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Given the celestial coordinates of a certain star and the time it takes to pass across your telescope's eyepiece, how can you calculate the field of view of the telescope?

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This technique for determining the field of view of a telescope and eyepiece is called drift timing. Since the sidereal day is about 4 minutes shorter than the usual solar day, a fixed point on the celestial equator rotates at about 15.04 arc seconds per second of time. Thus the true field of view in arc seconds is given by $$TFOV=15.04 \hspace{2pt} t \cos(\delta)$$ where $t$ is the time in seconds for the star to drift across the field, and $\delta$ is the declination of the star. Divide by 60 to convert to arc minutes, or by 3600 to degrees.

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