AI 中文总结
本研究运用现代天文学技术计算犹太传统中Ts'eit HaKokhavim与Motsa'ei Shabbat的时间，评估近似方法的准确性，探究光污染的影响，并提供了相关计算工具。
AI 中文摘要
在犹太传统中，日与日的分界并非午夜，而是黄昏。黄昏是人们必须进行ma'ariv祈祷、计算omer、且可在安息日后开展活动的时刻。尽管安息日结束时刻（Motsa'ei Shabbat）与其他用途（Ts'eit HaKokhavim）对黄昏的定义略有不同，但多数 minhagim（犹太教习俗）将黄昏定义为天空中能观测到三颗特定大小和距离的恒星的时刻。这一定义存在一定困难：不仅这些条件难以界定，还会因天气、云量和光污染而进一步复杂化。因此，虔诚的犹太人通常通过将黄昏定义为太阳降至地平线以下特定距离的时刻来近似这些时间。尽管这些近似方法已被证明有效，但现代天文学使我们能够精确计算这些条件满足的时刻。本研究应用这些技术计算Ts'eit HaKokhavim和Motsa'ei Shabbat的时间，评估近似方法的准确性，并探究光污染对这些时间的影响。结果显示，标准方法对Ts'eit HaKokhavim的近似较为准确，但Motsa'ei Shabbat的条件通常出现在近似时间之后；光污染对Ts'eit HaKokhavim的偏移不超过1分钟，但会显著改变Motsa'ei Shabbat的时间，实际上在每个人口中心的至少部分夜晚，光污染会导致Motsa'ei Shabbat的条件永远无法满足。最后，本研究提供了一个工具（http://www.*****.com），可计算地球上任意时间和地点的Ts'eit HaKokhavim与Motsa'ei Shabbat时间。
英文摘要
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.
Comments14 pages, 4 figures. Accepted for publication in Masorti Fall 2026. An interactive calculator is provided at halakhic-nightfall.streamlit.app
