From: fortunati.luigi@gmail.com   
      
   Mike Fontenot martedì 15/03/2022 alle ore 19:57:00 ha scritto:   
   > I made a careless mistake in my previous post.  Here is that post, down to   
   where my mistake occurred:   
   >   
   > On 3/15/22 2:36 AM, Mike Fontenot wrote:   
   >>   
   >> Suppose the two twins have just been born when the traveling twin starts   
   >> his trip.  So they are each zero years old then.  If the traveling twin   
   >> (he) travels for 4 years of his time, he will be 4 yours old when he   
   >> stops.  (His age when he stops is an EVENT that all observers must agree   
   >> about, and so she also agrees that he is 4 years old when he stops. He   
   >> says he has traveled (0.866)(4) = 3.464 lightyears away from his twin   
   >> (her) then.  She says he traveled 8 years of her time ... i.e., she says   
   >> she is 8 years old when he stops.  She says he is (0.866)(8) = 6.928   
   >> lightyears away when he stops.   
   >>   
   >> After he stops, she says that he remains 6.928 lightyears away from her   
   >> after that.  And she says they age at the same rate after he stops.  He   
   >> says that, during his essentially instantaneous stopping time, his age   
   >> essentially doesn't change during his stopping.  She agrees with that.   
   >   
   > The above is all correct.  But here is the sentence where I made the   
   careless error:   
   >   
   >> But he says that during his essentially instantaneous stopping, SHE   
   >> essentially instantaneously gets older by 4 years ... i.e., he says that   
   >> she essentially instantaneously goes from being 4 years old to being 8   
   >> years old during the essentially instantaneous time in his life it takes   
   >> him to stop.   
   >   
   > According to him, her age right before he stops is 2 years old, not 4 years   
   old as I said above.  Immediately after he stops, they both agree about their   
   respective ages.  He says she is now 8 years old, so he says her age increases   
   by 6 years during    
   his essentially instantaneous stopping, not by 4 years as I stated in my   
   previous post.   
   >   
   > I should also have pointed out that each of the twins, during his outbound   
   trip, are entitled to use the famous time dilation equation for inertial   
   observers:  That equation says that any inertial observer will conclude that a   
   person moving at speed "v"   
    with respect to them is ageing at a rate gamma times slower than they are,   
   where   
   >   
   >    gamma = 1 / sqrt { 1 / (1 - v * v) },   
   >   
   > where the asterisk indicates multiplication.  For v = 0.866, gamma = 2.0.    
   So on the outbound trip, each twin says the other twin is ageing half as fast   
   as their own rate of ageing.  So right before he stops, she says he is 4 and   
   she is 8, but he says    
   he is 4 and she is 2.  And immediately after he stops, they both agree that he   
   is 4 and she is 8. So he says she essentially instantaneously gets 6 years   
   older during his essentially instantaneous stopping.   
      
   Perfect, I was going to report this discrepancy between instant aging of   
   4 instead of 6 years, now I absolutely agree with everything you have   
   written.   
      
   But you didn't answer my question about the Earth's revolutions around   
   the Sun.   
      
   Since I want my question to be clear, I express myself with numbers and   
   dates.   
      
   The traveling twin leaves on January 1, 2022 and keeps his telescope   
   continuously pointed at the receding solar system at speed v = 0.866c,   
   so that he can count how many revolutions the Earth makes around the   
   Sun.   
      
   Obviously, the turns seen on the telescope will take place much slower   
   than one for each year, both for the finite speed of the light (which,   
   due to the recession, takes more and more time to get to the spaceship   
   from the solar system) and for the time dilation   
      
   And all this greatly complicates the calculations.   
      
   This is why I ask: is it possible to calculate how many turns the   
   traveler twin will have * seen * make from the Earth around the Sun on   
   the spacecraft's telescope, after its 4-year journey, before starting to   
   brake?   
      
   --- SoupGate-Win32 v1.05   
    * Origin: you cannot sedate... all the things you hate (1:229/2)