How is it possible for binary stars to not show changes in aberration angles?

[xox]

Computer problems here. Thanks for all the responses! I will study them. I have a short follow-up for XOX. I wonder if I understand your post #23. Are you saying that there ARE observable differences in the annual changes in the aberration angles from binaries versus non-binary stars? Can you give me some references for that - hopefully that I can get from the internet as it is difficult for me to get to a technical library?

No, this is not what I said. What I said is that the aberration is calculated (see http://en.wikipedia.org/wiki/Stellar_aberration_%28derivation_from_Lorentz_transformation%29) by using the velocity of the Earth and of the stars wrt. a frame anchored in the Sun. So, we need to know the motion of the star wrt. the Sun. (we know pretty well the motion of the Earth wrt. the Sun). Binary stars may have a different (more complicated) motion wrt. the Sun than single stars, that's all.
BTW: are you an ex-marine (I am ex-special forces).

 

[exmarine]

BTW: are you an ex-marine (I am ex-special forces).

Is it appropriate to post that kind of stuff here? If we keep it brief I guess. Yes, I was a Marine chopper pilot; VMO-2 believe it or not; Khe Sanh, 68 Tet, the whole 9 yards; 800 combat missions, 38 air medals, 2 distinguished flying crosses, etc. But now I am retired engineer, finally get to study physics, and pester all you kids with my dumb questions! Like this one I guess.

I understand what you are trying to explain. Not to belabor the point, but my problem is with significant changes in a binary source’s contribution over a short period of time to the changes in our relative transverse velocity NOT having any apparent influence on the observable changes in the aberration angle. See my original post for definitions of "significant" and "short".

Still trying to recover my computer and can’t keep up with all the responses. But I see none that confirm the equation I gave in post (11?) for the first and second order aberration angle being correct. I assume it is a standard result. Anyone? So how can one define "relative velocity" to exclude the source’s contribution to changes therein, and only include those of the observer’s contributions? Do we have to use General Relativity to address this problem? After all, both a binary source and our observation platform are accelerating. It is really about a photon going between the binary's geodesic and the Earth's - or actually 2 photons, one now, and another a month or two from now when BOTH velocities have changed.

Thanks again for all the responses. Semper Fi

 

[jartsa]

How about this aberration formula:Velocity of light according to a moving observer = Velocity of that light according to a static observer "+" velocity of the moving observer "+" means relativistic velocity addition

Velocity of light means the speed and the direction of light, velocity vector.

 

[Meir Achuz]

Velocity of light according to a moving observer = Velocity of that light according to a static observer

 

[xox]

Is it appropriate to post that kind of stuff here? If we keep it brief I guess. Yes, I was a Marine chopper pilot; VMO-2 believe it or not; Khe Sanh, 68 Tet, the whole 9 yards; 800 combat missions, 38 air medals, 2 distinguished flying crosses, etc.

Impressive.

I understand what you are trying to explain. Not to belabor the point, but my problem is with significant changes in a binary source’s contribution over a short period of time to the changes in our relative transverse velocity NOT having any apparent influence on the observable changes in the aberration angle.

The link I sent you says exactly the opposite, the formula is valid if and only if the change in position of the observed star is much smaller than the distance star-observer (Earth).

See my original post for definitions of "significant" and "short".

I'll look at your example. In the meanwhile, check http://en.wikipedia.org/wiki/Stellar_aberration_%28derivation_from_Lorentz_transformation%29#Application:_Aberration_in_astronomy example of calculation.

 

[xox]

How about this aberration formula:


Velocity of light according to a moving observer = Velocity of that light according to a static observer "+" velocity of the moving observer


"+" means relativistic velocity addition

Velocity of light means the speed and the direction of light, velocity vector.

The above is false, why do you keep posting fringe stuff?

 

[xox]

I thought I understood how stellar aberration conformed to Special Relativity. The CHANGE in that angle comes from the CHANGE in our orbital velocity direction about the sun over six months. And it is the same for all stars. That is fine if there are no significant changes in a star’s state of motion relative to our sun over short periods of time. “Significant” is relative to our orbital velocity; and “short” is relative to six months.

Correct.

Now I read that there are binary stars out there that DO have significant velocity component changes parallel to the plane of our orbit during short periods of time. Yet we observe no corresponding changes in the aberration angles from those stars.

Do you have a reference?

