Is interstellar travel impossible due to kinetic energy magnitude?

[BitWiz]

There is no point invoking relativistic complications until this much is understood.

Thanks, jbriggs, I'll work on it.

Chris

 

[D H]

For propulsion of a rocket ship at non-relativistic speeds, if it takes mass ratio 1/x to get from 0 m/s to 1 m/s then it takes mass ratio 1/x² to get from 0 m/s to 2 m/s

That's not how rockets work, jbriggs.

Let's suppose the effective exhaust velocity of this rocket is 10 km/s. With your small velocities, Δv is proportional to fuel mass consumed. Double the quantity of consumed fuel mass and you double the change in velocity.

On the other hand, if you want to look at how much fuel is needed to get that rocket to 10 km/s versus 20 km/s, that factor of two becomes a factor of 4.67. From 20 km/s to 40 km/s, that factor of 4.67 becomes a factor of 47. To make matters worse, you aren't going to be able to more than quadruple (let alone that factor of 47) the amount of fuel without having bigger fuel tanks. Now you have more dead weight. The only way to get the final velocity equal to double the exhaust velocity is to use a multistage rocket. Getting to four times the exhaust velocity? That's about as fast as rockets can be pushed, even with multiple stages.



@BitWiz: If the classical rocket equation is a bad dream, the relativistic rocket equation is Nightmare on Elm Street.

 

[Nugatory]

That's why I'm having trouble with rocket KE measured from Earth. A rocket is an independent object in its own frame as soon as its acceleration overcomes gravity, imo, and its KE is undefined. It's KE would be exhibited in a collision with Earth, but then it would no longer be independent.

When we say "the frame of <something>" or "its frame" where "it" is some thing, that's just a convenient and somewhat sloppy shorthand for the more precise "a frame in which <something> has velocity zero".

Thus, the kinetic energy of the rocket is perfectly well defined in both the Earth's frame and the rocket's frame, just as the kinetic energy of the Earth is defined in both frames. All objects can always be described in any and all frames, and the dynamical quantities such as momentum and kinetic energy are defined for all objects no matter which frame you choose to do the arithmetic in. The numerical values of some of these (momentum and kinetic energy, for example) may be frame dependent, but they are not undefined.

 

[BruceW]

With classic Tsioilkovsky, delta-v is based in part on the difference in mass before and after the burn. In the example where I accelerated a single proton as the propellant, these masses are effectively the same such that

ln Mbefore/Mafter

is close to zero, which requires the specific impulse (Isp) to be huge. That's fine, but Isp, is based on exhaust velocity, and in relativistic Tsiolkovsky, I think Isp = effective velocity = actual exhaust velocity in a vacuum.

Since effective velocity is capped < c, we can never get to this Isp unless we allow the mass of the propellant to grow. I don't see this term in relativistic Tsiolkovsky. I presume I'm missing something very important, I just don't know what it is.

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.

 

[sophiecentaur]

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.

But, presumably, we want to slow up at the other end of the journey and stop of at the star Shangrila.

 

[jbriggs444]

That's not how rockets work, jbriggs.

Yes it is how rockets work. Do the math.

You have a 10 km/sec exhaust stream and you want to 1 m/s delta v. The required mass ratio is exp(0.0001) ~= 1.0001. If you start with mass m, you end with mass m/1.0001

Equivalently, if you start with 10000 kg of fuel, you end with approximately 9999 kg of fuel.

Repeat but now you want a 2 m/s delta v. The required mass ratio is exp(0.0002) ~= 1.0002. If you start with mass m, you end with mass m/1.0002.

Equivalently, if you start with 10000 kg of fuel, you end with approximately 9998 kg of fuel.

But guess what? 1/1.0001² ~= 1/1.0002

 

[BruceW]

But, presumably, we want to slow up at the other end of the journey and stop of at the star Shangrila.

yeah, true. So for the first stage of the journey, we could accelerate the rocket to something like 10% speed of light, then coast for most of the journey, then near the end of the journey, we'd need to accelerate in the opposite direction, to get back to zero velocity relative to the sun. The mass of fuel required for the deceleration is roughly 10% of the payload. And so (with a quick calculation), the mass of fuel required for the acceleration would need to be 11/10 of the mass for the deceleration. So the total mass of fuel needs to be 21% of the payload.

But, we might need to travel a lot further than just the nearest solar system, to find shangri-la :)

 

[sophiecentaur]

I know the answer to this (my following) comment will be "Technology will take care of it" but . . .

