Re: The GPS GR Correction, put to Rest.

From: John Kennaugh (JKNG_at_kennaugh2435hex.freeserve.co.uk)
Date: 10/07/04 

Date: Thu, 7 Oct 2004 23:19:04 +0100

Androcles writes
>
>For shift from a source in the direction of motion, the ballistic theory
>gives
>f' = f.(c+v)/c. (See Doppler)

Correct

>
>For shift from a source at right-angles to the direction of motion, the
>ballistic theory gives
>f' = f.

You would think so but No! This is the point I am making

Imagine you are on a train travelling at v and you aim your gun at a
target and fire when your line to the target is exactly at right angles
to the train tracks.
                          train --->v
           -------------| S |--------------
                                 |
                                 |
                                 |
                                 |
                                 |
                                 |
                                 T

You will miss because you, your gun and the bullet have a velocity
component v. and you will hit x

                           Train --->v
           -------------| S |--------------
                                 |.
                                 | .
                                 | .
                                 | .
                                 | .
                                 | .
                                 T x
                                  < vt >

In order to hit T when you are at S you have to aim at y.

                            Train --->v
           -------------| S |--------------
                                .|
                               . |
                              . |
                             . |
                            . |
                           . |
                          y T

 Think of it the other way around. Speed is relative so the same thing
if train stationary and target moving.

                            Train stationary
           -------------| S |--------------
                                .|
                               . |
                              . |
                             . |
                            . |
                           . |
                          y v<-T

You have to aim ahead of the moving target so that the bullet reaches y
at the same time as T does. Suppose v is much greater.

                            Train stationary
              -------------| S |--------------
                              . |
                          . |
                      . |
                  . |
              . |
          . |
       y v<-------------- T

Suppose we call the muzzle velocity c. As the bullet and T converge at y
it is obvious that they both have a velocity component in the -x
direction and their relative velocity is less than c.

 The same applies to light according to the ballistic theory. Light
travels in the direction Sy at c just as the bullet you fired travels at
muzzle velocity in the direction Sy.

There is a velocity triangle where the speed of the light in the
direction ST is by Pythagoras Sqr((Sy)^2 - (yT)^2)
Sy = ct,
yT = vt
so the effective speed is Sqr(c^2 - v^2)

Frequency is proportional to velocity

So f'/f = Sqr(c^2 - v^2)/c = Sqr(1 - v^2/c^2)

Exactly the same mathematically as SR. Relativists will say that what
they are measuring is time dilation and that it proves that SR is
correct. Ballistic theory says no. It is not time dilation just an old
fashioned velocity triangle and Pythagoras and the simplest explanation
of an experimental result should be accepted until disproved.

If you now go back to my earlier post where the source is rotating
around a fixed point as per GPS it may make more sense. 

-- 
John Kennaugh
to email convert the number from hex to decimal

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