 

[jartsa]

Velocity of light according to a moving observer = Velocity of that light according to a static observer

Now you are thinking about composition of parallel velocities, I guess.

When light's and observer's velocities are parallel or anti-parallel, then the combined velocity is the light's velocity. So no change of velocity in those cases, so no aberration.

In other cases there is a change of velocity, and aberration.

 

[mfb]

The above is false, why do you keep posting fringe stuff?

It is not false, it follows from the definition of relativistic velocity addition.

Now I read that there are binary stars out there that DO have significant velocity component changes parallel to the plane of our orbit during short periods of time. Yet we observe no corresponding changes in the aberration angles from those stars.

Do you have a reference?

See any introductory relativity book or astronomy book. It is so basic that you won't find it mentioned in publications any more.
There are binaries orbiting each other with a significant fraction of the speed of light. If this would lead to abberation, their apparent position would move wildly through the sky and it would be impossible to observe them properly (or even give their positions in the sky).

The link I sent you says exactly the opposite, the formula is valid if and only if the change in position of the observed star is much smaller than the distance star-observer (Earth).

This is true for all observations of objects outside the solar system humans ever made.

 

[xox]

Now you are thinking about composition of parallel velocities, I guess.

When light's and observer's velocities are parallel or anti-parallel, then the combined velocity is the light's velocity. So no change of velocity in those cases, so no aberration.

In other cases there is a change of velocity,

The above is a collection of misconceptions.

u'_x=\frac{u_x+V}{1+u_xV/c^2}
u'_y=\frac{u_y}{\gamma(V)(1+u_xV/c^2)}


Making (u_x,u_y)=(c,0) produces (u'_x,u'_y)=(c,0)

and aberration.

Aberration, yes. "Change in velocity", not so much.

 

[xox]

It is not false,

So, according to you "Velocity of light according to a moving observer = Velocity of that light according to a static observer "+" velocity of the moving observer " is not false?

You seem to agree with jartsa that the second SR postulate is false. Interesting.

it follows from the definition of relativistic velocity addition.

The formula (not definition) of relativistic velocity is derived from the assumption that light speed is invariant, so, it does not support jartsa's claim "Velocity of light according to a moving observer = Velocity of that light according to a static observer "+" velocity of the moving observer ".
Actually, (and unsurprisingly) it supports exactly the opposite, see post 40.

 

[jartsa]

The above is a collection of misconceptions.

u'_x=\frac{u_x+V}{1+u_xV/c^2}
u'_y=\frac{u_y}{\gamma(V)(1+u_xV/c^2)}Making (u_x,u_y)=(c,0) produces (u'_x,u'_y)=(c,0)

Aberration, yes. "Change in velocity", not so much.

The math is wrong because:

When you see aberration happening, you see light rays turning. (When you are accelerating)

Light ray turninig = light ray's velocity changing.

 

[PAllen]

So, according to you "Velocity of light according to a moving observer = Velocity of that light according to a static observer "+" velocity of the moving observer " is not false?

You seem to agree with jartsa that the second SR postulate is false. Interesting

Jarts said '+' meant relativistic velocity addition. For light, this means the speed stays the same, but for all but parallel/antiparallel motion, the direction changes. Direction is part of velocity. Point is, the full relativistic velocity addition formula works for light as well as for material bodies.

That is also what mfb obviously meant as well.

 

[PAllen]

The math is wrong because:

When you see aberration happening, you see light rays turning.

Light ray turninig = light ray's velocity changing.

The math is actually right. xox only plugged in the parallel case. If uy is not zero, you get the appropriate change in direction for the primed velocity.

 

[mfb]

xox: I think you confuse velocity (which depends on speed and direction) with speed.
The velocity of light can change while its speed is constant - this just means a change in direction.

 

[PAllen]

You must have a way of reading and interpreting nonsense as meaningful stuff.

It's called reading without assuming everyone is an idiot. Here is the direct quote from Jartsa's post:

"Velocity of light according to a moving observer = Velocity of that light according to a static observer "+" velocity of the moving observer


"+" means relativistic velocity addition

Velocity of light means the speed and the direction of light, velocity vector.
"

I see nothing incorrect in this.

 

[xox]

xox: I think you confuse velocity (which depends on speed and direction) with speed.

Clearly, I don't, I showed the transformation for both components.

The velocity of light can change while its speed is constant - this just means a change in direction.

