Groups > sci.physics.relativity > #674357

Re: GPS clocks should run Slow Not Fast.

From	"Paul B. Andersen" <paul.b.andersen@paulba.no>
Newsgroups	sci.physics.relativity
Subject	Re: GPS clocks should run Slow Not Fast.
Date	2026-10-12 20:55 +0200
Organization	A noiseless patient Spider
Message-ID	<11ajabc$3ss4t$1@dont-email.me> (permalink)
References	<18dd9f33b63d4fa4$584$2574533$4006de53@news.newsgroupdirect.com>

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Den 12.10.2026 02:01, skrev HenryWilson:
> Here is one to argue about. According to GR, light experiences a redshift
> in frequency when sent into lower gravity potential. How come clocks are
> claimed to run fast when sent into orbit. Clocks merely count cycles of an
> oscillator, which according to GR should run slow.

Confused, Ralph? :-D

In the following we will assume that the Earth is not rotating.

This is what GR say:

Clocks always run at their proper rate, one second per second.

If a clock on the ground is emitting a signal with
frequency f₀ = 1 GHZ, then the frequency received at
a position r above the centre of the Earth is:
   Δf/f₀= (GM/c²)⋅(1/r - 1/R) = -5.2996e-10
where:
GM = 3.986004418e14 m³/s² Geocentric gravitational constant
c  = 299792458 m/s speed of light in vacuum
R  = 6363691 m radius of Earth
r  = 26561763 m radius of GPS orbit

This means that the received frequency is:
f = 1GHz⋅(1 + Δf/f₀) =  999999999.47 Hz, a gravitational red shift.

Observed from the position r above Erth's centre
the ground clock appears to run slow.

If a clock at a position r above the centre of the Earth is emitting
a signal with frequency f₀ = 1 GHZ, then the frequency received at
the ground is:
   Δf/f₀= (GM/c²)⋅(1/R - 1/r) = 5.2996e-10

This means that the received frequency is:
f = 1GHz⋅(1 + Δf/f₀) = 1000000000.53 Hz, a gravitational blue shift.

Observed from the ground the clock at r appears to run fast.

-----------------

The Earth is obviously rotating, so in the GPS we have:

The gravitational blue shift of the SV signal is Δf/f =  5.2996e-10
The kinetic red shift (due to motion) is         Δf/f = -0.8349e-10
The total(gravitational + kinetic) blue shift is Δf/f =  4.4647e-10

