Is interstellar travel impossible due to kinetic energy magnitude?

[phyzguy]

Agreed, I often get annoyed at this comparison. The thing is about space is that there isn't any destination remotely analogous to on on Earth. Here there's a free biosphere to keep us supplied with everything we need from food to a microbiome. The first European settlers to the Americas might have had a hard crossing on the ocean but when they got there they had plenty of natural resources to untilise.

Furthermore people underestimate how many people are needed to sustain a high tech economy. When you live in wooden houses and most of what you need can be built by a blacksmith or carpenter all you need is a few hundred, perhaps less, people to maintain a healthy society. Filling all the specialised roles of a modern economy would take far more, potentially hundreds of thousands of people. If we were ever to build a self sufficient colony somewhere not on Earth not only would we have to make massive advances in ecosystem design and maintainence as well as mass manned space travel but we'd need to find a way to transport thousands upon thousands of people as well as supply them with a small industrial city's worth of infrastructure. The rugged Wild West it is not, Hong Kong in space maybe.

I agree with most of what you said here. "Hong Kong in space" is a good way to think of it. However, just because it will be difficult doesn't mean that it will forever be impossible. As I said earlier, assuming economic growth continues (and there's no reason to assume that it will not), then the resources to build a colony on Mars or out in space will be relatively accessible in another century or so. Note that a colony in space (not necessarily on a planet) need not be self-sufficient from the very beginning. It would be perfectly acceptable to be dependent on resources from Earth for a period of time, even a long period of time, while the infrastructure in space grew.

 

[BitWiz]

Hi, Bruce,

This is a very neat conversation.

It does take that into account. That's why it's called the relativistic Tsiolkovsky equation :)

I don't think we care about propellant mass, per se. What we care about is the amount of force we can apply to whatever propellant mass we have, even if it's a single proton. Theoretically (I think), we can pump unlimited KE into a proton, and as it approaches the speed of light, its effective mass will increase to allow us to keep pumping it in. This is where specific impulse (and Tsiolkovsky) go off the rails, imo, because the effective propellant mass is variable, and we're not using the propellant as a reactant.[/QUOTE]

If you think about it intuitively, the rest mass of the fuel you carry on board only needs to be very small, to give a huge amount of momentum to the spaceship, as long as you expel the propellant at close to the speed of light. Of course, the problem is that our technology is most likely not able to do such a thing. But this comes back to the statement that our technology is not nearly advanced enough to allow for interstellar space travel. This is different than the statement that it is not possible even in principle.

I think it was a statement in principal. I believe it takes about a petajoule to accelerate a kg to 10% c at 50% efficiency using Earth-frame KE as the standard. That's doable if several percent of the original kg is antimatter, but fusion is out. There are two problems: 1) antimatter is never going to be feasible, imo, not least due to the lack of antimatter filling stations in the galaxy; and 2), 10% c does not cut it. Much, much too slow.

I made a point of stating that the propulsion system accelerated propellant over a distance of a single meter to simplify the KE of the propellant. "Distance" is a variable relativistically, and I would think a propellant cranked up to a high gamma will see a correspondingly shortened path through the accelerating field. You mentioned later that there is no "proper KE," but I wonder if our accelerated proton would agree with its KE measurement by a shipboard observer, not to mention an Earth-based observer.

I'm not sure what you mean here.

I think "distance" is an overemphasized dimension in our units of measure regarding space travel. Doesn't distance vary depending on the closing or opening velocity between an observer and any object?

As for using one-meter to accelerate propellant, that just simplifies the KE discussion by assigning "1" to the numerator of propellant velocity.

Uh, the KE with respect to sun is important because the sun is effectively the inertial reference frame that the spaceship initially has zero velocity according to.

I think I get that. What I don't get is why in gravity free space my KE goes up in a power curve while my fuel use is linear. I guess that goes back to my original question. Why does my rocket need three times the energy to double its speed?

yeah, thanks for making this thread :)

;-)

 

[jbriggs444]

I don't think we care about propellant mass, per se. What we care about is the amount of force we can apply to whatever propellant mass we have, even if it's a single proton. Theoretically (I think), we can pump unlimited KE into a proton, and as it approaches the speed of light, its effective mass will increase to allow us to keep pumping it in. This is where specific impulse (and Tsiolkovsky) go off the rails, imo, because the effective propellant mass is variable, and we're not using the propellant as a reactant.

Unlimited KE is not free. It has to come from somewhere. If it comes from carried fuel then it has mass and Tsiolkovsky applies. If it comes from the outside then it carries momentum and you might as well use the momentum directly.

I think "distance" is an overemphasized dimension in our units of measure regarding space travel. Doesn't distance vary depending on the closing or opening velocity between an observer and any object?

Irrelevant if we're talking about the requirement to maintain a particular proper acceleration for a given period of time using on-board fuel and reaction mass.

What I don't get is why in gravity free space my KE goes up in a power curve while my fuel use is linear. I guess that goes back to my original question. Why does my rocket need three times the energy to double its speed?

Velocity is relative. What does it even mean to double speed? Where did you decide that it takes three times the energy to do so. Three times what energy?

 

[BitWiz]

Hi, jbriggs, thanks for the reply.

Unlimited KE is not free. It has to come from somewhere. If it comes from carried fuel then it has mass and Tsiolkovsky applies. If it comes from the outside then it carries momentum and you might as well use the momentum directly.

If we can, I'd like to separate the source of the energy from the propulsion mechanism to help me understand this.

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.

Velocity is relative. What does it even mean to double speed? Where did you decide that it takes three times the energy to do so. Three times what energy?

Agreed. 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.

The "three times" has to do with a mass having four times the KE at 2 m/s than at 1 m/s. If I've already accelerated from at-rest to 1 m/s, then I will have to add triple the amount of energy expended so far to get to 2 m/s. At least according to KE.

Thanks for your help! ;-)

Chris

 

[jbriggs444]

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,

Frames of reference are not physical. They are notional. You can use whatever frame of reference you like. But if you want it to be inertial, you need to be consistent. Having picked one you need to keep using it. Or transform out of it.

You do not enter or leave a frame of reference because your "acceleration overcomes gravity".

The original problem here involved interstellar travel. It would be "cheating" to adopt a frame of reference in which a spacecraft starts at rest while two stars whip past at speeds barely below the speed of light (and with a coordinate separation that is very small) and then claim to have solved the problem of interstellar travel. Adopting a frame of reference in which the Earth is at rest is a reasonable starting point.

The "three times" has to do with a mass having four times the KE at 2 m/s than at 1 m/s. If I've already accelerated from at-rest to 1 m/s, then I will have to add triple the amount of energy expended so far to get to 2 m/s. At least according to KE.

But that has nothing to do with rocket propulsion.

For propulsion of a car on the highway using the Earth as its reaction mass, if it takes x energy to get from 0 m/s to 1 m/s then it takes 4x energy to get from 0 ms to 2 ms.

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

The difference in the two scenarios involves the energy being pumped into the exhaust stream. If your "exhaust stream" is the planet Earth and you are accelerating a Chevy to 1 m/s, you can ignore the energy being imparted to the Earth -- it's negligible.

If your exhaust stream is produced by a solid-fueled rocket motor and you are accelerating the same Chevy, the energy being imparted to the exhaust stream is quite significant.

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

 

[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.