It will not just be a matter of traveling to another particular star - chosen as a result of Earthbound (or at least, Solar bound) observations. This imagined trip would need to be totally open ended. It is highly unlikely that our Scientists will have successfully selected one ideal planet, remotely. The 'trip' will be more of a 'tour', which would include visits to a number of candidate solar systems, separated by 'inter-stellar' distances (i.e. probably thousands of light years) before a serious candidate could be found for 'colonisation' and terraforming. So you need to multiply all the previous resource calculations several times. The 'ship' will need to be incomprehensibly massive and a nice place to live in.
I don't think this is so much of a technological problem as a sociological one. Any ship that's designed to suit human passengers on a permanent basis (i.e. over several generations) is actually going to be a very suitable environment to live in anyway. If a suitable ship design were ever to be completed then you would already have your ideal replacement for Earth. It would need to be; after all, it would consume a large chunk of terrestrial (or even solar system) resources. Humans would have, in fact, come up with their own artificial planet environment so why would they want to get off that onto a hostile, unknown world?
If the reason for leaving Earth were some impending disaster then, by leaving the Solar System, they would have achieved that. All they would need is a 'nearby' star to orbit (no Goldilocks planet needed) with some nearby asteroids that could be used as a source of materials.

As for the need for the human population to expand (a commonly held belief), in the next few generations, humans will have intellectually grown out of the Darwinian urge to breed and breed and be going for quality of life rather than quantity of people. Birth rate and standard of living are already strongly connected - despite the influence of the existing primitive religious beliefs.

 

[Ryan_m_b]

yeah. But once the exhaust velocity is a significant fraction of the speed of light,

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[/PLAIN] 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.

 

[phyzguy]

I know the answer to this (my following) comment will be "Technology will take care of it" but . . .

It will not just be a matter of traveling to another particular star - chosen as a result of Earthbound (or at least, Solar bound) observations. This imagined trip would need to be totally open ended. It is highly unlikely that our Scientists will have successfully selected one ideal planet, remotely. The 'trip' will be more of a 'tour', which would include visits to a number of candidate solar systems, separated by 'inter-stellar' distances (i.e. probably thousands of light years) before a serious candidate could be found for 'colonisation' and terraforming. So you need to multiply all the previous resource calculations several times. The 'ship' will need to be incomprehensibly massive and a nice place to live in.
I don't think this is so much of a technological problem as a sociological one. Any ship that's designed to suit human passengers on a permanent basis (i.e. over several generations) is actually going to be a very suitable environment to live in anyway. If a suitable ship design were ever to be completed then you would already have your ideal replacement for Earth. It would need to be; after all, it would consume a large chunk of terrestrial (or even solar system) resources. Humans would have, in fact, come up with their own artificial planet environment so why would they want to get off that onto a hostile, unknown world?
If the reason for leaving Earth were some impending disaster then, by leaving the Solar System, they would have achieved that. All they would need is a 'nearby' star to orbit (no Goldilocks planet needed) with some nearby asteroids that could be used as a source of materials.

As for the need for the human population to expand (a commonly held belief), in the next few generations, humans will have intellectually grown out of the Darwinian urge to breed and breed and be going for quality of life rather than quantity of people. Birth rate and standard of living are already strongly connected - despite the influence of the existing primitive religious beliefs.

The "planet-centric" idea is in error. The odds of finding a planet sufficiently close to Earth to live on is effectively zero. We are simply too finely tuned to conditions on Earth. Terraforming some suitable planet will simply take too long. The answer is in the second part of your statement - we will build artificial space habitats in the resource-rich environment of space. I envision us slowly spreading through the solar system over a period of centuries or millenia in artificial habitats until someone takes the difficult leap to a nearby star. In this scenario, there is no need for a suitable planet - any star has the necessary energy and resources. I highly recommend O'Neill's "The High Frontier" to those interested.

As to why will people do this - because they can. They may simply be looking for new resources or new challenges. We don't all have to agree to do it. It just takes one adventurous group to decide to do it. The resource requirements are not as great as you make it sound, especially after a long period of economic growth in the solar system. Another answer is that it appears that life on Earth is a rare, possibly unique thing. I (and others like me) believe that as stewards of this rare and wonderful planet, we have an obligation to spread our form of life through the galaxy, as opposed to simply sitting back and enjoying what we have until our environment here is snuffed out, as it certainly will be.

 

[sophiecentaur]

"Obligation"? To whom?

 

[sophiecentaur]

The main obligation is to look after this Earth that suits us so well. We are obliged to do this for the sake if all Earthbound life.

 

[phyzguy]

"Obligation"? To whom?

To our future descendants. Suppose you lived on a volcanic island in the middle of an ocean surrounded by an uninhabited world. You know the volcano is going to explode and obliterate the life on the island, but that won't happen for 100 years, well after you will be dead. Do you enjoy life while you are alive and feel happy that you aren't one of the ones that will be fried by the volcano, or do you undertake the difficult journey across the ocean to ensure that future generations have the chance to live? It sounds like you would choose the former, while I would definitely choose the latter. The only difference between that scenario and our life on Earth is a matter of timescale. As I said, I am not advocating we should head out to the stars today. I agree that the first order of business is to develop a sustainable lifestyle here on earth. But we need to recognize the fragility of life on Earth and take steps to spread it as far and wide as possible. I think it was Heinlein that said, "The Earth is too fragile a basket for the human race to keep all its eggs in."

