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Staticman
2011-Apr-08, 12:03 PM
Taking into account conservation of energy, If an orbiting star (say a pulsar in a binary system) was emitting EM radiation (x-rays for instance) at such a rate that its mass would decrease in a significative amount per time in relation to its total mass, how would that affect its orbit? would it alter it in some way?

Hornblower
2011-Apr-08, 12:31 PM
Taking into account conservation of energy, If an orbiting star (say a pulsar in a binary system) was emitting EM radiation (x-rays for instance) at such a rate that its mass would decrease in a significative amount per time in relation to its total mass, how would that affect its orbit? would it alter it in some way?

I would expect the same effect as with an aging star that is losing mass through a strong stellar wind. Its gravitational hold on an orbiting body would be weakened, and the orbit would gradually spiral out. That of course is assuming that the emission is spherically symmetrical so there is no net jet action.

Staticman
2011-Apr-08, 03:55 PM
I would expect the same effect as with an aging star that is losing mass through a strong stellar wind. Its gravitational hold on an orbiting body would be weakened, and the orbit would gradually spiral out. That of course is assuming that the emission is spherically symmetrical so there is no net jet action.

I thought the same thing, but then I saw the formula for elliptical orbits specific orbital energy on wikipedia : E=-G(M+m)/2a and it would seem to indicate that if we keep the left side constant a mass decrease must go along with a semimajor axis distance decrease, so the orbit should rather spiral in. I'm not sure this is right, though.
Any hint?

Strange
2011-Apr-08, 04:00 PM
But you are not keeping the LH side constant; you are radiating away energy.

jfribrg
2011-Apr-08, 04:12 PM
Let's assume that the mass of the satelite is negligible compared to the star that it is orbiting. Momentum is conserved so if mass is lost in the form of xray radiation, wouldn't that potentially affect the momentum and therefore the orbit? If the xrays are emanating evenly in all directions, then I would think that the satelite would continue in its same orbit, but lets say that all of the xrays are directed away from the star. In that case, wouldn't the satelite move closer in compensation for the momentum of the mass that was lost in the form of xrays? Or is conservation of momentum different when you are dealing with mass-energy equivalence?

Staticman
2011-Apr-08, 04:23 PM
But you are not keeping the LH side constant; you are radiating away energy.

Hmm.That's a tricky point, I was assuming local conservation of total energy, but I'm not sure actually. Still, intuitevely to me it seems that by radiating energy away, it substracts from the orbital energy so the star should spiral in.

Staticman
2011-Apr-08, 04:29 PM
Let's assume that the mass of the satelite is negligible compared to the star that it is orbiting. Momentum is conserved so if mass is lost in the form of xray radiation, wouldn't that potentially affect the momentum and therefore the orbit? If the xrays are emanating evenly in all directions, then I would think that the satelite would continue in its same orbit, but lets say that all of the xrays are directed away from the star. In that case, wouldn't the satelite move closer in compensation for the momentum of the mass that was lost in the form of xrays? Or is conservation of momentum different when you are dealing with mass-energy equivalence?
This is an interesting point too, I was considering a pulsar in the OP, it gets complicated because of the spin of the beam, could it make a difference whether the pulsar spins one way or the other wrt the star in the binary?

Cougar
2011-Apr-08, 08:07 PM
Taking into account conservation of energy, If an orbiting star (say a pulsar in a binary system) was emitting EM radiation (x-rays for instance) at such a rate that its mass would decrease....

Well, I was surprised to learn that the EM radiation from a pulsar can originate from (large magnetic field) acceleration of protons and electrons from the pulsar surface, resulting in an electromagnetic beam emanating from the poles of the magnetic field. This would indeed, obviously, reduce the mass of the pulsar.

Apparently there is another category of pulsars: Accretion-powered pulsars, which account for most but not all X-ray pulsars, in which case the pulsar would be gaining mass (ETA: or at least not losing mass).

Regarding orbits, just logically, the space around a smaller central mass will be "less curved," resulting in 'wider' orbits. But I guess you're concerned about that equation and its association with this logic...

