Figure: A long-exposure image of the night sky looking toward Polaris from Ehrenbuerg, Germany

Image 1 Caption: The night sky looking toward Polaris in a long-exposure image from Ehrenbuerg, Bavaria, Germany.

Further explication:

1. The exposure time was about 45 minutes. This means the star trails will be about (15 degrees per hour) times (3 quarters of an hour) = approximately 11° as measured from the north celestial pole (NCP).

2. From such an image, it is easy to understand how some of the Presocratic philosophers of ancient Greece came to believe that the Earth was a rest inside a cosmic vortex.

3. Polaris is within 1° of the NCP, and so to casual observation does NOT seem to move at all. In the image, it is on the axis of the "cosmic vortex". (Polaris actually revolves on a very small small circle on the celestial sphere every day.)

   Because it is so close to the NCP, Polaris is the Northern Hemisphere pole star of our historical period.

   For Northern Hemisphere observers, it is always just hanging there at nearly the same place in the sky, but you can't see it during the daytime.

4. Image 2 Caption: A derviation of the field of view (FOV) angular diameter formula.

   Note:

     Earth rotation angular velocity = ω = 360 degrees per day
                                         = 15 degrees per hour
                                         = 15 arcminutes per minute  , 

   and therefore for δ significantly less than 90°

     φ = Δt*( 15 arcminutes per minute )*cos(δ) in general.
       = Δt*( 15 arcminutes per minute ) at the celestial equator.
       = indeterminate by this formula for δ close to 90°.

   Note, the time units are formally sidereal times (e.g., sidereal days, hours, minutes). However, those are close enough to ordinary times for our purposes. For example, one sidereal day = 86164.0905 s = 1 day - 4 m + 4.0905 s (on average) and the other sidereal units scale with the sidereal day. A sidereal day is a complete rotation relative to the observable universe.

   

   Credit and/or file tracking information follows to the divider line:

   Images:

   1. Credit/Permission: Udo Kuegel, 2001 (uploaded to Wikipedia by User:Slomojoe, 2006) / Public domain.
      Image link: Wikipedia: File:Sterneamwalberla2.jpg.
      
   2. Credit/Permission: David Jeffery, 2026 / Own work, Public domain.
      Image link: Itself.
      

   Local file: local link: sky_swirl_polaris_ehrenbuerg.html.
   Celestial sphere file: sky_swirl_polaris_ehrenbuerg.html.
   

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