 

[sophiecentaur]

It always makes me smile when Science Fiction stories are given as references on PF in connection with Space Travel. Never in other contexts. SciFi is the ultimate in speculation and PF does its best to discourage that.

 

[Ryan_m_b]

It's probably for the best if we all try to steer the discussion back to the original question on the technical/economic feasibility of propulsion good enough to make interstellar crossings in a reasonable time frame. Discussions of why this should be done (if possible) are interesting but tangential.

 

[phyzguy]

It's probably for the best if we all try to steer the discussion back to the original question on the technical/economic feasibility of propulsion good enough to make interstellar crossings in a reasonable time frame. Discussions of why this should be done (if possible) are interesting but tangential.

I'll shut up about the motivations. One comment on the feasibility that hasn't come up in these discussions. This is the idea that you "leave your rocket at home". A large stationary laser or mass driver can fire a beam into space which the space vessel intercepts to provide propulsion. This way the fuel does not have to be carried by the vessel, and it greatly improves the trade-offs. For example, suppose I want to send a small probe to Alpha Centauri. I build a large stationary laser, and aim it at the probe, which has a large reflector to reflect the laser light, thus continuously gaining momentum. Since for light, E = pc, the probe will accelerate with an acceleration a = 2P/(mc), where P is the power of the laser, and m is the mass of the probe. A 100 kg probe and a 1 Gigawatt laser will give you a proper acceleartion of about 0.07 m/s^2, and get you to Alpha Centauri in about 40 years, at which point you are traveling at about 0.2c. Of course, this assumes that a 100 kg probe is big enough to actually be useful, that you don't want to decelerate when you get there, and that you can keep a 1 GWatt laser aimed at it over interstellar distances, but you get the idea.

 

[Nugatory]

...and that you can keep a 1 GWatt laser aimed at it over interstellar distances

Both aimed and properly collimated.

 

[sophiecentaur]

I'll shut up about the motivations. One comment on the feasibility that hasn't come up in these discussions. This is the idea that you "leave your rocket at home". A large stationary laser or mass driver can fire a beam into space which the space vessel intercepts to provide propulsion. This way the fuel does not have to be carried by the vessel, and it greatly improves the trade-offs. For example, suppose I want to send a small probe to Alpha Centauri. I build a large stationary laser, and aim it at the probe, which has a large reflector to reflect the laser light, thus continuously gaining momentum. Since for light, E = pc, the probe will accelerate with an acceleration a = 2P/(mc), where P is the power of the laser, and m is the mass of the probe. A 100 kg probe and a 1 Gigawatt laser will give you a proper acceleartion of about 0.07 m/s^2, and get you to Alpha Centauri in about 40 years, at which point you are traveling at about 0.2c. Of course, this assumes that a 100 kg probe is big enough to actually be useful, that you don't want to decelerate when you get there, and that you can keep a 1 GWatt laser aimed at it over interstellar distances, but you get the idea.

That could be an excellent idea for some scenarios but, eventually, the inverse square law comes into play and there will be some distance where you just can't focus your 'motive beam' effectively and most of your energy gets lost. I don't know the optics of this but I reckon you would be limited to launching small vehicles into big solar orbits and no more.
It puts me in mind of a suggestion to use a vast, very fine net of reflecting wires, suspended over the Earth by radiation pressure from a transmitter. The reflected signal could cover almost a hemisphere of footprint. It was in the New Scientist many years ago and I think someone had done some valid sums to suggest that a few GW would do it. Choosing the right shape would ensure the reflector held itself in place (better than geostationary because it could be over any point on the Earth . It would need a pretty wide exclusion zone for space launches, which may not have been considered too much when the original article was written.

 

[BitWiz]

When we say "the frame of <something>" or "its frame" where "it" is some thing, that's just a convenient and somewhat sloppy shorthand for the more precise "a frame in which <something> has velocity zero".

Thanks, Nugatory. I think I'm looking for the term or usage that means "two observers accurately measure the same thing, but MUST get different results." I think that occurs if the two observers have a non-zero velocity in any axis with respect to each other -- and -- they are not using an independent third object to establish their reference frame.

EDIT: I should probably say "CAN" instead of MUST, since there can be cancelling terms.

