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The video Earth's Rotation Visualized in a Timelapse of the Milky Way Galaxy - 4K (linked below) and discussion below this answer to Why does a timelapse video of a stationary Milky Way make the horizon appear to move from horizontal to vertical? about field rotators has got me thinking.

In addition to the benefit of (essentially) single axis constant speed tracking for distant celestial objects, an equatorial mount also rotates the telescope tube about it's axis such that there is no rotation of the image on the focal plane during long exposures.

This was probably essential for hours-long exposures of single emulsion plates.

But for the very largest and heaviest reflecting telescopes equatorial mounts are massive and unwieldily and require huge counterbalances compared to alt-az mounts which can have the azimuth bearing right on the ground and the altitude bearing straight through the telescope's center of mass.

Question: Did astronomers ever use photographic plate rotation along with alt-az mounts?

uhoh
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Absolutely! The Bol’choï Teleskop Azimutal’ny (Large Azimuth Telescope), built by the former USSR in 1979 and the largest telescope in the world from then until the Gemini telescopes were built in 1999—BTA has a diameter of 6 metres—uses an azimuth mount. Obviously, any long-exposure imaging done with it requires a field derotator. Read more about it here.

Pierre Paquette
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    Excellent and speedy answer! I've only been inside two major observatories; the Yerkes refractor and the Hale reflector and in both cases I was really impressed by how much volume and in the second case mass and complexity there was. I can see why the BTA was groundbreaking, thanks! – uhoh Dec 26 '21 at 04:19
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    You’re very welcome! I never went to visit the BTA, but some people I know did. It was impressive indeed. Mind you, they had problems with the mirror. The first blank they poured cracked when they tried to turn it solid faster than the glass would normally (by cooling it), and the second had a lot of bubbles that rose to the surface. The “final” mirror was the third, and there were still quite a few bubbles, so the mirror is “littered” with spots of black paint over them so they won’t affect the image quality. – Pierre Paquette Dec 26 '21 at 04:21