<p>There is no dependence of aberration on the velocity of the source. None is seen, and none is predicted by special relativity.</p>
<p>The error in the text that you quoted seems to be the implicit assumption that because of the principle of relativity, the amount of aberration can only depend on the relative velocity of the emitter and receiver. Actually, there is a third relevant quantity in this problem—the spacetime separation of the emitter and receiver—and the principle of relativity only tells you that the answer must be some frame-independent function of those three quantities. It turns out to depend only on the receiver's velocity and the direction of the separation vector.</p>

CC BY-SA 4.0
2022-11-06T04:48:43.340Z
2022-11-06T04:48:43.340Z
benrg
<p>This is easy to understand if you consider the problem in terms of classical plane wave optics:</p>
<p>the apparent position of the star is defined by the orientation of the wavefront we receive. Ignoring any changes of this due to physical effects like refraction etc. along its path, this can only change if the position of the source (the star) changes. If you assume the star is displaced by a distance <span class="math-container">$\Delta x$</span> transversely to the direction of observation, then the orientation of the wave front will change by an angle</p>
<p><span class="math-container">$$\Delta \alpha = arctan(\frac{\Delta x}{R})$$</span></p>
<p>where <span class="math-container">$R$</span> is the distance of the star.</p>
<p>For Mizar, the distance R is 83 light years = <span class="math-container">$4.9 \cdot 10^{14} miles$</span>, so if it is displaced by  <span class="math-container">$\Delta x = 18 \cdot 10^6 miles$</span>, the apparent position will change only by about</p>
<p><span class="math-container">$$\Delta \alpha \approx 2 \cdot 10^{-6} deg = 7.6 \cdot 10^{-3} arcsec$$</span></p>
<p>This is completely negligible compared to the aberration due to the Earth's orbital motion of about 20 arcsec.</p>

CC BY-SA 4.0
2022-11-07T00:59:48.020Z
So this is why there is no need to adjust the angle of the telescope?  Any stellar aberration effect due to the change in each stars position (ie. normal to your line of observation) will be incredibly small.  Many thanks for everyone's answers - most appreciated.
Dubious
CC BY-SA 4.0
2022-11-07T08:14:14.193Z
@Dubious Yes, that would be the explanation in terms of classical wave optics.
Thomas
CC BY-SA 4.0
2022-11-06T16:51:57.877Z
2022-11-07T08:10:02.190Z
2022-11-07T08:10:02.190Z
Thomas
<p>You can measure red and blue shift of binary stars, but you can't see it.</p>
<p>The Hydrogen spectrum peak taken on the east side of the sun (left side) is a wavelength of 434.044nm and from the west-side (right side) is a 434.050nm. For aligned binary stars the shift if far higher.</p>
<p>It cant be always be seen for binary because:
The period of change is too slow, 5+ minutes</p>
<p>The binary rotation has to be aligned with the viewer.</p>
<p>The chances that the stars occlude one another is minimal.</p>
<p><a href="http://www.alevelphysicsnotes.com/astrophysics/doppler_effect.php" rel="nofollow noreferrer">http://www.alevelphysicsnotes.com/astrophysics/doppler_effect.php</a></p>

CC BY-SA 4.0
2022-11-06T06:23:14.483Z
2022-11-06T12:42:19.083Z
2022-11-06T12:42:19.083Z
bandybabboon
<p>I read this article, <a href="http://www.naturalphilosophy.org/pdf/abstracts/abstracts_5363.pdf" rel="nofollow noreferrer">Questioning Einstein: Is Relativity Necessary?</a> (Bethell (2010), Proc. Natural Philosophy Alliance, v.6, no. 2), regarding the 2 stars of Mizar A and wondering if it is true that we do not see back and forth aberration effects when observing binary star systems? If true, is there a known explanation?</p>
<blockquote>
<p>In 1889 Edward Pickering had discovered spectroscopic binary stars, orbiting a common center of mass so closely that they appear as a single star even in the most powerful telescopes. The two stars of Mizar A, in the handle of the Big Dipper, are only 18 million miles apart. Their separate character is apparent only from the alternating Doppler shifts in their spectral lines. They orbit one another at a velocity of 50 kilometers per second, or 1.7 times the Earth’s orbital velocity.</p>
<p>It follows that even if we still don’t know the true velocity of the binary systems with respect to the sun, we do know that there is a difference, sometimes large, between the separate stars of the binary system relative to us. In the case of Mizar A, at a given moment in its 104-day cycle, one star is approaching us at the high velocity of 50 kilometers per second (relative to the center of mass of the system) while the other star is moving away from us at the same velocity. Irrespective of the movement of the system as a whole, then, the twin elements of the orbiting pair are moving at velocities that exceed the Earth’s orbital velocity by quite a large margin.</p>
<p>By Einstein’s formula, alternating back and forth aberrations should therefore be observed, corresponding to the period of their orbits. The aberration angle of each star should increase and then decrease as they circle each other. This would be easily observable by modern instruments. The differential aberration would be so large that the stars would become visibly separate in the sky before closing again.
In the case of Mizar A, the angular separation of the binary components would be more than a minute of arc. But they always remain as an unresolvable point in the sky. And because binary systems are so common, we should be seeing this back and forth apparent motion of binary components all over the heavens. But we never do</p>
</blockquote>

