# Stellar aberation, a One way measurement of c?

1. Jan 30, 2012

### 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?

Last edited: Jan 30, 2012
2. Jan 30, 2012

### 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.

3. Jan 31, 2012

### Tracer

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

4. Jan 31, 2012

### ghwellsjr

Yes, many, starting with Einstein.

5. Jan 31, 2012

### 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.

6. Jan 31, 2012

### ghwellsjr

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

7. Jan 31, 2012

### 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.

8. Jan 31, 2012

### ghwellsjr

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

9. Feb 1, 2012

### 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!

10. Feb 2, 2012

### harrylin

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

11. Feb 2, 2012

### 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.

12. Feb 2, 2012

### 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?

13. Feb 2, 2012

### 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 wich in the case of some binaries is well known and important enough to produce significant corrections?

14. Feb 2, 2012

### PAllen

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.

15. Feb 3, 2012

### harrylin

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.

16. Feb 3, 2012

### harrylin

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.

17. Feb 3, 2012

### TrickyDicky

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"

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?

18. Feb 3, 2012

### harrylin

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.
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.
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.
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.

19. Feb 3, 2012

### TrickyDicky

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

20. Feb 3, 2012

### harrylin

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).

Last edited: Feb 3, 2012