-- 
Paul

https://paulba.no/

Thread

GPS clocks should run Slow Not Fast. HenryWilson <Hgw@home.com> - 2026-10-12 00:01 +0000
  Re: GPS clocks should run Slow Not Fast. Emanuele Babuh <uh@elbbem.ru> - 2026-10-12 07:40 +0000
  Re: GPS clocks should run Slow Not Fast. "Paul B. Andersen" <paul.b.andersen@paulba.no> - 2026-10-12 20:55 +0200
    Re: GPS clocks should run Slow Not Fast. Maciej Woźniak <mlwozniak@wp.pl> - 2026-10-13 07:30 +0200
      Re: GPS clocks should run Slow Not Fast. Clancy Balanovski <av@sysal.ru> - 2026-10-13 07:07 +0000
    Re: GPS clocks should run Slow Not Fast. Thomas 'PointedEars' Lahn <PointedEars@web.de> - 2026-10-13 10:27 +0200
      Re: GPS clocks should run Slow Not Fast. "Paul B. Andersen" <paul.b.andersen@paulba.no> - 2026-10-13 22:32 +0200
        Re: GPS clocks should run Slow Not Fast. Thomas 'PointedEars' Lahn <PointedEars@web.de> - 2026-10-14 14:20 +0200
          Re: GPS clocks should run Slow Not Fast. "Paul B. Andersen" <paul.b.andersen@paulba.no> - 2026-10-14 21:08 +0200
            Re: GPS clocks should run Slow Not Fast. Thomas 'PointedEars' Lahn <PointedEars@web.de> - 2026-10-14 23:08 +0200
              Re: GPS clocks should run Slow Not Fast. "Paul B. Andersen" <paul.b.andersen@paulba.no> - 2026-10-15 23:10 +0200
                Re: GPS clocks should run Slow Not Fast. The Starmaker <starmaker@ix.netcom.com> - 2026-10-15 22:05 -0700
                Re: GPS clocks should run Slow Not Fast. The Starmaker <starmaker@ix.netcom.com> - 2026-10-18 16:54 -0700
                Re: GPS clocks should run Slow Not Fast. Ross Finlayson <ross.a.finlayson@gmail.com> - 2026-10-19 03:09 -0700
                Re: GPS clocks should run Slow Not Fast. The Starmaker <starmaker@ix.netcom.com> - 2026-10-19 09:50 -0700
                Re: GPS clocks should run Slow Not Fast. The Starmaker <starmaker@ix.netcom.com> - 2026-10-19 23:20 -0700
                Re: GPS clocks should run Slow Not Fast. The Starmaker <starmaker@ix.netcom.com> - 2026-10-21 12:25 -0700
                Re: GPS clocks should run Slow Not Fast. The Starmaker <starmaker@ix.netcom.com> - 2026-10-22 11:34 -0700
                Re: GPS clocks should run Slow Not Fast. The Starmaker <starmaker@ix.netcom.com> - 2026-10-22 12:28 -0700
                Re: GPS clocks should run Slow Not Fast. The Starmaker <starmaker@ix.netcom.com> - 2026-10-22 14:30 -0700
                Re: GPS clocks should run Slow Not Fast. Ross Finlayson <ross.a.finlayson@gmail.com> - 2026-10-22 19:46 -0700
                Re: GPS clocks should run Slow Not Fast. The Starmaker <starmaker@ix.netcom.com> - 2026-10-22 22:14 -0700
    Re: GPS clocks should run Slow Not Fast. HenryWilson <Hgw@home.com> - 2026-10-13 15:20 +0000
      Re: GPS clocks should run Slow Not Fast. Thomas 'PointedEars' Lahn <PointedEars@web.de> - 2026-10-14 14:12 +0200
        Re: GPS clocks should run Slow Not Fast. HenryWilson <Hgw@home.com> - 2026-10-16 10:36 +0000
          Re: GPS clocks should run Slow Not Fast. Thomas 'PointedEars' Lahn <PointedEars@web.de> - 2026-10-19 03:28 +0200
      Re: GPS clocks should run Slow Not Fast. "Paul B. Andersen" <paul.b.andersen@paulba.no> - 2026-10-14 21:07 +0200
        Re: GPS clocks should run Slow Not Fast. Wildo Zhmulev <vedlml@hlhiudlo.ru> - 2026-10-15 07:52 +0000
        Re: GPS clocks should run Slow Not Fast. HenryWilson <Hgw@home.com> - 2026-10-16 10:39 +0000
  Re: GPS clocks should run Slow Not Fast. Thomas 'PointedEars' Lahn <PointedEars@web.de> - 2026-10-13 09:42 +0200
    Re: GPS clocks should run Slow Not Fast. HenryWilson <Hgw@home.com> - 2026-10-13 15:54 +0000
      Re: GPS clocks should run Slow Not Fast. Python <python@cccp.invalid> - 2026-10-13 16:01 +0000
        Re: GPS clocks should run Slow Not Fast. Ross Finlayson <ross.a.finlayson@gmail.com> - 2026-10-13 09:10 -0700
          Re: GPS clocks should run Slow Not Fast. Ross Finlayson <ross.a.finlayson@gmail.com> - 2026-10-14 06:18 -0700
      Re: GPS clocks should run Slow Not Fast. Thomas 'PointedEars' Lahn <PointedEars@web.de> - 2026-10-14 17:30 +0200
        Re: GPS clocks should run Slow Not Fast. Ross Finlayson <ross.a.finlayson@gmail.com> - 2026-10-14 09:32 -0700
  Re: GPS clocks should run Slow Not Fast. Mikko <mikko.levanto@iki.fi> - 2026-10-21 11:04 +0300
    Re: GPS clocks should run Slow Not Fast. Maciej Woźniak <mlwozniak@wp.pl> - 2026-10-21 10:07 +0200
    Re: GPS clocks should run Slow Not Fast. ram@zedat.fu-berlin.de (Stefan Ram) - 2026-10-24 20:18 +0000
      Re: GPS clocks should run Slow Not Fast. HenryWilson <Hgw@home.com> - 2026-10-27 11:25 +0000
    Re: GPS clocks should run Slow Not Fast. Thomas 'PointedEars' Lahn <PointedEars@web.de> - 2026-10-27 21:32 +0100
      Re: GPS clocks should run Slow Not Fast. HenryWilson <Hgw@home.com> - 2026-10-27 23:03 +0000
        Re: GPS clocks should run Slow Not Fast. Thomas 'PointedEars' Lahn <PointedEars@web.de> - 2026-10-29 00:47 +0100
          Re: GPS clocks should run Slow Not Fast. HenryWilson <Hgw@home.com> - 2026-10-29 16:41 +0000

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