gain mass according to our frame of reference then the rocket is no longer behaving as if it's in our space/time, so i suppose pretty much anything could happen.

12. Originally Posted by daver
The people aboard the rocket don't think they've gotten any heavier, and don't think the rocket is any heavier.
Of course, because they and the rocket are at rest relative to themselves.

Originally Posted by daver
They also don't think they've gotten any closer to the speed of light.
Surely this is false? Not only will they think that they have got closer to the speed of light, it will even seem to them (eventually) that they have exceeded it. An accelerating frame of reference is not inertial; so it's possible to measure the speed of light from a light-source as greater or less than c. No?

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Originally Posted by Eroica
Originally Posted by daver
They also don't think they've gotten any closer to the speed of light.
Surely this is false? Not only will they think that they have got closer to the speed of light, it will even seem to them (eventually) that they have exceeded it. An accelerating frame of reference is not inertial; so it's possible to measure the speed of light from a light-source as greater or less than c. No?
OK, then don't play with the accelerating reference frame. Shut down the engines and measure the speed of light to see how close they've gotten. Of course, they will never get any closer--it will always take the same amount of time for a flash of light from the stern to reach the bow (and the same amount for a flash from the bow to reach the stern).

14. You never see yourself approach the speed of light because no matter what your speed or acceleration relative to anything, c is c. When you start accelerating though, the path that light takes is distorted because of the gravity equivalence. Gravity bends light. In your non-inertial frame of reference, you perceive a gravitational field backwards equal to that of the rocket's acceleration relative to an inertial frame. So light is bent accordingly.

jgravatt, think of thrust not in terms of speed, but in terms of momentum, which is of course dependant on speed. A certain mass, m, of exhaust is propelled out of the rocket and at a certain speed, v, each second. Therefore each second, the exhaust material, that was initally at rest relative to the rocket, has been given a momentum of mv backwards from the rocket.

By Newton's Third Law of motion, this cannot just happen. In order for exhaust to gain momentum, something else must receive equal and opposite momentum in that time, ergo the rocket. So the rocket too receives mv forwards each second. Hence, it is propelled forwards. Therefore, as long as their is exhaust to be expelled backwards, the rocket can continue to accelerate forwards.

This of course means that theoretically, there is no top speed according to Newtonian mechanics, but there is obviously a top practical speed, which depends on how much change in momentum can be given to the rocket before it exhausts its fuel.

15. It is all a matter of frame of reference. Given unlimited fuel, your rocket will:
A) Approach ever closer to the speed of light - as seen by an outside observer.
B) Accelerate continuously, eventually exceeding the speed of light - as seen by occupants of the rocket.

16. t is all a matter of frame of reference. Given unlimited fuel, your rocket will:
A) Approach ever closer to the speed of light - as seen by an outside observer.
B) Accelerate continuously, eventually exceeding the speed of light - as seen by occupants of the rocket.
Ok keep in mind im not a scientist, ect. But from what I understand, the rocket would never reach the speed of light. It would come closer and closer but never attain light speed.

Similar to take taking an inch:1----------0 and cutting the distance in half each time you move. you will never reach 0. 1 1/2 1/4 1/8 1/16 ect

17. From the point of view of an outside observer, you are correct. But, from the point of view of an occupant, the universe will appear to be speeding by faster and faster, without limit. As I said, it depends on your frame of reference. If you were to travel at the speed of light (as seen from an outside POV) any trip, of any distance, would be instantaneous (from your POV). Welcome to the stange world of relativity.

18. Originally Posted by Kaptain K
It is all a matter of frame of reference. Given unlimited fuel, your rocket will:
A) Approach ever closer to the speed of light - as seen by an outside observer.
True.

Originally Posted by Kaptain K
B) Accelerate continuously, eventually exceeding the speed of light - as seen by occupants of the rocket.
False. You would never see yourself approach the speed of light. Relative to you, you are at rest and light is travelling at c. That is a fact for all frames. But the observer, who sees you approaching the speed of light, would become contracted. But light will still appear to travel at the same speed relative to you.

19. Originally Posted by Glom
Originally Posted by Kaptain K
It is all a matter of frame of reference. Given unlimited fuel, your rocket will:
A) Approach ever closer to the speed of light - as seen by an outside observer.
True.

Originally Posted by Kaptain K
B) Accelerate continuously, eventually exceeding the speed of light - as seen by occupants of the rocket.
False. You would never see yourself approach the speed of light. Relative to you, you are at rest and light is travelling at c. That is a fact for all frames. But the observer, who sees you approaching the speed of light, would become contracted. But light will still appear to travel at the same speed relative to you.
If you are traveling at 99.99+% of 'c' (from an external POV) and pass Sirius in 5 minutes of subjective time, I would say that (from your POV) you are going faster than light!

20. Wrong. Sirius was appear to you be only about four light minutes away in subjective space. It's not just time that is contracted. It's also length.

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Yeah, what Glom said.

If you knew that Alpha Centauri was 4.3 light years away and you saw it pass by only two years after you passed the earth, you might think that your effective speed was greater than the speed of light. But if looked outside your window you'd see the universe flying past at 90%c and notice that the sun was only 1.8 l.y. from Alpha C.

22. Originally Posted by Glom
Relative to you, you are at rest and light is travelling at c. That is a fact for all frames.
That is a fact for all inertial frames. In an accelerating frame of reference, light travels faster or slower than c.

23. Originally Posted by Eroica
In an accelerating frame of reference, light travels faster or slower than c.
As I understand it, and of course I could be wrong, a non-inertial frame doesn't affect the speed of light, merely its trajectory. The light path will bend towards the equivalent gravity field, but it will still be travelling at c.

24. If you are accelerating directly towards a star and you measure the time it takes a pulse of starlight to pass your ship, you will get a value greater than c. If you are accelerating away from the star, the value will be less than c. The light is moving in a straight line, so where does it bend? The equivalent gravity field is directly in front of or behind you.

Of course, I too could be wrong. :-k

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