# Is interstellar travel impossible due to kinetic energy magnitude?

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P: 3,462
 Quote by BitWiz T A hollow comet is closing in on Earth. I am perched inside the comet, and to my way of thinking, I'm weightless and at rest. There is no measurable velocity or acceleration. To me, my comet has undefined KE.
It's not undefined, it's zero - this follows from the fact that the comet has zero velocity relative to you. You don't need to open the window to know that the comet has zero velocity relative to you.

 I drift over to my comet window and look out. Holy cow, a planet is coming at me. Look at all that KE! And it's accelerating. What incredible power is required to make a planet accelerate that fast?
Its the same physics whether you're looking out the window or not. The comet's KE was zero relative to you before you looked out the window and it's still zero after you've looked out the window.

 Is something similar going on when using Earth-bound KE measurements to determine the fuel requirements of an interstellar rocket? I am inside my rocket. When not accelerating, I am virtually at rest. Whenever I DO accelerate, I will always experience the same amount of acceleration per fuel unit (disregarding mass loss of the propellant), yet Earth-bounders will see huge jumps in KE. Where is the disjunct?
You being at rest in the rocket is something of a red herring here. The travel problem that we're trying to solve is: start with a spaceship that is at rest relative to the earth, and supply enough kinetic energy to it to change its speed sufficiently to get it to arrive at a nearby star at a given time (let's ignore the relativistic issues about how we would define that given time in a frame-independent way - you need to understand the classical physics before we introduce relativistic complications - for now it suffices to say that it can be done).

We can solve that problem using inertial coordinates in which the earth is at rest or in which the earth is moving at any speed in any direction, or non-inertial coordinates in which the ship or anything else we want is at rest. No matter which we choose, the ship will experience the same proper acceleration; that's a frame-independent quantity.

The calculation may be more or less hairy according to which coordinates we choose, and the initial and final speed and kinetic energy of the ship and its exhaust gases may be wildly different according to coordinate system we choose.

We usually solve this problem using coordinates in which the earth is at rest and the initial kinetic energy of the ship is zero, but that's just because the calculation is less hairy using that frame than many others. But whichever we coordinates we choose... we will find that the same amount of fuel must be burned to accelerate the ship through its journey. That's a frame invariant quantity.
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 Quote by Ryan_m_b An exhaust velocity that high would require significant advances (but then again every suggestion in this thread would). The highest estimate I could find is for a beamed-core antimatter rocket that could have an effective exhaust velocity of ~.7c Beamed Core Antimatter Propulsion: Engine Design and Optimization Ronan Keane, Wei-Ming Zhang But that would require significant amounts of antimatter. The second order consequences of a world in which antimatter can be mass produced are far more daunting than sending something interstellar.
very true. I'm only trying to counter what BitWiz seems to think - that it is not even possible in principle. I agree that sending people on an interstellar voyage is definitely not possible with technology in the near future. It would be the very far future. And by that time, it is possible that other technology would have arisen, which we can't even predict at the moment. So maybe rockets are not the kind of technology that would get people there anyway.

edit: or as sophiecentaur says, we may all get wiped out before anyone ever travels to another solar system. Who knows? I'm just saying it could be possible in principle. I'm not suggesting that it is likely.
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Hi, Nugatory, ;-)

 Quote by Nugatory It's not undefined, it's zero - this follows from the fact that the comet has zero velocity relative to you. You don't need to open the window to know that the comet has zero velocity relative to you.
I didn't explain myself very well. I'm the observer. I'm trying to determine the KE of the comet to something else. There is no something else, therefore I think my KE is undefined.

 Its the same physics whether you're looking out the window or not. The comet's KE was zero relative to you before you looked out the window and it's still zero after you've looked out the window.
I was referring to the KE of Earth. As far as I'm concerned in the comet, I'm at rest. I have no sense of velocity and no sense of measurable acceleration. I'm adrift in gravity-space-time. But now I see out the window that not only do I have a planet's worth of KE coming at me, it's increasing exponentially as the planet accelerates.

My point is (I think) that KE is not symmetrical. When multiple views are available, an Earth observer may see a set of circumstances that conform to his/her expectations, but that does not invalidate the circumstances seen by the observer on the other object.

