On Wednesday, November 6, 2019 at 2:08:29 AM UTC-6, PengKuan Em wrote:   
   > Le jeudi 31 octobre 2019 21:56:14 UTC+1, richali...@gmail.com a écrit :   
   > >   
   > > Special Relativity only applies to inertial frames in flat space-time.   
   > > Satelites in orbit are not in flat space-time, even though they are in   
   > > locally inertial frames.  To properly analyze this case you need GR,   
   > > which I assume would handle it correctly.   
   > >   
   > > Rich L.   
   >   
   > The local frame at any point in general relativity is a locally inertial   
   > frame. In such frame, relativity of simultaneity applies, so the time of   
   > point 1 and 2 are different. Suppose they are t'1 and t'2 and   
   > dt'=t'2-t'1 in frame 1. then, in frame 2 next to frame 1, we have   
   > dt'=t'3-t'2. So, we have   
   > t'2=dt'+t'1 in frame 1. Suppose t'1=0. Then,t'2=dt'. Then, we have   
   > successively,   
   > t'3=dt'+t'2=2*dt' in frame 2   
   > t'4=dt'+t'3=3*dt' in frame 3   
   > ...   
   > t'(n+1)=dt'+t'n=n*dt' in frame n   
   >   
   > So, the time of the satellite n+1 is n*dt' even in GR. But satellite n+1   
   > is satellite 1 and its time should be 0. Hence, even in GR, relativity   
   > of simultaneity leads to contradiction.   
   >   
   > PK   
      
   The satellites are not in an inertial frame as required by SR, at any   
   instant they can be considered in an inertial frame at some velocity,   
   but a moment later they are in a different frame.  In SR boosts to   
   different frames is not a linear process.  You can't just add the time   
   differences as you are suggesting.  Look up Thomas Precession.   
      
   Consider viewing the satellites from the north pole, with all the   
   satellites in an equatorial orbit.  If all the satellites are at the   
   same altitude the (GR) gravitational red shift will be equal for all of   
   them.  They are all moving at the same speed in this orbit, so the SR   
   time dilation will also be the same.  You could synchronize the clocks   
   with a single pulse from the north pole.  The orbiting clocks are now   
   synchronized and running at the same speed.  Doesn't that counter your   
   argument?   
      
   Rich L.   
      
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