Stellar aberation, a One way measurement of c?

[Tracer]

Why isn't Stellar aberation considered to be a one way measurement of c?

if the angle of aberation (Theta) is 20.5 arcseconds and the Earth's orbital speed is 29.79 Kilometers/second normal to the arriving star light. The value of c should be:
c= Vt/tan(Theta) = 29.79/9.94E-5 = 299737.98 Kilometers/second.

If more acurate values of Vt and Theta are used why would this not confirm a one way measurement of c?

 

[Bill_K]

Sure, in fact the guy who discovered stellar aberration, James Bradley, used his measurements to determine a more accurate value for the speed of light. This was in 1725.

 

[Tracer]

Sure, in fact the guy who discovered stellar aberration, James Bradley, used his measurements to determine a more accurate value for the speed of light. This was in 1725.

Yet there are persistent comments claiming that the measurement of the One Way speed of light is not possible.

 

[ghwellsjr]

Yet there are persistent comments claiming that the measurement of the One Way speed of light is not possible.

Yes, many, starting with Einstein.

 

[Bill_K]

Anyone who claims the one-way speed of light cannot be measured is, to put it mildly, wrong. We learn as freshmen that the speed of light was first determined by Romer's observations of the moons of Jupiter. It's true that many determinations are round-trip, but that's for added accuracy.

 

[ghwellsjr]

From the wikipedia article on the One-way speed of light:

Rømer's measurement

The first experimental determination of the speed of light was made by Ole Christensen Rømer. It may seem that this experiment measures the time for light to traverse part of the Earth's orbit and thus determines its one-way speed, however, this experiment was carefully re-analysed by Zhang, who showed that the measurement does not measure the speed independently of a clock sychronization scheme but actually used the Jupiter system as a slowly transported clock to measure the light transit times.

 

[Bill_K]

I agree that measuring the one-way speed of light requires clock synchronization. That does not mean it can't be done, or that there is anything suspect about the result. Without the use of clock synchronization, solar system observations would make no sense.

 

[ghwellsjr]

Do you also agree with this quote from the same article:

The one-way speed

Although the average speed over a two-way path can be measured, the one-way speed in one direction or the other is undefined (and not simply unknown), unless one can define what is "the same time" in two different locations. To measure the time that the light has taken to travel from one place to another it is necessary to know the start and finish times as measured on the same time scale. This requires either two synchronized clocks, one at the start and one at the finish, or some means of sending a signal instantaneously from the start to the finish. No instantaneous means of transmitting information is known. Thus the measured value of the average one-way speed is dependent on the method used to synchronize the start and finish clocks. This is a matter of convention.

 

[Bill_K]

All right, I guess I see the point. Stellar aberration basically measures the ratio v/c where v is the Earth's orbital velocity. But the determination of v rests on the observed Doppler shift of stellar spectral lines. Which in fact only gives you v/c also, so the argument is circular.

However I still maintain that the limitation is only a practical one. In principle one could determine the Earth's velocity directly from Kepler's laws, by measuring the astronomical unit with a meter stick and counting the number of atoms in the sun!

 

[harrylin]

All right, I guess I see the point. Stellar aberration basically measures the ratio v/c where v is the Earth's orbital velocity. But the determination of v rests on the observed Doppler shift of stellar spectral lines. Which in fact only gives you v/c also, so the argument is circular.

However I still maintain that the limitation is only a practical one. In principle one could determine the Earth's velocity directly from Kepler's laws, by measuring the astronomical unit with a meter stick and counting the number of atoms in the sun!

Kepler's laws are classical. How would you measure v= (x2-x1)/(t2-t1) without clocks and without knowing the speed of the sun?

 

[Bill_K]

harrylin, I see there's another long thread elsewhere on this same topic, so further discussion should probably be done there. If a discussion is going to go anywhere, it's important to read the previous comments carefully, or else most of it degenerates into misunderstandings of the form "I didn't say that".

"Kepler's laws are classical." - the orbital equations of motion, if you must. But the situation we are talking about, the Earth's orbit about the sun, is classical. Relativistic corrections are completely negligible.

"without clocks" - Without clocks?? You can't time anything without clocks. I said the 'slow transport' of synchronizing clocks was a good one. However it's not relevant. To determine the orbital velocity of the Earth, we only need to (hypothetically) measure the radius or circumference of the orbit with a meter stick, and time the period with an Earthbound clock.

