Re: GR frequency shift formula


Hexenmeister wrote:
<mluttgens@xxxxxxxxxx> wrote in message news:1145885127.359964.148740@xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
| Here is again my last response, because it is not necessary to
| reproduce the whole discussion:
|
| The problem was finding a *general* GR solution for the following
| scenario:
|
| Two non-rotating spherical celestial objects 1 and 2 are orbiting along
|
| their common center of gravity.

"Barycentre" in English (or if American, "barycenter", it means the same).
http://en.wikipedia.org/wiki/Barycentre



| The masses and radii of the objects are respectively M1, R1 and M2,R2.
| the distance between centers is d.
| Object 1 emits a light of frequency Nu1. What is the frequency Nu2
| of the light received by an observer situated on object 2 at a distance
|
| d - (R1+R2) from the emitter?

Actually an intriguing question since it isn't (in general) Nu1 by
Celestial Mechanics.
Unfortunately you haven't supplied sufficient information.
The problem is d, which is not constant for an elliptical orbit
and in the general case the orbit is elliptical. Thus there is a velocity
component along the line of separation and consequently
a frequency shift, sometimes red and sometimes blue.

Androcles, you rightly wrote:

"The problem is d, which is not constant for an elliptical orbit
and in the general case the orbit is elliptical. Thus there is a
velocity
component along the line of separation and consequently
a frequency shift, sometimes red and sometimes blue."

I was not interested in what you called the general case, where
the orbit is elliptical.

My aim was to bring to the fore that GR, or more particularely, the
GR experts who "rule" this NG, are unable to solve two elementary
problems, i.e.

1) A light signal of frequency Nu0 is emitted at a distance
aR from the center of a transparent uniform star of mass M
and radius R.
What is the GR formula giving the signal frequency Nu1 observed
at the surface of the star, knowing that 0 <= a < R ?"

Notice that the GR solution is straightforward in this case, on
one condition, the GRists must understand and be able to use their
formulae.

2) Two non-rotating spherical celestial objects 1 and 2 are orbiting
along their common center of gravity.
The masses and radii of the objects are respectively M1, R1 and M2,R2.
the distance between centers is d.
Object 1 emits a light of frequency Nu1. What is the frequency Nu2
of the light received by an observer situated on object 2 at a distance

d - (R1+R2) from the emitter?

One honest response was given by Tom Roberts:

"There is no useful approximation that applies, and this is a
quite complicated computation that can only be performed via numerical
simulation."

He was right, GR can't give a general formula!

Marcel Luttgens


Nu2 = Nu1 (c+v)/c

Androcles.

| What is your general formula?
| Obviously not the one you presented, as it gives a wrong result
| when M1=M2, R1=R2 and d big.
|
| Recognize that you can't derive such general GR formula.
| But if you can, there really is a good reason to go further.
|
| Marcel Luttgens
|

.

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