If I set up my long exposure camera on a tripod and point it at the sky at night with the pole star in the centre we get a lovely image of concentric circles or arcs of circles depending on exposure times. Once one of the legs of the tripod went faulty (slowly collapsed a few mm) and the image was fuzzy and no longer circles. But it occurred to me that if this trivial angular movement distorted the image so much then why does the relative rotation of the earth on its axis not have the same effect on the photograph. Surely movement of the earth on its axis with a fixed camera would produce an angular displacement of the image in the same way as an accidental movement of the camera. What is the explanation for this?
The answer: it does.
You know those lovely concentric circles or arcs that you're photographing? That is the result of the earth rotating about its axis. If it were not for the earth rotating, those circles would be the point-source stars that you you see with your eye.
Without seeing the result, it is difficult to do anything more than make a guess. But I suspect the explanation is mechanical rather than optical. A nearby image would be shifted out of focus if the lens or photographic plate were tilted relative to each other, but such blurring would not occur for distant objects or if the whole camera were tilted smoothly.
If the motion of the tripod had been as smooth and precise as the rotation of the Earth then your photograph would not have been blurred. The fact that the tripod leg was loose meant that the camera could have wobbled slightly due to breezes. Also the leg probably collapsed jerkily, in slip-stick motion, which could have set up small vibrations in the tripod.
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