Spacecraft With Solar Mass Energy Equivalent Kinetic Energy

[Devin-M]

Suppose in a different star system, a space shuttle sized spacecraft acquired a solar mass energy equivalent amount of kinetic energy, then passed through our solar system. While it was passing through the solar system would the craft’s gravitational effects be more similar to the space shuttle or to the sun?

 

[berkeman]

Kinetic energy? So a Space Shuttle traveling at 0.99c?

 

[Devin-M]

Yes.

 

[Ibix]

Space shuttle.

"Relativistic mass" is not a source of gravity in any naive sense. Look at it in the rest frame of the shuttle - it's at rest. Why would it expect to go around yanking planets out of orbit?

"Relativistic mass" is a concept best forgotten. It just confuses people.

 

[Vanadium 50]

would the craft’s gravitational effects be more similar to the space shuttle or to the sun?

Is a kumquat more like a saxophone or a pigeon?

It's not like either one.

 

[PeterDonis]

Moderator's note: Thread moved to relativity forum.

 

[PeterDonis]

While it was passing through the solar system would the craft’s gravitational effects be more similar to the space shuttle or to the sun?

The source of gravity in GR is not "mass" (relativistic or otherwise), it is the stress-energy tensor. It is true that in the solar system rest frame, the SET of the craft in your scenario would include a very large kinetic energy component; but it would also include a very large momentum component, and when you work out the math, it turns out that the momentum has the opposite effect from the kinetic energy, so they pretty much cancel. That means the intuitive answer that @Ibix gave--look at the source in its own rest frame--is pretty much correct. Certainly it is much closer to being correct than just looking at the total energy and ignoring everything else.

 

[jartsa]

Look at it in the rest frame of the shuttle - it's at rest. Why would it expect to go around yanking planets out of orbit?

With its rest-mass, helped by extreme gravito-magnetism, perhaps?

Can I say that, moderators? Maybe Ibix can understand?

 

[Ibix]

With its rest-mass, helped by extreme gravito-magnetism, perhaps?

So, you are proposing that in the rest frame of the shuttle we can observe a planet (very blue shifted) orbiting its sun for millenia suddenly fly out of orbit when it gets near a small shuttle because of gravitomagnetism?

Or are you referring to the direction change of the shuttle relative to distant stars, from the perspective of the shuttle?

 

[jartsa]

So, you are proposing that in the rest frame of the shuttle we can observe a planet (very blue shifted) orbiting its sun for millenia suddenly fly out of orbit when it gets near a small shuttle because of gravitomagnetism?

Or are you referring to the direction change of the shuttle relative to distant stars, from the perspective of the shuttle?

First one. In the frame of the shuttle there exists gravito-magnetism between the sun and the planet.

(Let us keep in mind that the speed of the solar system is ridiculously close to c in the frame of the shuttle)

(It's less weird in the frame of the planet)

 

[Ibix]

First one. In the frame of the shuttle there exists gravito-magnetism between the sun and the planet.

And you think the shuttle will affect this?

I'd love to see some maths.

 

[jartsa]

And you think the shuttle will affect this?

I'd love to see some maths.

In the planet frame math is easy. Just a super energetic particle (shuttle) passes the planet.

 

[Ibix]

In the planet frame math is easy. Just a super energetic particle (shuttle) passes the planet.

You haven't shown that it yanks the planet out of its orbit. Peter already stated why the effect of the passage of the shuttle is negligible.

 

[jtbell]

"Relativistic mass" is not a source of gravity in any naive sense. Look at it in the rest frame of the shuttle - it's at rest. Why would it expect to go around yanking planets out of orbit?

Expanding on this a bit... Suppose you're inside the shuttle, looking out the window at the planets zipping past you at 0.99c. Everything inside the shuttle is normal. Why would you expect the planets' paths to be deflected?

 

[PeterDonis]

With its rest-mass, helped by extreme gravito-magnetism, perhaps?

Can I say that, moderators?

No. You are cluttering the thread with uninformed and wrong speculation.

As such, since you explicitly asked for moderator feedback, you have now been banned from further posting in this thread.

 

[PeterDonis]

In the planet frame math is easy. Just a super energetic particle (shuttle) passes the planet.

If the math is so easy, go do it. And find out what the answer is, instead of waving your hands and cluttering the thread.

 

[Ibix]

@pervect usually cites Olson and Guarino. I think only the abstract is available, but the conclusion stated there is that the deflection angle of a high speed object is higher by a factor of $1+\beta^2$ than a Newtonian analysis, where $\beta=v/c$ is the speed of the shuttle.

 

[PeterDonis]

@pervect usually cites Olson and Guarino. I think only the abstract is available, but the conclusion stated there is that the deflection angle of a high speed object is higher by a factor of $1+\beta^2$ than a Newtonian analysis, where $\beta=v/c$ is the speed of the shuttle.