"without knowing the speed of the sun" - this is all done in the sun's reference frame.

 

[TrickyDicky]

What I fail to understand is why the stellar aberration formula gives us the ratio between the Earth's speed and c precisely in the sun's reference frame. What is special about the sun reference frame in this context?

 

[TrickyDicky]

Stellar aberration is explained by SR as being due to the relative motion between the Earth and the distant star the aberrated light is sent from. But I don't understand why in the usual formula for stars at 90º from our observation point: tan theta=v/c, v should refer to Earth's speed wrt the sun, what does the sun have to do with the relative motion between the Earth and a remote star?
Also why are all astronomical charts corrected for the motion of the Earth and not for the motion of the light source which in the case of some binaries is well known and important enough to produce significant corrections?

 

[PAllen]

Stellar aberration is explained by SR as being due to the relative motion between the Earth and the distant star the aberrated light is sent from. But I don't understand why in the usual formula for stars at 90º from our observation point: tan theta=v/c, v should refer to Earth's speed wrt the sun, what does the sun have to do with the relative motion between the Earth and a remote star?
Also why are all astronomical charts corrected for the motion of the Earth and not for the motion of the light source which in the case of some binaries is well known and important enough to produce significant corrections?

We don't know the 'true' angular position of stars. We observe, for example, a seaonal variation in the position. Independent of the motion of the solar system as a whole, the seasonal variation depends only on the Earth's orbital speed.

 

[harrylin]

harrylin, I see there's another long thread elsewhere on this same topic, so further discussion should probably be done there.
[..]
"without knowing the speed of the sun" - this is all done in the sun's reference frame.

OK, I'll just end with putting attention to the fact that "in the sun's reference frame" the one-way speed of light relative to that same reference frame is defined as equal to the two-way speed - so we came full circle... The whole concept of local time arose from the fact that we can equally well assign a velocity vector to the sun, in which case the speed of light is assumed to be isotropic relative to another reference system and anisotropic relative to the sun.

 

[harrylin]

Stellar aberration is explained by SR as being due to the relative motion between the Earth and the distant star the aberrated light is sent from. [..]

Hmm not exactly, but this is a common misunderstanding.

The relative motion of Earth and star matters for the calculation of the Doppler effect. However, according to SR the motion of a distant star is irrelevant for aberration (second postulate!) and SR doesn't really try to explain - it just predicts the necessary consequences of the postulates.

Stellar aberration is predicted to be an effect from the change of motion of the Earth and the effect can be calculated relative to any freely chosen inertial reference system. The Sun is most convenient.

 

[TrickyDicky]

Stellar aberration is predicted to be an effect from the change of motion of the Earth

only the Earth's motion counts then? then what is "relativistic" about stellar aberration?
I guess the incoming light ray is considered to be at rest. And we are calculating the transverse velocity of the Earth wrt incoming star's light.
Here's how this is explained in wikipedia:
"stellar aberration is independent of the distance of a celestial object from the observer, and depends only on the observer's instantaneous transverse velocity with respect to the incoming light beam, at the moment of observation. The light beam from a distant object cannot itself have any transverse velocity component, or it could not (by definition) be seen by the observer, since it would miss the observer. Thus, any transverse velocity of the emitting source plays no part in aberration. Another way to state this is that the emitting object may have a transverse velocity with respect to the observer, but any light beam emitted from it which reaches the observer, cannot, for it must have been previously emitted in such a direction that its transverse component has been "corrected" for. Such a beam must come "straight" to the observer along a line which connects the observer with the position of the object when it emitted the light"

and the effect can be calculated relative to any freely chosen inertial reference system. The Sun is most convenient.

I still can't see it. How exactly is the sun chosen as a reference for the Earth's speed relative to the distant star light ray received on the earth? How is that implicit in the formula Tracer mentioned in the OP?
The Earth is also moving wrt the galaxy and wrt the CMB with different speeds, why is precisely the Earth's orbital speed that shows up in that formula?
The wikipedia article mentions this as Secular aberration, and says it is difficult to observe and therefore ignored, but considering a extragalactic star if our galaxy is moving 600 km/s, shouldn't that speed show up in the calculations?

