From: relativity@paulba.no   
      
   Den 04.03.2026 16:57, skrev Thomas 'PointedEars' Lahn:   
   > Paul B. Andersen wrote:   
   >> Den 03.03.2026 03:33, skrev Thomas 'PointedEars' Lahn:   
   >>> amirjf nin wrote:   
   >>>> https://drive.google.com/file/d/1PdTWHOo5TW0GKKyGN6HGLhYkI5JWTqMl/view   
   >>>   
   >>> Crackpottery.   
   >>>   
   >>> His claim   
   >>>   
   >>> | Such a tilt [requiring the telescope to be tilted in order to observe a   
   >>> | star] could be discovered only because the Earth's velocity is   
   >>> | continuously changing.   
   >>> is wrong.  Does he not realize that stellar aberration is observed on a   
   >>> *rotating* planet?   
   >>   
   >> His explanation of stellar aberration may be a bit awkward,   
   >> but his conclusion is correct.   
   >> It is the change of the velocity of the Earth as it orbits   
   >> the Sun that is the cause of stellar aberration.   
   >   
   > Nonsense.   
      
   I find it rather puzzling that you think so.   
   A physics student should know better.   
      
   >   
   > His conclusion is that special relativity is wrong, which is crackpot   
   nonsense.   
      
   That's not his conclusion. Quite the contrary!   
      
   He writes:   
   "Einstein's aberration formula (the formula)...   
     When one considers two positions of the Earth six month apart   
     and applies Einstein's aberration formula to both locations,   
     the result shows only the effect of the reversal of the Earth's   
     velocity."   
      
   He states that SR correctly predicts that it is the change   
   (reversal) of the velocity of the Earth that is the cause of   
   the stellar aberration.   
      
   >> It is the change of the velocity between the star and   
   >> the Earth that causes stellar aberration.   
   >   
   > First of all, that is wrong.  No change of velocity (i.e. acceleration) is   
   > required for stellar aberration to be observed; it is only required that the   
   > velocity of the star relative to the observer (or vice-versa) is not zero.   
   > This is facilitated by at least two circumstances:   
   >   
   >    1. The rotation of the planet of the observer who is at a fixed position   
   >       on the surface of the planet, relative to the star; this leads to   
   >       a "diurnal" stellar aberration;   
      
   Right.   
   Since a point on the surface of Earth always has a speed in   
   the ECI-frame which is v < 465.2 m/s, the observer will during   
   a sidereal day observe the star to be moving along an ellipse with   
   major axis less than arcsin(2v/c) ≈ 0.64".   
      
   Note that the diurnal aberration only depend on the change of   
   the observer's velocity in the ECI-frame.   
      
   >   
   >    2. the orbit of the planet of the observer around *its* star --   
   >       this leads to an "annual" stellar aberration.   
      
   Right.   
   An observer at Earth will during a year observe the star   
   to move along an ellipse with major axis arcsin(2v/c) ≈ 41",   
   and minor axis sin(star's ecliptic latitude)⋅41",   
   where v is the orbital speed of the Earth, and c is the speed of light.   
      
   Note that the annual aberration only depend the change of   
   the observer's velocity in the Solar frame.   
      
   Since the centre of the diurnal ellipse always will be at   
   the annual ellipse, the diurnal aberration will add nothing   
   to the annual aberration. It will only make the annual   
   ellipse have 365 'waves' with amplitude < 0.32".   
      
   As the above is basic knowledge for all astronomers,   
   I would advise you to think very carefully before you   
   claim it to be nonsense.   
      
   >   
   > Second, that the velocity of the star relative to the rest frame of the   
   > observer would be relevant is precisely what he denies :-D   
      
   The star is inertial, so its velocity never change. (assuming   
   the star is not a component of a multiple star system.)   
   He correctly claims that the velocity of the star is irrelevant   
   to stellar aberration.   
      
   He correctly claims that it is the change of the velocity of   
   the star relative to the rest frame of the observer that is relevant.   
      
   Since only the observer is changing his velocity, the change of   
   the velocity of the star relative to the rest frame of the observer   
   is equal to the change of the velocity of the observer.   
      
      
   >>   
   >> "Stellar aberration" is the annual change in the star's   
   >> observed position.   
   >   
   > No, nonsense.  Learn to read.   
   >   
   > What you are describing is called "annual _parallax_";   
      
   SIC! Are you serious? :-D   
      
   -----------------------------   
      
   Let us take it from the beginning.   
      
   The aberration of the light from a star can be   
   stated very simple:   
      
   We will always see the star where it was at   
   the time of emission.   
   That means that the aberration is the angle   
   between the observed position of the star and   
   its real position.   
   Both are positions in our rest frame.   
      
   This is true even if the star is not inertial.   
      
   Let v be the orbital speed of the Earth. v = 29.78 km/s   
   Let a star be at the ecliptic north pole, a distance d from the Sun.   
   Let our observer be at the north pole (no diurnal aberration).   
   Let his coordinate system be such that the x-axis is tangential   
   to Earth's orbit, the y-axis is pointing towards the Sun and   
   the z-axis is pointing towards the Sun.   
      
   At any time, the true position of the star in the observer's   
   rest frame is:   
     x = 0, y = 1 AU, z = d.   
      
   Since the star in the observer's rest frame is moving   
   at the speed v in the negative x-direction, the observed   
   position of the star will at any time be:   
     x = -vt, z = d   
   where t is the transit time for the light to go from   
   the star to the observer.   
      
   The angle to the observed star in the x-z plane is:   
      __vt__   
      \     |   
       \    |  aberration angle θ = arcsin(v/c) ≈ 20.5"   
        \ θ |d   
       ct\  |   
          \ |   
           \|   
     -------O--->x   
      
   At any time, the observer will observe the star 20.5"   
   in the  negative x-direction from the true position of   
   the star at x = y = 0.   
   Since the rest frame of the observer is rotating once   
   per year, the observer will during a year observe   
   the star to move along a circle with radius 20.5".   
   This is annual stellar aberration.   
      
   Since there is a distance between the observer and   
   the star in the y-direction, the observer will observe   
   the star to be an angular distance from its true position.   
   If d = 100 pc, this angle will be 0.01" (per definition of parsec)   
   This angle is parallax, and depend on the distance to the star.   
   It has nothing to do with stellar aberration.   
   Note that the parallax is perpendicular to the aberration.   
      
   https://paulba.no/pdf/Stellar_aberration.pdf   
      
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   Paul   
      
   https://paulba.no/   
      
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