Staticman
2011-Apr-09, 10:09 PM
Well, I was surprised to learn that the EM radiation from a pulsar can originate from (large magnetic field) acceleration of protons and electrons from the pulsar surface, resulting in an electromagnetic beam emanating from the poles of the magnetic field. This would indeed, obviously, reduce the mass of the pulsar.

Apparently there is another category of pulsars: Accretion-powered pulsars, which account for most but not all X-ray pulsars, in which case the pulsar would be gaining mass (ETA: or at least not losing mass).
This quote from the WP page on pulsars is not very encouraging: "The theory of how pulsars emit their radiation is still in its infancy, even after nearly forty years of work."



Regarding orbits, just logically, the space around a smaller central mass will be "less curved," resulting in 'wider' orbits. But I guess you're concerned about that equation and its association with this logic...
But remember that curvature comes not only from mass, the stress energy tensor includes the EM radiation so the curvature would remain as long as the EM radiation persisted.
For instance in the case of radiating away energy in the form of gravitational waves, stars end up spiraling in. I just wonder if the same thing would happen if enough power in relation with the total mass of the pulsar in a binary was radiated away in the form of EM radiation.

Hornblower
2011-Apr-10, 01:54 AM
snip...

But remember that curvature comes not only from mass, the stress energy tensor includes the EM radiation so the curvature would remain as long as the EM radiation persisted.
For instance in the case of radiating away energy in the form of gravitational waves, stars end up spiraling in. I just wonder if the same thing would happen if enough power in relation with the total mass of the pulsar in a binary was radiated away in the form of EM radiation.

I don't think so. We are talking about two fundamentally different actions here. If two inert bodies are losing kinetic energy to gravitational radiation, they are not losing any of their mass, so their gravitational attraction toward each other is not being weakened. If one of them is losing mass fast enough in a spherically symmetrical manner, either by EM radiation or by blowing away whole atoms in a stellar wind, then I would expect the aforementioned tendency to spiral out to prevail. If this mass loss is a small enough trickle, then the gravitational radiation effect may prevail.

Staticman
2011-Apr-10, 10:50 AM
If two inert bodies are losing kinetic energy to gravitational radiation, they are not losing any of their mass, so their gravitational attraction toward each other is not being weakened.

I have not said anything about attraction being weakened. I think you missed my point.
The example about gravitational radiation was just to underline that radiating energy away from a binary system leads to orbital decay, I didn't mean to mix the two forms of radiation.
I guess you are thinking about your example on post #2, but I don't think it is the same case we are dealing with here. Yours was a central star loosing mass to stellar wind, so that an orbiting object with negligible mass wrt the central mass (acting as a test particle) would certainly spiral out if the loss of mass was significative.
However in a binary system with two objects with almost the same mass, they orbit around their center of mass and if one of them is radiating x-rays or gamma-rays with enough intensity, I would think the orbital energy of the system would have to adjust to it and probably produce orbital decay.

WayneFrancis
2011-Apr-11, 06:14 AM
Taking into account conservation of energy, If an orbiting star (say a pulsar in a binary system) was emitting EM radiation (x-rays for instance) at such a rate that its mass would decrease in a significative amount per time in relation to its total mass, how would that affect its orbit? would it alter it in some way?

I'm trying to get my head around "was emitting EM radiation (x-rays for instance) at such a rate that its mass would decrease in a significative amount per time in relation to its total mass"

I know that pulsars slow down their spin fairly rapidly but loose significant mass? As I understand it xray pulsars are caused in binary systems where the neutron star has the accretion material end up on its magnetic poles where the impact is responsible for the xray emission. In this case it is the companion star that is loosing mass. Regardless of this loosing mass in itself won't change the orbit. Anything at a given orbit will have the same orbital period. IE A 1kg rock at 1AU will have the same orbital period as the Earth does.

Staticman
2011-Apr-11, 10:28 AM
I know that pulsars slow down their spin fairly rapidly but loose significant mass?.....
It is more of a thought experiment, I'm not saying pulsars do indeed loose significant mass, as the quote of WP I wrote above says, there seems to be little real knowledge about the radiative processes in pulsars.


Regardless of this loosing mass in itself won't change the orbit.
I already explained that it is not so much the mass loss as the energy carried away from the orbit.