I am fully familiar with that. PAllen managed to decipher jartsa's weirdly phrased claim as a case when \vec{c} is not parallel with \vec{V}. I (and Meir Achuz) interpreted his claim as old ballistic theory of light.

 

[xox]

It's called reading without assuming everyone is an idiot. Here is the direct quote from Jartsa's post:

"Velocity of light according to a moving observer = Velocity of that light according to a static observer "+" velocity of the moving observer"+" means relativistic velocity addition

Velocity of light means the speed and the direction of light, velocity vector.
"

I see nothing incorrect in this.

Meir Achuz read exactly the same way I read it, as a support for ballistic theory.

 

[xox]

See any introductory relativity book or astronomy book. It is so basic that you won't find it mentioned in publications any more.

Please don't talk down.

There are binaries orbiting each other with a significant fraction of the speed of light. If this would lead to abberation,[/color] their apparent position would move wildly through the sky and it would be impossible to observe them properly (or even give their positions in the sky).

You are unclear, are you saying that there is NO aberration?
Besides, the exact claim that I questioned was that changes in speed do not lead to changes in the aberration angle. What is your exact take on this, you seem to be answering a different issue than the one being discussed.

 

[PAllen]

You are unclear, are you saying that there is NO aberration?
Besides, the exact claim that I questioned was that changes in speed do not lead to changes in the aberration angle. What is your exact take on this, you seem to be answering a different issue than the one being discussed.

If you see a formula that includes speed of the source, that formula is based on a reference angle in the rest frame of the source. Since the source is changing speed, the reference angle is changing as well. These effects balance such that speed of source has no direct contribution to observed aberration at all. For sources with changing motion [actually, in all cases IMO], it is much easier to analyze Earth's changing frame relative to a fixed inertial frame (e.g. sun's). In this analysis, there is no term for source speed at all, only source angular position (in the reference frame). The only speed terms are for Earth's orbital speed.

There is a secondary impact for an accelerating source. It's orbit has certain shape observed in the reference frame. The periodic change in the Earth's frame leads to a very small periodic change in the shape of the binary star orbit. That is, if the Earth observer plots the binary orbit against the background of the stellar COM position (with its periodic aberration), they see a very slightly different shape for the orbit than the solar observer does. I do not know if any of this is observable, in practice.

 

[PhilDSP]

I'd like to submit one particular geometric solution in as simple manner as possible:
\textrm{aberration} = \Theta = tan(\frac{\textrm{r}_{\textrm{T}} \times (\hat{\textrm{r}_{\textrm{H}}} \cdot \hat{\textrm{o}_{\textrm{N}}})}{\textrm{r}_{\textrm{L}}})
The vector $\textrm{r}_{\textrm{T}}$ is the transverse displacement of the observer from the point of photon emission.
The vector $\textrm{r}_{\textrm{L}}$ is the longitudinal displacement of the observer from the star in the same inertial system as the star.
The vector $\textrm{r}_{\textrm{H}}$ is the displacement of the observer from the point of photon emission. It represents the ray of the photon.

The unit vector $\hat{\textrm{r}_{\textrm{H}}}$ is $\textrm{r}_{\textrm{H}}$ normalized to have length 1.
The unit vector $\hat{\textrm{o}_{\textrm{N}}}$ is normal to the plane containing the Earth's orbit.

Crossing $\textrm{r}_{\textrm{T}}$ with the other terms should give the correct adjustment for the angle of the star with respect to the orbital pole of the Earth (where aberration is maximum).

 

[PhilDSP]

Since an Earth-based observer will have a non-inertial relation to either the Sun or the star, the total of all motions needs to be summed during the time period that the photon was in flight. That will allow us to determine, geometrically, what the trajectory vector is for the impinging photon. Fortunately that's not terribly complicated, as I reported earlier

\Delta \textrm{r} = \int_{t_e}^{t_a} v(t) \ dt
t_e is the time that the photon was emitted
t_a is the time that the photon was absorbed by the observer
v(t) is the relative velocity between the point of emission and the observer at time t

Then

\textrm{r}_\textrm{H} = \textrm{r}_\textrm{L} - \Delta \textrm{r} \ \ \ \ \ \ \textrm{r}_\textrm{T} = \textrm{r}_\textrm{L} \times (\textrm{r}_\textrm{L} + \Delta \textrm{r})

 

[PAllen]

