The Astronomy of Halakhic Nightfall: Calculating Ts'eit HaKokhavim and Motsa'ei Shabbat

arXiv:2608.04064v1 Announce Type: new Abstract: In Jewish tradition, the boundary between days is not midnight, but nightfall. Nightfall is when one must pray ma'ariv, count the omer, and may engage in activity after Shabbat. While there are slightly different definitions of nightfall for Shabbat restrictions (Motsa'ei Shabbat) versus other purposes (Ts'eit HaKokhavim), most minhagim define nightfall to be when three stars of some specified size and proximity are visible in the sky. This definition presents some difficulty. Not only are these conditions difficult to define, they are further complicated by weather, cloud cover, and light pollution. Observant Jews therefore usually approximate these times by defining nightfall to be when the sun has reached a certain distance below the horizon. Although these approximations have been effective, modern astronomy enables us to calculate precisely when these conditions are met. This work applies these techniques to calculate the time of Ts'eit HaKokhavim and Motsa'ei Shabbat evaluates the accuracy of the approximations, and explores the effects of light pollution on these times. While Ts'eit HaKokhavim is reasonably well-approximated by standard methods, the conditions for Motsa'ei Shabbat generally occur after the time predicted by the approximations. Light pollution does not shift Ts'eit HaKokhavim by more than a minute but significantly changes Motsa'ei Shabbat. In fact, light pollution causes the conditions of Motsa'ei Shabbat to never be met on at least some nights in every population center. Finally, I provide a tool (halakhic-nightfall.streamlit.app) for calculating Ts'eit HaKokhavim and Motsa'ei Shabbat at an arbitrary time and location on Earth.