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Due to the rotation of the Earth, over the course of the night, stars will appear to turn around the celestial pole. This means we can photograph star trails (desired or not). Physically, any star trail should form a circle of latitude over the celestial sphere, and in most photographs of star trails, this is indeed the case:

Star trails, ESO
Source: ESO via Wikimedia Commons

Yet I have also seen photographs where star trails form a spiral or seem to be coming into or out of a line. There are several examples in this photographylife blog, including one where the stars appear as a complicated vector field, one where they make a full circle (which should be possible during 24 hours of clear weather poleward of 85° only, with a 24-hour exposure), and one where the star trails appear like half-parabolas eminating from a line. How can such images be created?

  • 14 mm is pretty wide angled. 10 mm is a 90 degree view. – Thorbjørn Ravn Andersen Apr 27 '18 at 15:12
  • @scottbb You are right. Only the ones on the equator form great circles. Corrected. – gerrit Apr 28 '18 at 9:34
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The example image in your question is probably affected by geometric distortion which is a property of the lens' projection of an image of a three dimensional world onto a two-dimensional image plane.

This distortion is exaggerated by placing the axis of rotation off-center in the frame.

The "wild" looking images at the link in the question appear to have computer generated "stars" drawn over the actual star field. If you look closely at the "panoramic" shot you can see stars without trails in the sky behind the layer of CGI swirls and spirals.

On the other hand, the author mentions things such as image stacking, bulb ramping, automatic panoramic tripod heads, sliders (camera dollies that allow a "tracking shot"), and the like. What little discussion he does of these advanced techniques seem to assume the reader already knows how to do them. He's pretty clear he takes the terrestrial portions of his image separately at different exposures. So the eccentric "motion" of the stars could actually be due to the motion of the camera on a slider/tracking/pano mount during the successive exposures used to build the final image. Be sure to read pages 2-4 of the article using the drop down menu at the bottom of the first page.

Going from top to bottom of page one at the link:

  • The image is labeled a 30 second exposure using a 14mm lens. Using the 1/600 rule-of-thumb, we would need to use an exposure shorter than 42 seconds to avoid star trailing with a 14mm lens on a FF camera such as the Nikon D700. In addition to the stars, what appears to be aurora borealis are visible in the sky. Some of the outlines of the mountains in the foreground hint that the entire non-sky portion of the image may have been composited in.
  • A chart showing the sun's position above or below the horizon during golden hour, civil twilight (which can be designated by statute differently in different jurisdictions), blue hour, etc.
  • This appears to be a 19 minute exposure during which the sky will appear to rotate about five degrees around the celestial pole. There does appear to be one moving light source in the lower left portion of the image that is not a star. With the sky only rotating 1/72 of a complete circle, the fact that stars across the celestial pole from each other are not equidistant from the celestial pole can make it appear that the "circle" is distorted when, in fact, we are seeing 5° arcs of tens of thousand of separate circles that each have different radii. The lens also appears to have some very mild geometric distortion.
  • This image is far more than a long exposure. It purports to be a four hour exposure taken with a 14mm focal length, yet it reveals a much wider area of sky from right to left than can be captured with a static 14mm lens on a FF camera. Based on the apparent position of a celestial pole above the horizon at about one-eighth the image width from the left, and the other celestial pole below the horizon just to the right of the middle of the panorama, this is a 360° pano that could not have been taken with a 14mm lens pointed in the same direction for 4 hours! If one looks carefully, there are very dim stars that appear as single points in the sky in addition to the "swirly" patterns with larger "head" on one end than the trails behind those heads. We also see the reflection of a few bright stars in the water to the left that have no trails at all! This is most likely a composite image of who knows what.
  • I'm guessing this one was shot in the winter when the sky is dark for over twelve hours. The mount shooting the star field could have been rotated counter to the motion of the stars on the celestial axis during collection of the many images to stack. Doing so will give a full circle in much less than 24 hours. After the many frames have been stacked, applying lens correction for geometric distortion to the perfect circles produced by rotating the camera around the polar axis would "stretch" it out of round. The foreground was produced separately and used several different light painting techniques.
  • If those weird patterns are even stars, they were photographed using the aforementioned computerized panoramic head to create those patterns by moving the camera in some irregular motions as the stars were exposed.
  • This one is certainly a composite of several different groups of images. The Milky way is nowhere near as bright as the horizon at twilight. Higher effective exposures of the Milky Way have been combined with much lower exposures of the horizon shortly after sunset. The landscape and cloud cover are probably a third set of exposures as they are also too bright to be seen at the same time as the Milky Way.

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