Since an Earth-based observer will have a non-inertial relation to either the Sun or the star, the total of all motions needs to be summed during the time period that the photon was in flight. That will allow us to determine, geometrically, what the trajectory vector is for the impinging photon. Fortunately that's not terribly complicated, as I reported earlier

\Delta \textrm{r} = \int_{t_e}^{t_a} v(t) \ dt
t_e is the time that the photon was emitted
t_a is the time that the photon was absorbed by the observer
v(t) is the relative velocity between the point of emission and the observer at time t

Then

\textrm{r}_\textrm{H} = \textrm{r}_\textrm{L} - \Delta \textrm{r} \ \ \ \ \ \ \textrm{r}_\textrm{T} = \textrm{r}_\textrm{L} \times (\textrm{r}_\textrm{L} + \Delta \textrm{r})

What theory of aberration is this? In SR, it is only based on the Lorentz transform. Instantaneously colocated inertial frames are all that is required for either an observer with acceleration or a source with acceleration (if you choose to involve the source frame at all - which is unnecessary and complicates things - but is not wrong). Past motion is irrelevant. There is no need for any integration.

 

[mfb]

Please don't talk down.

I don't do that, I give a reason why there won't be papers about it.

You are unclear, are you saying that there is NO aberration?
Besides, the exact claim that I questioned was that changes in speed do not lead to changes in the aberration angle. What is your exact take on this, you seem to be answering a different issue than the one being discussed.

There is no aberration from the motion of stars in binary systems.
Changes in speed of Earth change the aberration angle. Changes in speed of stars have no special effect.

 

[PAllen]

So far this has purely been classical - non-relativistic, as it hasn't invoked the Lorentz transform. I believe the OP is interested in the numeric differences between the two, I certainly am.

Past motion is irrelevant for any single observation. For 2 or more different observations it would also be irrelevant if the velocity was constant over the period that those observations were made. The integration is one means of making the different observations compatible.

Where do you get that? From the very first post, this as been about stellar aberration in the context of SR.

The references in Histspec's #5 cover all the issues in this thread and more. In some sense, all after that is redundant.

 

[xox]

If you see a formula that includes speed of the source,

All formulas are based on the relative speed between source and observer.

that formula is based on a reference angle in the rest frame of the source.

Are you talking about the formula cos \theta_{obs}=\frac{cos \theta_{src}-v/c}{1 -v/ccos \theta_{src}}? Because I am talking about something totally different: \tan \theta_{obs}=\frac{v}{c}, where v=v(t) is the relative speed between the source and the observer. See here. Even in cos \theta_{obs}=\frac{cos \theta_{src}-v/c}{1 -v/ccos \theta_{src}} v=v(t) is the relative speed between the source and the observer.

Since the source is changing speed, the reference angle is changing as well.

Yes, obviously. But this is not what I am talking about.

These effects balance such that speed of source has no direct contribution to observed aberration at all.

The "speed of the source" (the star) in the baricentric reference frame of the Sun is a definite contributor to the aberration, just as much as the speed of the Earth , in the Sun reference frame. See here

For sources with changing motion [actually, in all cases IMO], it is much easier to analyze Earth's changing frame relative to a fixed inertial frame (e.g. sun's).

Yes, ..which is exactly what I posted earlier.

In this analysis, there is no term for source speed at all, only source angular position (in the reference frame). The only speed terms are for Earth's orbital speed.

Well, the source-angular position is nothing but a function of the source velocity in the Sun - anchored frame. So, to say that "aberration is not a function of the speed of the star wrt. the Sun-based frame" is just a misnomer. As an aside, could you put what you said in words into math, the way I did it? This would make things a lot clearer.

 

[xox]

I don't do that, I give a reason why there won't be papers about it.

The way you phrased it, sure sounded like it.

There is no aberration from the motion of stars in binary systems.

Could you please prove this?

Changes in speed of Earth change the aberration angle.

Yes, obviously. See my post here.

Changes in speed of stars have no special effect.

Aberration depends on the relative velocity between source (the star) and the observer. How can you claim that the "changes in the speeds of stars have no (special? what is special?) effects"? Can you prove your claim mathematically? How does your claim jibe with the definition of aberration (either relativistic or non-relativstic)?