Hornblower
2011-Apr-11, 12:20 PM
It is more of a thought experiment, I'm not saying pulsars do indeed loose significant mass, as the quote of WP I wrote above says, there seems to be little real knowledge about the radiative processes in pulsars.


Regardless of this loosing mass in itself won't change the orbit.
I already explained that it is not so much the mass loss as the energy carried away from the orbit.

My opinion from post #2 stands.

As I think I understand the OP, this is indeed a thought experiment, a hypothetical case in which one body loses a significant fraction of its original mass by whatever means. This is different from a case in which the bodies gradually lose orbital energy by means of gravitational radiation, but retain all of their initial mass.

Suppose the mass ejection is in the direction of the orbital motion. The result is a retrograde recoil of the remaining body, as when the retro rockets are used to bring an orbiting spacecraft down. The orbit will decay.

Suppose the ejection is in the opposite direction. Now we have a prograde recoil, as when a spacecraft in a parking orbit is inserted into an escape trajectory. The orbit expands.

Now suppose we have a momentary spherically symmetrical mass ejection, at high speed compared to the orbital velocity. Here is where it gets interesting. Let us start with both bodies losing mass this way, to make it geometrically simple.

Before the event let us have two bodies of equal mass, in circular orbits around their barycenter. Let the two bodies undergo identical symmetrical ejections, so that there is no net recoil on either one. For the moment their velocities and separation are unchanged, but the gravitational deflection of each one toward the center is reduced. That reduces the curvature of their trajectories and they start moving farther apart. What they are doing now is moving in elliptical orbits that are tangent to the original circular orbit at their periapsis points. The mean value of the separation, the major axis of the new ellipse, is greater than the original separation.

If instead of a momentary, large ejection we have a gradual sustained process, we will get a gradual spiralling out instead of a sudden change from the original circle to a larger ellipse. If the ejection is slow enough, the gravitational radiation decay just might overpower it and cause the orbits to decay instead of expanding.

Now suppose only one body loses mass this way. Start with body A and body B of equal mass. Body A ejects part of itself with the remnant initially retaining its original velocity. Now the curvature of A's trajectory is unchanged initially because heavy and light bodies gravitate toward the other body at the same rate. B's curvature is diminished when the shell of ejecta passes its position and its gravitational influence self-cancels. Thus the two bodies start moving farther apart as before. The subsequent motion becomes more complicated to analyze in this unbalanced case, but I remain completely confident in my opinion that the new orbit is an enlarged ellipse.

What I have done here is a Newtonian analysis in which relativistic complications such as gravitational radiation are taken as negligible in proportion to the magnitude of the hypothetical mass losses. The orbital elements can be checked with rigorous analysis of the potential and kinetic energy of the moving bodies. If anyone does it correctly and finds any errors in my presentation, please speak up. I am here to learn as well as comment.

Clear as mud? As usual it is a pain in the neck to try to demonstrate it visually in a forum like this. It is an awkward substitute for walking pupils through the exercise on a blackboard in a classroom, or one-on-one with pencil and paper at a desk.

Staticman
2011-Apr-11, 02:58 PM
...........

What I have done here is a Newtonian analysis in which relativistic complications such as gravitational radiation are taken as negligible in proportion to the magnitude of the hypothetical mass losses. The orbital elements can be checked with rigorous analysis of the potential and kinetic energy of the moving bodies. If anyone does it correctly and finds any errors in my presentation, please speak up. I am here to learn as well as comment.


One thing, I'd say that if you include "curvature" in your analysis, it is no longer Newtonian. That's why I think is more useful to attack the problem from the energetic side.
It might be as Waynefrancis said, and the orbit would neither decay nor enlarge. But then wouldn't the star gain velocity as it loses mass to keep its kinetic energy unchanged?

Staticman
2011-Apr-12, 12:01 PM
To simplify, it all seems to come down to this, nobody has been able to refute the fact that orbital decay of binary pulsar systems indicates that energy gets radiated away in some form, GR seems to point to the gravitational radiation form even though the radiation hasn't been detected yet (many experiments currently trying hard to achieve this).
But in a thought experiment scenario, in a binary system of stars orbitally decaying, physically nothing impedes this energy from being radiated in the form of EM radiation, is this right?