So I come back to my original question: are Earth-observer-based KE calculations fair when determining fuel requirements for a rocket?

Thanks!

Chris
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P: 64
Hi, Bruce,

 Quote by BruceW yeah. But once the exhaust velocity is a significant fraction of the speed of light, the classical equation no longer works. The relativistic equation (when the exhaust velocity approaches the speed of light) is: $$\Delta v = c \frac{m_0^2 - m_1^2}{m_0^2+m_1^2}$$ where ##m_0## is total rest mass of the rocket (payload and propellant) at the start of the journey, and ##m_1## is the final rest mass of the rocket. And since we don't care about a return journey, we can just say ##m_1## is equal to the rest mass of the payload.
This is starting to make sense. And it looks familiar. Is this hypertrig?

Chris
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 Quote by BruceW very true. I'm only trying to counter what BitWiz seems to think - that it is not even possible in principle. I agree that sending people on an interstellar voyage is definitely not possible with technology in the near future. It would be the very far future. And by that time, it is possible that other technology would have arisen, which we can't even predict at the moment. So maybe rockets are not the kind of technology that would get people there anyway.
Hi, Bruce,

No, I'm not advocating the pessimistic position of the Joint Propulsion people, and in fact, I'm pretty upset about it. I really want my own starship, and how am I going to get one if the propulsion people have already given up?!

I admit to trying to "hide" my feelings since what I really want is unbiased information, but perhaps I went too far advocating the propulsion expert's position, which -- if the posts I've seen so far both here on PF and elsewhere represent the trend -- is a majority opinion. However, "Poppycock!" is not a reasoned counterargument, so I need bullets. Pass the ammo, please.

Chris
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P: 3,462
 Quote by BitWiz So I come back to my original question: are Earth-observer-based KE calculations fair when determining fuel requirements for a rocket?
And I'll give you the same answer I gave you in the previous post:

Yes, because no matter which observer you use to base the kinetic energy calculations on, you will get the same answer for the fuel burn and amount of energy that has to be generated by the rocket's propulsion system to send the rocket on its journey.

 I didn't explain myself very well. I'm the observer. I'm trying to determine the KE of the comet to something else. There is no something else, therefore I think my KE is undefined.
You don't need any something else to answer questions such as: "What is the kinetic energy of the comet using a frame in which the comet is at rest?"; "What is the kinetic energy of the comet using a frame in which the comet is moving at speed X?"; "what is the kinetic energy of the comet using a frame in which the comet is moving at speed Y?". In all questions of this form, the comet has well-defined kinetic energy (zero, for the first one).
Of course if the comet is approaching the earth at speed X, then you may expect that the earthlings are mostly asking the second question... but the question would be just as meaningful and would have the same answer if there were no earth and earthlings.
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 Quote by BitWiz Hi, Bruce, No, I'm not advocating the pessimistic position of the Joint Propulsion people, and in fact, I'm pretty upset about it. I really want my own starship, and how am I going to get one if the propulsion people have already given up?! I admit to trying to "hide" my feelings since what I really want is unbiased information, but perhaps I went too far advocating the propulsion expert's position, which -- if the posts I've seen so far both here on PF and elsewhere represent the trend -- is a majority opinion. However, "Poppycock!" is not a reasoned counterargument, so I need bullets. Pass the ammo, please. Chris
haha, awesome. Well, they were definitely talking about the near future. No-one can say anything for certain about technology in the far future. I think the bad news is that neither of us will be getting a starship anytime in the near future.

edit: to anyone who says that interstellar travel will never be possible (even in the far future), just say "Any sufficiently advanced technology is indistinguishable from magic" (Arthur C. Clarke).
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P: 64
Hi, Nugatory,

 Quote by Nugatory ... Yes, because no matter which observer you use to base the kinetic energy calculations on, you will get the same answer for the fuel burn and amount of energy that has to be generated by the rocket's propulsion system to send the rocket on its journey. ...
If I use a precise quantity of energy to accelerate an ideal rocket, ignoring gravity et al, then it will attain a final velocity that precisely corresponds to its measured KE from its zero velocity origin. Is this correct?

If an observer in the rocket integrates proper, measured acceleration with proper time, will he come up with the same final velocity?

Thanks,

Chris

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