tzais
This method returns the tzais (nightfall) based on the opinion of the Geonim calculated when the sun's position is 7.083˚ (or 7˚5′)) below the western horizon.
This is often referred to as 75' or 7 degrees and 5 minutes.
This calculation is based on
the observation of 3 medium sized stars by Dr. Baruch (Berthold) Cohn in his luach Tabellen enthaltend die Zeitangaben für den Beginn der Nacht und des Tages für die Breitengrade + 66 bis -38 published in Strasbourg, France in 1899.
This calendar was very popular in Europe, and many other calendars based their time on it.
Rav Dovid Tzvi Hoffman in his Sh"Ut Melamed Leho'il in an exchange of letters with Baruch Cohn in Orach Chaim 30 agreed to this zman (page 36),
as did the Sh"Ut Bnei Tziyon and
the Tenuvas Sadeh.
It is very close to the time of the Mekor Chesed of the Sefer chasidim.
It is close to the position of the sun 30 minutes after sunset in Jerusalem around the equinox / equilux, but not exactly. The actual position of the sun 30 minutes after sunset in Jerusalem at the equilux is 7.205 and 7.199 at the equinox.
See Hazmanim Bahalacha vol 2, pages 520-521 for more details.
Return
the Date representing the time when the sun is 7.083 below sea level. 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.