bain
Method to return the beginning of bain hashmashos of Rabbeinu Tam calculated when the sun is 13.24˚ below the western geometric horizon (90) after sunset. This calculation is based on the same calculation of bain hashmashos Rabbeinu Tam 58.5 minutes but uses a degree-based calculation instead of 58.5 exact minutes. This calculation is based on the position of the sun 58.5 minutes after sunset in Jerusalem around the equinox / equilux, which calculates to 13.24 below geometric zenith. NOTE: As per Yisrael Vehazmanim Vol. III page 1028, No. 50, a dip of slightly less than 13 should be used. Calculations show that the proper dip to be 13.2456 (truncated to 13.24 that provides about 1.5 second earlier (lechumra) time) below the horizon at that time. This makes a difference of 1 minute and 10 seconds in Jerusalem during the Equinox, and 1 minute 29 seconds during the solstice as compared to the proper 13.24 versus 13. For NY during the solstice, the difference is 1 minute 56 seconds.
Return
the Date of the sun being 13.24 below geometric zenith (90). If the calculation can't be computed such as northern and southern locations even south of the Arctic Circle and north of the Antarctic Circle where the sun may not reach low enough below the horizon for this calculation, a null will be returned. See detailed explanation on top of the AstronomicalCalendar documentation.