 

[harrylin]

only the Earth's motion counts then? then what is "relativistic" about stellar aberration?
[..]
I still can't see it. How exactly is the sun chosen as a reference for the Earth's speed relative to the distant star light ray received on the earth?

We can choose an inertial system in which the star is in rest (as Einstein did for his derivation) or one in which the sun is in rest (as is commonly done) or any other inertial reference system, it doesn't matter: the predicted observed aberration from Earth will still be exactly the same.

I guess the incoming light ray is considered to be at rest.

Something went wrong here... perhaps you meant the star? But see my remark here above, we may pretend any inertial frame to correspond to a virtual light medium.

And we are calculating the transverse velocity of the Earth wrt incoming star's light.
Here's how this is explained in wikipedia:
"stellar aberration is independent of the distance of a celestial object from the observer, and depends only on the observer's instantaneous transverse velocity with respect to the incoming light beam, at the moment of observation. [..]"
[..]
The Earth is also moving wrt the galaxy and wrt the CMB with different speeds, why is precisely the Earth's orbital speed that shows up in that formula?

Wikipedia is inaccurate; I think that it was better last time that I looked at it. PAllen said it better: we observe a seasonal variation. That's why the orbital speed shows up in the formula. Zero aberration would be observed at constant observer velocity.

[..] considering a extragalactic star if our galaxy is moving 600 km/s, shouldn't that speed show up in the calculations?

No. The speed of the light rays coming from that star is not affected by its motion, and the angular change of position over time is negligible for distant stars. For sure this is why Einstein put "infinitely distant source of light", to avoid discussing such effects.

 

[TrickyDicky]

We can choose an inertial system in which the star is in rest (as Einstein did for his derivation) or one in which the sun is in rest (as is commonly done) or any other inertial reference system, it doesn't matter: the predicted observed aberration from Earth will still be exactly the same.

This is the part I have difficulties reconciling with SR, I thought only light's speed was constant regardless the reference system.

 

[harrylin]

This is the part I have difficulties reconciling with SR, I thought only light's speed was constant regardless the reference system.

I don't understand the problem... so I'll do a shot in the dark. :tongue2:

The most essential feature of SR is the relativity principle, which originally was formulated as the impossibility to detect absolute (uniform) motion. An alternative formulation is that the laws of nature (such as about observed aberration) must be independent of the inertial reference system that one chooses for the calculations.

If for example the sun would correspond to a preferred frame for the laws of aberration as observed from Earth, then that would break the relativity principle. Instead, it is only "preferred" for convenience (simplicity) of calculation - just as it also simplifies mechanical calculations of the orbits of planets (more precisely, the solar system's centre of mass frame).

 

[Ken More]

There are at least three different models for predicting stellar aberration that are taught at mainstream universities or promoted by government organizations. Three of the most commonly discussed models are: James Bradley's Falling Rain model, Einstein's 1905 Doppler Stellar Aberration Model and the Stellar Aberration model used by the US Naval Observatory's NOVAS software to predict the location of a given star at a given future date and time. Although all three of these models claim to be able to predict the location of a given star to within a few arc seconds (say 3 or 4 arc seconds); the predictions of these three models do not agree. In fact, their predictions for a star when it is in the plane that is perpendicular to the Earth's velocity vector disagree by more than 20 arc seconds.

Does this disagreement between the predictions of models supported by the mainstream bother any of you "Physicists" that post to the Physics Forum. If it bothers you, you may be interested in learning more about this disagreement at: http://www.ken-more.com/Stellar_Aberration.html

 

[harrylin]

There are at least three different models for predicting stellar aberration that are taught at mainstream universities or promoted by government organizations. Three of the most commonly discussed models are: James Bradley's Falling Rain model, Einstein's 1905 Doppler Stellar Aberration Model and the Stellar Aberration model used by the US Naval Observatory's NOVAS software to predict the location of a given star at a given future date and time. Although all three of these models claim to be able to predict the location of a given star to within a few arc seconds (say 3 or 4 arc seconds); the predictions of these three models do not agree. In fact, their predictions for a star when it is in the plane that is perpendicular to the Earth's velocity vector disagree by more than 20 arc seconds.