 

[mfb]

The "speed of the source" (the star) in the baricentric reference frame of the Sun is a definite contributor to the aberration, just as much as the speed of the Earth , in the Sun reference frame. See here

It is not. A moving star (relative to our sun) won't appear where it currently is, but this is not called aberration - it is just the time delay, the star had some years (or much more) time to move forward between the emission of light and our detection.

There is no aberration from the motion of stars in binary systems.

Could you please prove this?

Sure.

HM Cancri is a binary system where the white dwarfs orbit each other with velocities above .1% c, but they always appear at the same position in the sky.

For even higher speeds, this picture for example. The source of a relativistic jet and the relativistic jet appear directly next to each other.

Aberration depends on the relative velocity between source (the star) and the observer. How can you claim that the "changes in the speeds of stars have no (special? what is special?) effects"? Can you prove your claim mathematically? How does your claim jibe with the definition of aberration (either relativistic or non-relativstic)?

See the first part of this post. The effects of special relativity get split in different effects, a constant relative velocity between star and sun is not included in the aberration.

 

[xox]

It is not. A moving star (relative to our sun) won't appear where it currently is, but this is not called aberration

So, the argument boils down to the fact that the aberration "is not called aberration"? A ray of light coming from a (distant) source is no longer aberrated as a function of the relative speed between the source and the receiver?

- it is just the time delay, the star had some years (or much more) time to move forward between the emission of light and our detection.

While the ray of light covers the distance star-Earth ct, the star has moved by vt , where v is the relative speed between the star and Earth. This results into an aberration of \tan \theta'=\frac{vt}{ct}=\frac{v}{c}. Is this no longer called aberration?
We are discussing:
- whether the ray of light has a different angle in the frame of the emitter vs. the frame of the receiver, i.e. whether the well known phenomenon known as aberration of light is present
-whether or not changes in the speed of the star can be perceived as changes in the aberration angle.
Can you put this prose in math form, please? I asked this before, I am really interested in seeing the mathematical explanation.

Sure.

HM Cancri is a binary system where the white dwarfs orbit each other with velocities above .1% c, but they always appear at the same position in the sky.For even higher speeds, this picture for example. The source of a relativistic jet and the relativistic jet appear directly next to each other.

This may have a simple mathematical explanation, the variation in the velocity of the two stars may produce a variation in the aberration angle that is below the current measurement capabilities. Again, I would welcome a complete mathematical treatment, could you do this?

See the first part of this post. The effects of special relativity get split in different effects, a constant relative velocity between star and sun is not included in the aberration.

Can you explain this in mathematical terms? Stating it , even repeatedly, does not constitute a convincing argument. As a matter of fact, this is also the request of the thread originator.

 

[mfb]

So, the argument boils down to the fact that the aberration "is not called aberration"? A ray of light coming from a (distant) source is no longer aberrated as a function of the relative speed between the source and the receiver?

It boils down that you use a definition of aberration no one else does, I think. And one that fails as soon as the motion is not uniform any more.

This is obvious but we are not discussing the trivial fact that the star has moved between the time the ray of light was emitted and the time the ray arrived on Earth, we are discussing:

But that is exactly the (only) effect a relative velocity between star and sun has.

- whether the ray of light has a different angle in the frame of the emitter vs. the frame of the receiver, i.e. whether the well known phenomenon known as aberration of light is present

How do you compare angles and directions in frames with a relative motion?

-whether or not changes in the speed of the star can be perceived as changes in the aberration angle.

Certainly not, see the binary stars.

Can you put this prose in math form, please? I asked this before, I am really interested in seeing the mathematical explanation.

Just view everything in the frame of the sun and there is absolutely no reason to expect any aberration effect (and nothing to calculate). Light travels in a straight line and does not care about the velocity of the emitter.
For the moving star, the direction it has to emit light to hit our Earth will be different the point where the star sees our earth, this is the same effect of the time delay just seen from the other direction.

This may have a simple mathematical explanation, the variation in the velocity of the two stars may produce a variation in the aberration angle that is below the current measurement capabilities. Again, I would welcome a complete mathematical treatment, could you do this?

No. A .1% motion of the objects in the sky (corresponding to their .1% c velocity) would be plain obvious to every observer. See above, there is no mathematical treatment needed for a straight line.

Stating it , even repeatedly, does not constitute a convincing argument. As a matter of fact, this is also the request of the thread originator.

Reducing a physical problem to one that can be solved without any calculation is one of the most convincing arguments I know.