Hornblower
2011-Apr-12, 03:01 PM
To simplify, it all seems to come down to this, nobody has been able to refute the fact that orbital decay of binary pulsar systems indicates that energy gets radiated away in some form, GR seems to point to the gravitational radiation form even though the radiation hasn't been detected yet (many experiments currently trying hard to achieve this).
I have not attempted to refute the GR prediction that gravitational radiation would carry away orbital energy and cause the orbit to decay, and neither has anyone else in this thread. In fact, I believe the physicists whose calculation knowhow in GR exceeds mine. I accept the prediction that in the absence of opposing actions, the orbit will decay. Reports of observations of orbital decay in pulsar binaries reinforces my acceptance.

What I did was present my opinions about three hypothetical scenarios in which one or both of the orbiting bodies eject some of their mass. The three possibilities involved a prograde recoil, a retrograde recoil, and a symmetrical ejection in which there is no recoil of the remnant. I gave partial predictions of the effects on the orbital motion, and explained why I expected those results. In addition I said that if even a prograde action is slight enough, I would expect the gravitational radiation decay action to overpower it.

Your OP appears to involve a hypothetical mass ejection event of some sort, with a resulting reduction in the mass of what's left of the body. Whether the ejecta consists of electromagnetic radiation or intact atoms and ions is beside the point, if I am not mistaken. If you meant something else, you may need to review your writing and post a revision with appropriate explanation.


But in a thought experiment scenario, in a binary system of stars orbitally decaying, physically nothing impedes this energy from being radiated in the form of EM radiation, is this right?

It is my understanding that gravitational radiation is different from EM radiation.

Staticman
2011-Apr-12, 06:07 PM
Your OP appears to involve a hypothetical mass ejection event of some sort, with a resulting reduction in the mass of what's left of the body. Whether the ejecta consists of electromagnetic radiation or intact atoms and ions is beside the point, if I am not mistaken. If you meant something else, you may need to review your writing and post a revision with appropriate explanation.
Actually in the OP nothing is said about ejecting matter or mass transfers from one star to the other, that was added by you and others in posterior posts, in those particular cases I agree the orbit period increases.
The OP just considers the "what if" posibility of a big output of EM radiation from a pulsar, much bigger than is currently observed, and asks what kind of orbital change it would produce. By parallelism with the explanation of the decay of binary systems orbits by radiating away energy in the form of gravitational radiation I figured that radiating away an excess of energy similar to that radiated in the form of gravitational radiation but in the form of EM radiation would lead to the same kind of orbital change, since energy is energy regardless of the specific form. If something is wrong with this reasoning I would like for someone to correct me. Just remember there is no mass transfer involved and the EM radiation would be perfectly spherically symmetric to avoid mixing up the problem with gravitational radiation (wich demands some asymmetry of the source to be radiated).

It is my understanding that gravitational radiation is different from EM radiation. Sure, the only thing they have in common and that I'm highlighting is that they can both carry away energy from system.

chornedsnorkack
2011-Apr-12, 07:41 PM
Consider the following:

1) A orbiting test body of small mass compared to primary radiates EM (for example heat) in centrally symmetric fashion in its own reference frame.

Then it is neither accelerated nor decelerated. Its energy decreases and so does its mass. Its orbit is unchanged.

From the reference frame of primary, the EM is slightly concentrated in forward direction because of Doppler shift, so carrying away angular momentum.

2) It is the primary that is radiating EM in centrally symmetric manner.

Now it is the angular momentum of secondary that stays constant. Its energy decreases, because it spirals out and the primary mass decreases.

3) The small mass secondary is radiating EM, for example because it carries an electric monopole charge.

Radiation of orbiting monopole does cause the orbit to shrink. And the obvious explanation is that such an aerial EM radiation is far more concentrated in forwards direction that radiation which is centrally symmetric in the secondary frame of reference.

Regarding gravitational radiation, I expect that gravitational radiation should, like electromagnetic radiation, cause orbital decay because it is concentrated in forward direction.