CC BY-SA 4.0
2022-11-06T01:22:51.427Z
Can you add a reference for that article?
JohnHoltz
CC BY-SA 4.0
2022-11-06T01:36:56.287Z
A 300+ wall of text doesn’t spark answers. Try to cut down and add paragraphs
Topcode
CC BY-SA 4.0
2022-11-06T02:15:51.467Z
I think you are quoting "the following article regarding the 2 stars of Mizar A" so I've used block quotes to indicate it's not your words. To make this complete though you need to double check it and also **add a link or citation** to the article. *Thanks!*
uhoh
CC BY-SA 4.0
2022-11-06T12:02:59.927Z
What is it referring to "by Einstein;s formula"?
ProfRob
CC BY-SA 4.0
2022-11-07T04:02:12.590Z
@ProfRob it's looking like the article is published in the Proceedings of the Natural Philosophy Alliance. Per Wikipedia's [list of organizations opposing mainstream science](https://en.wikipedia.org/wiki/List_of_organizations_opposing_mainstream_science#List_of_organizations) it is "(a)n organization which believes there are fundamental flaws in theories such as relativity, the big bang, and plate tectonics". So I guess it doesn't matter which one considering "they're all wrong". :-)
uhoh
CC BY-SA 4.0
2022-11-07T13:31:38.863Z
...are they somehow confusing relativity with emission theory, where the speed of light depends on the speed of the emitter? That theory was *obsoleted* by Special Relativity.
Christopher James Huff
CC BY-SA 4.0
2022-11-08T15:07:07.097Z
I think the article is saying that if there were no stellar aberration for binary stars , such that you couldn't distinctly see each star (during their rotaton about the systems COM), that could be evidence of an aether or 'aether drag'.  Forum poster 'Thomas' has provided the answer that makes sense to me. Yes, so the claim made in the article seems to be wrong and that was what I was looking for (a logical explanation).
Dubious
<binary-star>
Is there a logical reason why we see no back and forth aberration effects when observing binary stars?
Dubious
# Is there a logical reason why we see no back and forth aberration effects when observing binary stars?

(Asked by: username_0 on 2022-11-06)

I read this article, [Questioning Einstein: Is Relativity Necessary?](http://www.naturalphilosophy.org/pdf/abstracts/abstracts_5363.pdf) (Bethell (2010), Proc. Natural Philosophy Alliance, v.6, no. 2), regarding the 2 stars of Mizar A and wondering if it is true that we do not see back and forth aberration effects when observing binary star systems? If true, is there a known explanation?

> In 1889 Edward Pickering had discovered spectroscopic binary stars, orbiting a common center of mass so closely that they appear as a single star even in the most powerful telescopes. The two stars of Mizar A, in the handle of the Big Dipper, are only 18 million miles apart. Their separate character is apparent only from the alternating Doppler shifts in their spectral lines. They orbit one another at a velocity of 50 kilometers per second, or 1.7 times the Earth’s orbital velocity.
>
> It follows that even if we still don’t know the true velocity of the binary systems with respect to the sun, we do know that there is a difference, sometimes large, between the separate stars of the binary system relative to us. In the case of Mizar A, at a given moment in its 104-day cycle, one star is approaching us at the high velocity of 50 kilometers per second (relative to the center of mass of the system) while the other star is moving away from us at the same velocity. Irrespective of the movement of the system as a whole, then, the twin elements of the orbiting pair are moving at velocities that exceed the Earth’s orbital velocity by quite a large margin.
>
> By Einstein’s formula, alternating back and forth aberrations should therefore be observed, corresponding to the period of their orbits. The aberration angle of each star should increase and then decrease as they circle each other. This would be easily observable by modern instruments. The differential aberration would be so large that the stars would become visibly separate in the sky before closing again.
> In the case of Mizar A, the angular separation of the binary components would be more than a minute of arc. But they always remain as an unresolvable point in the sky. And because binary systems are so common, we should be seeing this back and forth apparent motion of binary components all over the heavens. But we never do