Does this disagreement between the predictions of models supported by the mainstream bother any of you "Physicists" that post to the Physics Forum. If it bothers you, you may be interested in learning more about this disagreement at: http://www.ken-more.com/Stellar_Aberration.html

The classical "falling rain model" has been replaced by special relativity. If there is a refined model model that slightly differs from that of SR, I would expect it to include a GR correction accounting for the gravitational bending of light - and that does not bother me all.

Alternatively, if that isn't the case, there could be an error in that model and I think that that would bother astronomers. :tongue2:

So, could you please summarize in one line what you think is the cause?

 

[Ken More]

The classical "falling rain model" has been replaced by special relativity. If there is a refined model model that slightly differs from that of SR, I would expect it to include a GR correction accounting for the gravitational bending of light - and that does not bother me all.

Alternatively, if that isn't the case, there could be an error in that model and I think that that would bother astronomers. :tongue2:

So, could you please summarize in one line what you think is the cause?

The SR model predicts that a star near the ecliptic pole and in the plane that is perpendicular to the Earth's velocity vector has a declination aberration of over 20 arc seconds while the NOVAS model predicts aberration close to zero. There is not any significant gravitational bending due to the Earth's gravity and the gravitational bending from the Sun is very small (less than one arc second) for stars near the ecliptic pole. The NOVAS model's predictions of aberration for stars near the ecliptic pole and in the plane that is perpendicular to the Earth's velocity vector is close to zero and actual telescopic observations verify that aberration is close to zero when the star in the plane that is perpendicular to the Earth's velocity vector.

The issue here is whether there is a problem with the SR stellar aberration model's predictions or a problem with the NOVAS model's predictions that agree with empirical telescopic observations.

So, could you send me in one line what you think is the reason that the SR model (with or without GR corrections) predicts aberration close to 20 arc seconds for all stars near the ecliptic pole while their aberration is observed to be near zero when in the plane that is perpendicular to the Earth's velocity vector.

 

[PAllen]

The SR model predicts that a star near the ecliptic pole and in the plane that is perpendicular to the Earth's velocity vector has a declination aberration of over 20 arc seconds while the NOVAS model predicts aberration close to zero. There is not any significant gravitational bending due to the Earth's gravity and the gravitational bending from the Sun is very small (less than one arc second) for stars near the ecliptic pole. The NOVAS model's predictions of aberration for stars near the ecliptic pole and in the plane that is perpendicular to the Earth's velocity vector is close to zero and actual telescopic observations verify that aberration is close to zero when the star in the plane that is perpendicular to the Earth's velocity vector.

The issue here is whether there is a problem with the SR stellar aberration model's predictions or a problem with the NOVAS model's predictions that agree with empirical telescopic observations.

So, could you send me in one line what you think is the reason that the SR model (with or without GR corrections) predicts aberration close to 20 arc seconds for all stars near the ecliptic pole while their aberration is observed to be near zero when in the plane that is perpendicular to the Earth's velocity vector.

Can you provide any reference for this alleged discrepancy between telescope observations and SR abberation model besides your personal website? If not, this discussion is in gross violation of physicsforum rules.

 

[Ken More]

My "personal website" has all of the references and explains the problems with the state-of-the-art of stellar aberration prediction models. The reference to the SR model can be found in: "Einstein, A. 1905, On the Electrodynamics of Moving Bodies, revised and translated in The Principle of Relativity, Dover, NY, 1923, pp. 35-65". You can apply Einstein's Doppler Stellar aberration model to get its prediction of the aberration of stars near the Ecliptic pole. The reference to the equation used in the NOVAS model can be found in: The Astronomical Almanac 2010, Washington: U.S. Government Printing Office, p. B28 you can apply this equation to do the calculations of stars when they are in the plane that is perpendicular to the Earth's velocity vector or you can download a free C++ or Fortran version of the NOVAS software that uses this equation shown in the 2010 Astronomical Almanac and have it do the calculations of stars when they are in the plane that is perpendicular to the Earth's velocity vector.

