Halakhah for Berakhot 52:12

Astronomers begin the day with midday and it extends until midday of the following day, twenty-four hours. This is a complete day for their calculations. This is justified for their need because of two factors, which only geometers can understand.¹ Among the advantages of defining a day as extending from midday to midday (or midnight to midnight) is the fact that all inhabitants along a common meridian would begin and end the day at the same time. This is not the case if a day extends from sunrise to sunrise or from sunset to sunset. Also, from midday to midnight will always be 12 hours, which is not the case from sunrise to sunset. However, since the shadow at midday is always short and slants only slightly, sometimes an individual’s eye cannot discern this. Even with a sundial or an astrolabe, a scholar cannot recognize the moment of midday. Therefore our Rabbis found it necessary to tell us that the Minha prayer should be one-half hour after midday, for then the eye can discern that the sun has passed to the west. For this reason it is unlikely that midday should be the beginning of the day. All the more so with midnight, for no person can know it.