Speed of the Sun: Facts & Measurements

[W3pcq]

Is the doppler effect of EM radiation compatible with C according to special relativity?

 

[Janus]

Is the doppler effect of EM radiation compatible with C according to special relativity?

The standard Doppler effect equation has to be modified to a relativistic form, but the basic concept of the Doppler effect remains the same.

 

[marcus]

Is the doppler effect of EM radiation compatible with C according to special relativity?

The standard Doppler effect equation has to be modified to a relativistic form, but the basic concept of the Doppler effect remains the same.

To expand on what Janus said, the Doppler equation in Special Relativity (which only works for speeds less than c) says that the frequency ratio is
$$\sqrt{\frac{c-v}{c+v}}$$

Here v is the speed of the emitter relative to the receiver, and positive v denotes increasing distance. You can see that if v = 0.5c then the frequency ratio is
$$\sqrt{\frac{0.5}{1.5}} = 0.58$$
That means that the frequency of the received light is only 58 percent of the frequency of what was sent.

If you think in terms of wavelengths, they get longer and the formula is just the reciprocal. In astronomy the wavelength ratio can be written 1+z, so you might see this equation for a Doppler shift
$$1+z = \sqrt{\frac{c+v}{c-v}}$$

the point that needs emphasis IMO is that these Special Relativity formulas do not work for calculating the cosmological redshift.
In the case of redshift, the recession speeds are often greater than c, and the formulas break down in that case.
So in a beginning astronomy class you get taught a different formula for the redshift which does not depend on velocity.
$$1+z = \frac{a(t_r)}{a(t_e)}$$
Here t_e is the time the light was emitted and t_r is the time it was received. The a(t) is the scale factor at time t. The ratio is the factor by which the universe expanded during the time the light was in transit.

 

[John Richard]

What you say seems to be at odds with what is generally taught in college physics. Something's odd, either factually or in your use of terminology.

It was receding from us at a speed of about 60c (sixty times the speed of light).

Today, that same matter, whose light is just now reaching us as CMB, is about 45 billion LY from us, and receding at a speed of 3.3c (slightly over three times the speed of light).

Marcus, thank you for your reply. I think I was just factually wrong and I appologize to rbj.

Sometimes, stating what you think you know, gets a better answer than any question you may have asked. That is certainly true for me in this case.

You speak of speeds in excess of C and of CMB just reaching us and this makes it clear to me that I have a big gap in how I'm interpreting the big bang model. I understand that the CMB wave length will stretch as a result of the expansion. But, I am under the impression that we were inside the big bang, which means that the CMB will have to have been around us from the start.

I am also under the impression that nothing travels faster than light and that all points of observation will measure light at the same speed. I had assumed therefore, that the CMB that is around us is phase shifted from origin by a measure of light years equal to the time since the big bang. That the expansion has effected only the frequency.

I do not think it is fair of me to press on your time just to teach me. I would be very grateful if you could suggest some reading that might clear up my misconceptions.

Once again, thank you for taking time to help me.

John

 

[marcus]

... which means that the CMB will have to have been around us from the start.
...

Yes that is right! Caveat, we are talking about the mainstream picture here. there is a lot of evidence that it is right as far as it goes.

To get used to visualizing standard cosmology it can help enormously to play around with a cosmology calculatory. Several people here at PF have made their own----Jorrie, hellfire and I don't know who else. there are some threads where they discuss features.

but most of us use online java calculators by Ned Wright or Siobhan Morgan.
Go here
http://hubblesite.org/newscenter/archive/releases/2008/08/full/
http://scienceblogs.com/catdynamics/2008/02/liveblogging_the_high_redshift_1.php

It talks about a young galaxy at redshift z = 7.6 (if confirmed) observed as it was 12.8 billion years ago during the first wave of star formation
this is conference news, it hasn't been published yet AFAIK

So suppose you want to know the recession speed of a galaxy at z = 7.6
First try Ned Wright's
http://www.astro.ucla.edu/~wright/CosmoCalc.html
just plug in 7.6 for z, over on the left

what I get from Wright's is that the light travel time was 12.97 billion years which is a little off from the 12.8 they say in the press release but small discrepancies don't matter here. and I get that the age of the universe when the light was emitted was 0.7 billion years. Is that what you get?

the important thing to notice is over on the left Ned Wright puts in the default values of H=71, and Omega_matter = 0.27 and Lambda = 0.73. they are accepted parameter values, widely used. So when you go on to Morgan's calculator you should take them along with you and plug them in too. Morgan wants her students to work more and consciously put them in.

So then go here
http://www.uni.edu/morgans/ajjar/Cosmology/cosmos.html
and over on the left, put in 0.27 for matter, 0.73 for Lambda, and 71 for Hubble.
Then type 7.6 into the z box and see what you get. You should get some recession speeds!

Cosmology is largely non verbal. It is applying a mathematical model to the geometry of the universe, and fitting it to many different kinds of data.
That mathematical model is built into Wright's and Morgan's calculators.
When you play with those calculators you are playing with the best model of the universe we have today.

Truly enormous amounts of data of many different kinds are used to challenge the model. it must fit to the data. that is how the numbers 0.27, 0.73 and 71 are determined. The more data, the more accurate these estimates get, and the better the fit.

What do you get for the speeds? I get about 3.3c and 2.3c. 3.3c is the recession speed of the galaxy THEN when it emitted the light (some 12.8 billion years ago) and 2.3c is the recession speed NOW as the light is arriving to us and coming down the telescope.

The distance now should be greater than the distance then by a factor of 1+z which is 8.6.

How about checking to see if that is about right? 1+z is the factor by which the light wavelengths are stretched, so it must be the factor by which distances expanded in the universe while the light was in transit to us. If the ratio doesn't work out right, please tell me!
==========================
I gathered a bunch of useful links here:
https://www.physicsforums.com/showthread.php?p=1610331#post1610331

 

[AstroLiv]

I think I previously posted this comment wrongly:

Hi Marcus,

Do you have any idea where can I find a good multimedia, or other interaction to well understand the Solar Dopplergrams? I have difficulty answering the following question:

At about what speed is the right edge of the sun moving away (receding) from us at the equator?

Thank you in advance for your help.

Liv.