 

[PAllen]

My "personal website" has all of the references and explains the problems with the state-of-the-art of stellar aberration prediction models. The reference to the SR model can be found in: "Einstein, A. 1905, On the Electrodynamics of Moving Bodies, revised and translated in The Principle of Relativity, Dover, NY, 1923, pp. 35-65". You can apply Einstein's Doppler Stellar aberration model to get its prediction of the aberration of stars near the Ecliptic pole. The reference to the equation used in the NOVAS model can be found in: The Astronomical Almanac 2010, Washington: U.S. Government Printing Office, p. B28 you can apply this equation to do the calculations of stars when they are in the plane that is perpendicular to the Earth's velocity vector or you can download a free C++ or Fortran version of the NOVAS software that uses this equation shown in the 2010 Astronomical Almanac and have it do the calculations of stars when they are in the plane that is perpendicular to the Earth's velocity vector.

The issue is you're the one applying SR aberration in the way you think is correct, and claiming a discrepancy. I have a guess where your misunderstanding might be, but since you are claiming the discrepancy as fact, you must provide a reference to a reputable source describing the discrepancy. Otherwise, even if you are right (not likely), this constitutes original research at odds with peer reviewed opinion. It is therefore not allowed to be discussed here at all - unless you provide a reference for there being a discrepancy.

Note, for example, there are known anomalies in respect to expected results from GR. These can be discussed here because there are peer reviewed discussions of these discrepancies.

 

[zonde]

The SR model predicts that a star near the ecliptic pole and in the plane that is perpendicular to the Earth's velocity vector has a declination aberration of over 20 arc seconds

Am I missing something? Because ecliptic pole is always on the plane that is perpendicular to the Earth's velocity vector.
So obviously all stars near ecliptic pole have aberration at all times. The only change is in what direction their apparent position has shifted.

while the NOVAS model predicts aberration close to zero. There is not any significant gravitational bending due to the Earth's gravity and the gravitational bending from the Sun is very small (less than one arc second) for stars near the ecliptic pole. The NOVAS model's predictions of aberration for stars near the ecliptic pole and in the plane that is perpendicular to the Earth's velocity vector is close to zero and actual telescopic observations verify that aberration is close to zero when the star in the plane that is perpendicular to the Earth's velocity vector.

The issue here is whether there is a problem with the SR stellar aberration model's predictions or a problem with the NOVAS model's predictions that agree with empirical telescopic observations.

So, could you send me in one line what you think is the reason that the SR model (with or without GR corrections) predicts aberration close to 20 arc seconds for all stars near the ecliptic pole while their aberration is observed to be near zero when in the plane that is perpendicular to the Earth's velocity vector.

This (bold part) is plain wrong as far as I know.
For example if we look in wikipedia Aberration of light figure 4 shows apparent shift in star's position. A star near ecliptic pole has ecliptic latitude around 90° and it "draws" circle during a year.

Maybe you have mixed ecliptic plane with ecliptic pole somewhere along the way?

 

[Dale]

We don't know the 'true' angular position of stars.

I think that this is the key point. Abberation is a difference between a "true" and an observed angle. The angle is frame variant, so the designation of the "true" angle requires specification of some frame as being the frame whose angle represents truth. That is a matter of convention, the usual convention being the frame in which the sun is at rest.

 

[Ken More]

Am I missing something? Because ecliptic pole is always on the plane that is perpendicular to the Earth's velocity vector.
So obviously all stars near ecliptic pole have aberration at all times. The only change is in what direction their apparent position has shifted.


This (bold part) is plain wrong as far as I know.
For example if we look in wikipedia Aberration of light figure 4 shows apparent shift in star's position. A star near ecliptic pole has ecliptic latitude around 90° and it "draws" circle during a year.

Maybe you have mixed ecliptic plane with ecliptic pole somewhere along the way?

Zonde, you are not missing anything. A star near the ecliptic pole is always near the plane that is perpendicular to the Earth's velocity vector. Now can you tell me when annual aberration is zero for a star? Is it only when the star's vector is in the ecliptic plane or can a star above the ecliptic plane have zero aberration at any time of the year?

 

[zonde]

Zonde, you are not missing anything. A star near the ecliptic pole is always near the plane that is perpendicular to the Earth's velocity vector. Now can you tell me when annual aberration is zero for a star? Is it only when the star's vector is in the ecliptic plane or can a star above the ecliptic plane have zero aberration at any time of the year?

Aberration for a star is zero only when Earth is moving in direction of that star. That of course can happen only for a star that is in ecliptic plane.