Thus, the kinetic energy of the rocket is perfectly well defined in both the Earth's frame and the rocket's frame, just as the kinetic energy of the Earth is defined in both frames. All objects can always be described in any and all frames, and the dynamical quantities such as momentum and kinetic energy are defined for all objects no matter which frame you choose to do the arithmetic in. The numerical values of some of these (momentum and kinetic energy, for example) may be frame dependent, but they are not undefined.

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. Terrified Earthlings in the target zone disagree.

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?

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?

Thanks! ;-)

Chris

 

[Nugatory]

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.

 

[BruceW]

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[/PLAIN] 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.

 

[BitWiz]

Hi, 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

 

[BitWiz]

Hi, Bruce,

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

 

[BitWiz]

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

 

[Nugatory]

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.

 

[BruceW]

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).

 

[BitWiz]

Hi, 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

 

[bob012345]

When we say "the frame of <something>" or "its frame" where "it" is some thing, that's just a convenient and somewhat sloppy shorthand for the more precise "a frame in which <something> has velocity zero".

Thus, the kinetic energy of the rocket is perfectly well defined in both the Earth's frame and the rocket's frame, just as the kinetic energy of the Earth is defined in both frames. All objects can always be described in any and all frames, and the dynamical quantities such as momentum and kinetic energy are defined for all objects no matter which frame you choose to do the arithmetic in. The numerical values of some of these (momentum and kinetic energy, for example) may be frame dependent, but they are not undefined.

The kinetic energy in the Earth's frame is well defined and makes sense but the real question is does that accurately represent the energy actually expended from the ships point of view. I argued this with a friend who says yes, it does. I'm still struggling with the concept.

A simple example. Consider firing a bullet from a gun with velocity v. Call its kinetic energy K. Now, consider a big plane flying at the same v. Fire the gun in the direction of motion inside the plane. The kinetic energy wrt the planes frame is K. But the bullet is going at 2v wrt the ground if velocities add linearly as they do so the kinetic energy as computed from the ground is 4K. It started with K wrt the ground, being on board the plane moving at v yet the chemical energy released was the same in both cases. So the question is how did the bullet end up with 4K of kinetic energy wrt the ground frame when only K of additional chemical energy was added to its initial energy of K wrt the ground? I'm stumped.

 

[jbriggs444]

So the question is how did the bullet end end up with 4K of kinetic energy wrt the ground frame when only K of additional chemical energy was added to its initial energy of K wrt the ground? I'm stumped.

What about the recoil of the gun? If you choose to use a frame where the gun is moving, the energy subtracted from it by recoil is non-negligible and accounts for the discrepancy you see.

 

[bob012345]

What about the recoil of the gun? If you choose to use a frame where the gun is moving, the energy subtracted from it by recoil is non-negligible and accounts for the discrepancy you see.

The recoil would make the relative velocity wrt the ground frame less, not more. I could devise an equivalent frame such as another planet moving past us such that the recoil effects would be the same as in the ground frame. Basically, I think we can ignore the recoils. Treat it as an idealized problem please.

 

[jbriggs444]

The recoil would make the relative velocity wrt the ground frame less, not more. I could devise an equivalent frame such as another planet moving past us such that the recoil effects would be the same as in the ground frame. Basically, I think we can ignore the recoils. Treat it as an idealized problem please.

This is incorrect. Recoil is the source of the discrepancy. The recoil of the gun makes the gun's energy less, not more. That's what balances the books with the extra energy that shows up in the bullet.

 

[bob012345]

This is incorrect. Recoil is the source of the discrepancy. The recoil of the gun makes the gun's energy less, not more. That's what balances the books with the extra energy that shows up in the bullet.

I don't get that especially if the recoil is not going to change the velocity of the plane much since it has an almost infinite mass by comparison. Also, I showed a scenario where the recoil is the same in both frames.

The point not clear in you answer is what is the actual energy it takes to make the bullet go at basically 2v wrt the ground. Kinetic energies don't subtract. Thanks.

 

[jbriggs444]

I don't get that especially if the recoil is not going to change the velocity of the plane much since it has an almost infinite mass by comparison.

Infinite mass times an infinitesimal change in velocity gives a finite change in energy. The answer I have given twice now is still correct. Do the math.

 

[bob012345]

Infinite mass times an infinitesimal change in velocity gives a finite change in energy. The answer I have given twice now is still correct. Do the math.

I think you are saying that the whole plane slowed down due to recoil just enough to 'balance' the energy so the total amount of energy of the system of plane, gun and bullet is only increased by the the amount of energy the gun powder released. The bullet is going about 2v and has about 4K but borrowed some of it from the planes vast reserves.

 

[jbriggs444]

I think you are saying that the whole plane slowed down due to recoil just enough to 'balance' the energy so the total amount of energy of the system of plane, gun and bullet is only increased by the the amount of energy the gun powder released. The bullet is going about 2v and has about 4K but borrowed some of it from the planes vast reserves.

Yes, that is correct.