Hornblower
2011-Apr-13, 12:23 PM
Actually in the OP nothing is said about ejecting matter or mass transfers from one star to the other, that was added by you and others in posterior posts, in those particular cases I agree the orbit period increases.

The OP just considers the "what if" posibility of a big output of EM radiation from a pulsar, much bigger than is currently observed, and asks what kind of orbital change it would produce.

Reprint of the OP:

Taking into account conservation of energy, If an orbiting star (say a pulsar in a binary system) was emitting EM radiation (x-rays for instance) at such a rate that its mass would decrease in a significative amount per time in relation to its total mass, how would that affect its orbit? would it alter it in some way?

My bold. You did indeed specify a reduction in the mass of the body in question.


By parallelism with the explanation of the decay of binary systems orbits by radiating away energy in the form of gravitational radiation I figured that radiating away an excess of energy similar to that radiated in the form of gravitational radiation but in the form of EM radiation would lead to the same kind of orbital change, since energy is energy regardless of the specific form. If something is wrong with this reasoning I would like for someone to correct me. Just remember there is no mass transfer involved and the EM radiation would be perfectly spherically symmetric to avoid mixing up the problem with gravitational radiation (wich demands some asymmetry of the source to be radiated).

Sure, the only thing they have in common and that I'm highlighting is that they can both carry away energy from system.

My bold again. You are mentioning similarity, but there is an important difference. The emission of EM radiation from the body, if symmetrical, causes no net recoil on the body and leaves its velocity unchanged for the moment. If this action results in a significant reduction of the body's mass, as suggested in the OP, then I expect the reduced gravitational binding to allow the orbit to expand.

The asymmetry of the action that generates the gravitational radiation does indeed put a drag on the body, causing orbital decay if stronger than the aforementioned opposing tendency.

Hornblower
2011-Apr-13, 12:39 PM
Consider the following:

1) A orbiting test body of small mass compared to primary radiates EM (for example heat) in centrally symmetric fashion in its own reference frame.

Then it is neither accelerated nor decelerated. Its energy decreases and so does its mass. Its orbit is unchanged.

From the reference frame of primary, the EM is slightly concentrated in forward direction because of Doppler shift, so carrying away angular momentum.

...snip

The body now has slightly less mass than before. An extreme case would be fusion of a mass of hydrogen into helium, with about 0.7% of the original mass carried off as gamma radiation. What is left has less momentum, but if the emission was symmetrical it still has the same speed. As I think I understand it, no acceleration or deceleration in either frame of reference.

I realize that photons are considered massless and the trend is away from using "relativistic mass" in the current terminology, but it remains my understanding that before the radiation was emitted, the energy that was bottled up in the body gave it the practical effect of being more massive than afterward.

Staticman
2011-Apr-13, 04:24 PM
My bold. You did indeed specify a reduction in the mass of the body in question.
Sure, by the well known equation of E=mc^2, every radiating body loses mass, albeit at a really slow rate, our sun for example is losing lots of mass in the form of EM radiation, but very little in relation to its total mass. But there is a difference between this kind of mass loss and transfering or ejecting mass in the form of matter: stellar winds, accretion etc, that was all I wanted to point out with my comment, certainly this is a minor point that I don't think deserves further discussion.


My bold again. You are mentioning similarity, but there is an important difference. The emission of EM radiation from the body, if symmetrical, causes no net recoil on the body and leaves its velocity unchanged for the moment. If this action results in a significant reduction of the body's mass, as suggested in the OP, then I expect the reduced gravitational binding to allow the orbit to expand.

The asymmetry of the action that generates the gravitational radiation does indeed put a drag on the body, causing orbital decay if stronger than the aforementioned opposing tendency.

I think you are only considering here orbital decay due to recoil, or direct drag. Certainly symmetrical emission causes no recoil, but are you sure gravitational radiation produces orbital decay thru a recoil kind of effect, I haven't seen it explained that way, in terms of drag, maybe it works that way but I thought the gravitational waves were emitted by the binary system as a whole, since it is a quadrupole moment, and the decay explained by loss of energy of the system, not by recoil of one of the stars.