Companion

The zenith of 16.1 below geometric zenith (90). This calculation is used for determining alos (dawn) and tzais (nightfall) in some opinions. It is based on the calculation that the time between dawn and sunrise (and sunset to nightfall) is 72 minutes, the time that is takes to walk 4 mil at 18 minutes a mil (Rambam and others). The sun's position at 72 minutes before sunrise in Jerusalem around the equinox / equilux is 16.1 below geometric zenith.

The zenith of 8.5 below geometric zenith (90). This calculation is used for calculating alos (dawn) and tzais (nightfall) in some opinions. This calculation is based on the position of the sun 36 minutes after sunset in Jerusalem around the equinox / equilux, which is 8.5 below geometric zenith. The Ohr Meir considers this the time that 3 small stars are visible, which is later than the required 3 medium stars.