🚀 go-pugleaf

Max Keon skrev:
> "Eric Gisse" <jowr.pi@gmail.com> wrote in message
> news:cf7fd5a6-005e-4d73-aef9-ba788194923d@s8g2000prg.googlegroups.com...
>> Max Keon wrote:
>>> Eric Gisse wrote:
>>>> Max Keon wrote:
> 
>>>>> The results are the same as with GR. A clock fixed with the ECI
>>>>> frame at an Earth surface radius loses 5.28e-10 seconds per
>>>>> second of a GPS satellite radius clock. Multiply that by 86160
>>>>>  = 4.55e-5 seconds per sidereal day. What's wrong with that?
>>>> Are you unable to tell the difference between being a fair distance
>>>> from a point mass to being immersed in an isotopic spray of matter?
>>>>
>>>>>  1+V/c^2 is the gravitational redshift factor, and that applies
>>>>> to every electronic interaction, including clocks. V is GM/r. So
>>>>> that becomes  1+(G*M/r)/c^2  which is the same as my equation
>>>>>  t' = t+t*(G*M/r)/c^2  so long as "t" is specified as the time
>>>>> unit, which is always 1.
>>>> Your equation is wrong, as I already demonstrated.
>>> My equation gives the correct answer.
> 
>> Does it?
>>
>> Let's see the computation.
> 
> Firstly, all clocks are fixed with the ECI frame.
> 
>  1+(GM/r)/c^2: r=6378000 meters for the surface radius clock:
>  1+(6.67e-11*5.97e24/6378000)/3e8^2 = 1.000000000694 seconds
> per 1 second of a clock that's unaffected by Earth's gravity.

Wrong sign.
Should be (1-(GM/r)/c^2) = 1 - 6.94e-10
A clock at zero altitude, stationary in the ECI frame
runs slow by the factor (1 - 6.94e-10) compared to a clock
unaffected by Earth's gravity.

> 
>  1+(GM/r)/c^2: r=26570000 meters for the GPS radius clock:
>  1+(6.67e-11*5.97e24/26570000)/3e8^2 = 1.0000000001665 seconds
> per 1 second of a clock that's unaffected by Earth's gravity.

A clock at GPS altitude, stationary in the ECI frame
runs slow by the factor (1 - 1.665e-10) compared to a clock
unaffected by Earth's gravity.

>  1.000000000694 - 1.0000000001665 = 5.28e-10 difference.

(1 - 1.665e-10)/(1 - 6.94e-10)~= (1 - 1.665e-10 + 6.94e-10) = 1 + 5.28e-10

A clock at GPS altitude runs fast by the factor (1 + 5.28e-10)
compared to a clock at zero altitude. (Both stationary in the ECI-frame)

> The GPS radius clock is running 5.28e-10 seconds faster per
> second than the lower clock. Multiply that by 86160 = 4.55e-5
> seconds faster per sidereal day.
> 
> That's correct isn't it.

Right.
Your wrong signs cancel.


>>>>> The way it was written may have been confusing to you, but it
>>>>> wasn't wrong.
>>>> Actually, it is. You are taking the weak field approximation to GR,
>>>> and then you apply it incorrectly.
>>> But I get the right answer don't I.
> 
>> It has zero chance of getting the right answer for GPS since movement
>> is not taken into account,
> 
> I wasn't including movement. The description was, "A clock fixed
> with the ECI frame at an Earth surface radius loses 5.28e-10
> seconds per second of a GPS satellite radius clock." I thought
> it was clear that the two clocks were fixed with the ECI frame.
> 
>> and I see no comparison against Pound &
>> Rebka.
> 
> If radioactive iron is chosen as the frequency generator in an
> atomic clock, a GPS radius clock will run _slower_ than the
> surface radius clock (all fixed with the ECI frame), by 4.55e-5
> seconds per sidereal day. Not faster. The Pound and Rebka
> experiment proves that gamma rays are generated in a vastly
> different environment to that of lesser frequency rays.

How did you arrive at this remarkable conclusion?
It is wrong.

f_h/f_o = (1-(GM/r)/c^2)/(1-(GM/R)/c^2)~= 1-(GM/r)/c^2 + (GM/R)/c^2
where:
   f_h = frequency of gamma photon at the top of the tower
   f_o = frequency of gamma photon at the bottom of the tower
   r = the distance centre of the Earth - top of tower
   R = radius of the Earth (at the bottom of the tower)

  r = R + h, h = height of tower
  f_h/f_o ~= (1 + ((GM/R)/c^2)(1 - R/(R+h))
  When h/R << 1 :
  R/(R+h) ~= (1-h/R)

  f_h/f_o ~= 1 + ((GM/R)/c^2)(h/R)
  g = GM/R^2

  f_h/f_o ~= 1 + gh/c^2

  Which is in accordance with the Pound & Rebka experiment.


-- 
Paul

http://home.c2i.net/pb_andersen/