**Tags:** binary-star
> **Comments:**
> **username_1**: Can you add a reference for that article?  
> **username_2**: A 300+ wall of text doesn’t spark answers. Try to cut down and add paragraphs  
> **username_3**: I think you are quoting "the following article regarding the 2 stars of Mizar A" so I've used block quotes to indicate it's not your words. To make this complete though you need to double check it and also **add a link or citation** to the article. *Thanks!*  
> **username_4**: What is it referring to "by Einstein;s formula"?  
> **username_3**: @ProfRob it's looking like the article is published in the Proceedings of the Natural Philosophy Alliance. Per Wikipedia's [list of organizations opposing mainstream science](https://en.wikipedia.org/wiki/List_of_organizations_opposing_mainstream_science#List_of_organizations) it is "(a)n organization which believes there are fundamental flaws in theories such as relativity, the big bang, and plate tectonics". So I guess it doesn't matter which one considering "they're all wrong". :-)  
> **username_5**: ...are they somehow confusing relativity with emission theory, where the speed of light depends on the speed of the emitter? That theory was *obsoleted* by Special Relativity.  
> **username_0**: I think the article is saying that if there were no stellar aberration for binary stars , such that you couldn't distinctly see each star (during their rotaton about the systems COM), that could be evidence of an aether or 'aether drag'.  Forum poster 'Thomas' has provided the answer that makes sense to me. Yes, so the claim made in the article seems to be wrong and that was what I was looking for (a logical explanation).  

---

## 3 answers

### Answer by username_6 on 2022-11-06. Score: 6

There is no dependence of aberration on the velocity of the source. None is seen, and none is predicted by special relativity.

The error in the text that you quoted seems to be the implicit assumption that because of the principle of relativity, the amount of aberration can only depend on the relative velocity of the emitter and receiver. Actually, there is a third relevant quantity in this problem—the spacetime separation of the emitter and receiver—and the principle of relativity only tells you that the answer must be some frame-independent function of those three quantities. It turns out to depend only on the receiver's velocity and the direction of the separation vector.


---

### Answer by username_7 on 2022-11-06. Score: 4

This is easy to understand if you consider the problem in terms of classical plane wave optics:

the apparent position of the star is defined by the orientation of the wavefront we receive. Ignoring any changes of this due to physical effects like refraction etc. along its path, this can only change if the position of the source (the star) changes. If you assume the star is displaced by a distance $\Delta x$ transversely to the direction of observation, then the orientation of the wave front will change by an angle

$$\Delta \alpha = arctan(\frac{\Delta x}{R})$$

where $R$ is the distance of the star.

For Mizar, the distance R is 83 light years = $4.9 \cdot 10^{14} miles$, so if it is displaced by $\Delta x = 18 \cdot 10^6 miles$, the apparent position will change only by about

$$\Delta \alpha \approx 2 \cdot 10^{-6} deg = 7.6 \cdot 10^{-3} arcsec$$

This is completely negligible compared to the aberration due to the Earth's orbital motion of about 20 arcsec.

> **Comments:**
> **username_0**: So this is why there is no need to adjust the angle of the telescope?  Any stellar aberration effect due to the change in each stars position (ie. normal to your line of observation) will be incredibly small.  Many thanks for everyone's answers - most appreciated.  
> **username_7**: @Dubious Yes, that would be the explanation in terms of classical wave optics.  

---

### Answer by username_8 on 2022-11-06. Score: 2

You can measure red and blue shift of binary stars, but you can't see it.

The Hydrogen spectrum peak taken on the east side of the sun (left side) is a wavelength of 434.044nm and from the west-side (right side) is a 434.050nm. For aligned binary stars the shift if far higher.

It cant be always be seen for binary because:
The period of change is too slow, 5+ minutes

The binary rotation has to be aligned with the viewer.

The chances that the stars occlude one another is minimal.

<http://www.alevelphysicsnotes.com/astrophysics/doppler_effect.php>


---

