Can you use and move around a telescope on Shabbos?
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Yes, if you hold that you may study science on Shabbos, the Shulchan Aruch says, in Orach Chaim 307:17:
that there are those who permit studying "sifrei chochmos" (secular studies) on Shabbos, and that according to that reasoning, you may peer into an astrolabe on Shabbos.
Use of binoculars, a telescope, a tripod and glasses is permitted provided that there is no other prohibition involved such as carrying in a public domain, use of electricity, and on the condition that special skills are not required to assemble the equipment. It is permitted to adjust binoculars and a telescope in the normal manner. (Shmiras Shabbos Kehilchoso 16:45)
However, see footnote 111 there, where Rav Neuwirth brings an opinion that a telescope may be muktzah machmas chesron kis.