 

[Ken More]

Aberration for a star is zero only when Earth is moving in direction of that star. That of course can happen only for a star that is in ecliptic plane.

So, are you saying that declination aberration is zero only when declination (δ₀) is 0° and right ascension (α₀) is 0°? If you are saying this, then it is my openion that this disagrees with the Reduction for Annual Stellar Aberration equation: Aberration (δ - δ₀) = - x/c.cos α₀.sin δ₀ that is on page B28 in the 2010 Astronomical Almanac where x is the Earth's velocity and c is the velocity of light. When I do the math, declination aberration is zero when α₀ = 90° and δ₀ = 0° as well as when right ascension (α₀) is 0° and δ₀ = 0°. Also, since cos α₀ is always zero when α₀ = 90° then declination aberration is always zero for any declination (δ₀ from 0° to 90°) and this occurs for all stars three months from the time when α₀ = 0° when the star is in the plane that is perpendicular to the Earth's velocity vector.

If you or anyone else at Physics Forum has enough interest in this subject to get access to a copy of the 2010 Astronomical Almanac and check out my interpretation of its Reduction for Annual Stellar Aberration equation then I would be very grateful if you can tell me where I am going wrong.

 

[zonde]

So, are you saying that declination aberration is zero only when declination (δ₀) is 0° and right ascension (α₀) is 0°?

No, I was not talking about "declination aberration", I was talking about "aberration".

Astronomers probably care much more about "declination aberration" because that's much easier to measure than "right ascension aberration". So they might (I guess) shorten "declination aberration" for "aberration" but that would not be correct of course.

 

[Ken More]

No, I was not talking about "declination aberration", I was talking about "aberration".

Astronomers probably care much more about "declination aberration" because that's much easier to measure than "right ascension aberration". So they might (I guess) shorten "declination aberration" for "aberration" but that would not be correct of course.

zonde, I am very impressed! I believe you understand aberration better than anyone with whom I have ever discussed the subject. Since you are apparently an advanced stellar aberration guru, I would like to know if you think Einstein's Doppler Stellar Aberration equation in his 1905 paper "On the Electrodynamics of Moving Bodies" yields an accurate estimate of "declination aberration" or "right ascension aberration" or "intrinsic aberration" or neither. I would also like to know if you know who has an accurate model for estimating both "declination aberration" and "right ascension aberration" other than the USNO as described in the 2010 Astronomical Almanac?

 

[Ken More]

No, I was not talking about "declination aberration", I was talking about "aberration".

Astronomers probably care much more about "declination aberration" because that's much easier to measure than "right ascension aberration". So they might (I guess) shorten "declination aberration" for "aberration" but that would not be correct of course.

zonde, I will assume that you are acknowledging that astronomers can measure "right ascension aberration" as well as "declination aberration". Can they also measure "aberration" (which I will call "intrinsic aberration" henceforth)? Also, can you please tell me what kind of aberration is predicted by the Doppler Aberration equation that is in Einstein's 1905 paper "On the Electrodynamics of Moving Bodies"?

 

[PAllen]

Einstein's paper deals with total aberration, which is the combination of declination and ascension aberration (as a total displacement angle). I assume astronomers can detect both aberrations now. Having reviewed astronomic coordinates, I notice that stars at certain positions on the ecliptic will never undergo seasonal declination aberration; they will only have right ascension aberration. Stars at 90% on the ecliptic to these will have both aberrations, but the declination aberration will be smaller than the ascension aberration. Of course, for stars on the ecliptic, there will be no aberration at all twice a year.

For a star perpendicular to the ecliptic, there will always be aberration (of constant magnitude relative to position in a solar system frame), but twice a year it will include no declination aberration (it will be pure ascension aberration).

Stars in between, will have varying total aberration, and will also have no declination aberration twice a year.

Finally, I don't think any of this has to do with relativistic aberration per se. The size of the relativistic correction to classical aberration is, last I checked, undetectable for Earth's orbital speed. My guesstimate for the correction due to the difference between classical and relativistic aberration for seasonal aberration from Earth's motion would be of the order .002 arcseconds. Thus, none of this discussion has anything to do with special relativity. It only relates to the finite speed of light (Galilean versus Special relativity is not distinguished).