The abstract of that paper, though, shows a factor of $\gamma$ in what they call the "active gravitational mass", i.e., taken at face value, they seem to be saying that the relativistic mass is the source of gravit, with an extra GR factor of $1 + \beta^2$ that comes in for similar reasons as in the analysis of light bending by the Sun.

However, they are defining "active gravitational mass" in a very narrow way: it is "measured by the transverse (and longitudinal) velocities which such a moving mass induces in test particles initially at rest near its path". That is not the same as the kind of "gravitational effects" that the OP is asking about.

I have so far been unable to find a non-paywalled version of the Olson & Guarino paper (for example, a preprint does not appear to be on arxiv.org), so I can't comment on the details of their reasoning. But I would be cautious about interpreting it with regard to this discussion.

 

[Vanadium 50]

It has been a long time since I did this, but I believe the factor of ~2 is right. It's the same as the factor of 2 in the deflection of light.

Note that neither of the two suggestions of the OP is correct.

 

[Vanadium 50]

As far as "gravitomagnetism", while there is an effect that can be called that, I can think of exactly zero cases where this is the best way to solve problems in GR. There may be one or two where it's simpler by accident, but it's probably at least as much work to verify that the answer is right as to do it correctly in the first place. It's fairly useless.

 

[PeterDonis]

Note that neither of the two suggestions of the OP is correct.

I agree that neither one is exactly correct, but the question is which (if either) one is reasonably close to being correct.

 

[Vanadium 50]

But neither is reasonably close. One is off by a factor of 2 and the other by a factor of a zillion.

You can say 2 is closer, but that's like saying the American Revolution happened last week is more correct than saying it happened yesterday. In some sense it is, but still...

 

[PeterDonis]

You can say 2 is closer, but that's like saying the American Revolution happened last week is more correct than saying it happened yesterday. In some sense it is, but still...

No, it's like saying that the American Revolution happened two centuries ago is more correct than saying it happened yesterday. Yes, neither is exactly correct, but one is indeed a lot closer than the other. Just like a factor of 2 is a lot closer than a factor of a zillion.

 

[Vanadium 50]

Let's improve the analogy - Did the American revolution happen yesterday or in 1900 (factor of 2). If someone were to ask which is right, shouldn't we say neither?

If you present two wrong alternatives, making one more wrong does not make the other more right.

 

[PeterDonis]

Let's improve the analogy - Did the American revolution happen yesterday or in 1900 (factor of 2). If someone were to ask which is right, shouldn't we say neither?

I would say that which is "right" is not the important question. The important question is, which, if either, of these is close enough?

In the case of your analogy, I would agree that neither is close enough, because historically speaking, yesterday is not much more different from the 1770s and 1780s than 1900 was. They're both very different from the time of the American Revolution, and there are many significant historical events in between in both cases, so neither one is close enough. (Note that by this criterion, even saying that the American Revolution happened in the 1790s is not close enough, since the Constitution, a significant historical event, was in between then and the revolution. So I should indeed retract my earlier statement that "two centuries" would be reasonably close. You would need to say two and a half centuries.)

In the case of the OP's question, however, being only a factor of 2 off from the correct answer might well be close enough for many purposes. Sure, you'll be somewhat off when predicting the exact perturbations on test objects in the path of the flyby. But you will correctly predict that no significant disruption of the solar system as a whole will occur.

Whereas being off by a factor of a zillion won't be anywhere near close enough for anything. There you're expecting the solar system to be seriously disrupted, when nothing like that will actually occur.

 

[Ibix]

The abstract of that paper, though, shows a factor of $\gamma$ in what they call the "active gravitational mass"

Indeed. I think I need new glasses.

I have so far been unable to find a non-paywalled version of the Olson & Guarino paper (for example, a preprint does not appear to be on arxiv.org), so I can't comment on the details of their reasoning. But I would be cautious about interpreting it with regard to this discussion.

The obvious problem with the application of their reasoning here is that they are likely using the Schwarzschild metric, which implies that the shuttle must be a test particle with zero active mass. Thus the planet can't react at all.

We could try considering it as an elastic collision. The Earth has rest mass $M$ and initial and final Lorentz gamma factors $1$ and $\Gamma'$, and the shuttle has mass $m$ and initial and final gammas $\gamma$ and $\gamma'$. Conservation of the zeroth component of four momentum is $M+\gamma m=\Gamma' M+\gamma'm$, which becomes $\Gamma'=1+\frac mM(\gamma-\gamma')$. To escape from the solar system the Earth needs a gamma factor of about $1+10^{-9}$ and given a mass ratio between the shuttle and Earth of about $10^{-20}$ that means the shuttle has to decrease its gamma factor by about $10^{11}$ in the interaction.

I don't immediately see how that could happen.

 

[Nugatory]

Expanding on this a bit... Suppose you're inside the shuttle, looking out the window at the planets zipping past you at 0.99c. Everything inside the shuttle is normal.

Is the Aichelburg/Sexl solution relevant here?

 

[Ibix]

Is the Aichelburg/Sexl solution relevant here?

I believe that's how a test particle describes the Schwarzschild metric of the near-$c$ Earth, but I think that again implicitly assumes no gravitational effect of the test particle on the Earth.

 

[Nugatory]

I believe that's how a test particle describes the Schwarzschild metric of the near-$c$ Earth, but I think that again implicitly assumes no gravitational effect of the test particle on the Earth.

Ah - right.

 

[PeterDonis]

The obvious problem with the application of their reasoning here is that they are likely using the Schwarzschild metric, which implies that the shuttle must be a test particle with zero active mass.

I don't see how they could be since they are explicitly giving a nonzero active gravitational mass to the object (the shuttle in this scenario). That's why I want to look at the details of their paper: I want to see how they are actually modeling things mathematically.

 

[Ibix]

I don't see how they could be since they are explicitly giving a nonzero active gravitational mass to the object

Are they? I think pervect's description of the paper is that they fire an array of test particles at a Schwarzschild metric with mass $M$ with "speed at infinity" $\beta$ and look at the angles between the asymptotes of the orbit. The particle mass doesn't appear anywhere in the abstract, anyway. So I think only one of their objects is gravitationally active; here we're at least considering the possibility that both are.

 

[Vanadium 50]

Since we have decided this is A level....

It's not that the factor of 2 might be "close enough". It is conceptually wrong. It is implicitly saying that the g₀₀ part of the metric must be considered but not the equally large g₁₁ part. If it is saying anything at all, it's saying we only need to worry about spacetime curvature in the time direction, not in the spatial directions.

(If it is saying anything relativistically at all, of course. It looks to me more quasi-Newtonian - i.e. "GR is the same as Newtonian gravity, provided you plug in a different number for mass")

 

[PeterDonis]

Are they?

The abstract, which is all we have, gives an explicit expression for what they call the active gravitational mass of the object. That expression is not zero.

The particle mass doesn't appear anywhere in the abstract

Yes, it does. The formula explicitly given in the abstract is $\gamma M \left( 1 + \beta^2 \right)$.

 

[PeterDonis]

Since we have decided this is A level

I've split the difference with the OP and changed the thread level to "I".

 

[PeterDonis]

I think pervect's description of the paper is that they fire an array of test particles at a Schwarzschild metric with mass $M$ with "speed at infinity" $\beta$ and look at the angles between the asymptotes of the orbit.

But if we are going to translate that to this scenario, we would have to combine this solution with the metric of the solar system. And the question is how much doing that would change the final metric from the one we already have for the solar system. Our intuitive answer in this thread has been "not very much". But if we take the formula in Olson & Guarino's abstract at face value, as I said before, that would not be correct.

The problem I have with that face value answer, however, is that if we switch to the shuttle's rest frame, it is obvious, as you pointed out, that the shuttle's effect on the overall spacetime geometry is miniscule. And that can't change just because we changed frames--this is just another version of the answer (given in a number of previous PF threads) to the common question of why an object doesn't turn into a black hole if it goes fast enough.

Furthermore, again if we look at things in the shuttle's rest frame, what effect would we expect on the shuttle due to the solar system? Say due to the Sun, to make things simpler. Olson & Guarino's formula, taken at face value, says we should expect the Sun's effect to be $\gamma M_S \left( 1 + \beta^2 \right)$--in other words, a huge effect compared to the Sun's effect when at rest. At the gamma factor we are talking about, the result of that formula is something like $10^{20}$ solar masses, i.e., comparable to the total mass in our observable universe. Is that really the correct answer? It can't be that simple, because all that mass concentrated into a volume like that of the Sun would indeed be a black hole, but we already know that is not the correct answer.

As I say, I haven't looked at the detailed math, either in the Olson & Guarino paper or on my own, so all this is just intuitive. But it seems to me that there must be a disconnect somewhere since what the Olson & Guarino paper appears to say is so different from our intuitive answer in this thread.

One possible resolution of the disconnect might come from asking, where did all the energy come from to boost the shuttle to such a huge gamma factor? Suppose, for example, that we detonated a 2 solar mass star in such a way that it boosted two shuttles, each to the same gamma factor, in opposite directions (so total momentum in the original star's rest frame remains zero). We would have expected the original star to have a significant effect on the spacetime geometry around it, so it seems like we should also expect the two shuttles thrown off in the explosion to have a significant effect on the spacetime geometry surrounding them.

Then the real issue might be the specific form of the effect. The fact that the shuttles are each moving at a tiny smidgen less than the speed of light, in the original star's rest frame (which means, to a good approximation, in the rest frame of any other star systems they pass through) means that they are only within a short enough distance to have a significant effect for a short time--short enough that the overall effect remains small, as our intuitive answer in this thread has it. (That is one way of heuristically describing the effect of the momentum components of the stress-energy tensor that I talked about earlier.) In other words, instead of being a nice spherically symmetric Schwarzschild field as the original star's field was, we now have two narrow "world tubes" filled with stress-energy whose effects will be very different from those of the original star.