
Degree based Zmanim
Degree-based zmanim are considered most accurate by many poskim since zmanim calculated using degrees for alos and tzais have a consistent level of light at all dates and locations. The alternatives of using fixed minutes (for example 72 minutes) or percentage of the day-based calculations (1/10th of the day) result in alos and tzais zmanim having different levels of light at different dates and locations. The number of degrees for a given zman is calculated based on how many degrees the sun is below the horizon on an equal day in Yerushalayim. For example, the sun is 16.1° below the horizon 72 minutes before sunrise (or after sunset) on an equal day (defined below) in Yerushalayim. The subject of degree-based zmanim is extensive and deserves its own detailed article, עוד חזון למועד.
Equinox VS Equilux in Halacha
A question explored by poskim and luach authors is; how we define an equal day to use for degree-based zmanim calculations. Should it be calculated at the astronomically equal day of the equinox or the halachic equal day of the equilux. At the equinox, the 12-hour duration of the day is calculated astronomically without accounting for refraction or solar radius. At the equilux there are exactly 12 hours of daylight from sunrise to sunset. Due to these two factors, the halachic length of the day from sunrise to sunset at the equinox is longer than 12 hours. In Yerushalayim on March 20, 2021, the day of the March equinox, sea level sunrise is at 5:42:51 AM and sunset is at 5:50:33 PM, or a day length of 12 hours, 7 minutes and 42 seconds. You would have to go back four days to March 16, the equilux, for a 12-hour day. There are halachic opinions supporting both the equinox and the equilux as the equal day for zmanim calculations.
Practical Differences Between Equinox and Equilux Calculations
Many calendars and seforim list the 72-minute alos / tzais as 16.1° and 90 minutes as 19.8° (using the global refraction average + solar radius of 0.8333). Calculations using the KosherJava Zmanim API (utilizing the Jean Meeus / NOAA algorithms) show that the actual figures are 16.08° and 19.848° at the equilux, and 16.04° and 19.784° at the equinox. The table below shows the difference between these numbers at the summer solstice when twilight is the longest (the most extreme expected gap between two different degree-based times).
Difference Between the Equilux and Equinox Calculations at the Summer Solstice |
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Location | 7.199° VS 7.205° (30 Min) | 11.424° VS 11.442° (50 Min) | 16.04° VS 16.08° (72 Min) | 19.784° VS 19.848° (90 Min) |
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Jerusalem Lat: 31.7° | 2 sec | 7 sec | 15 sec | 26 sec |
Lakewood Lat: 40.1° | 2 sec | 7 sec | 20 sec | 38 sec |
Montreal Lat: 45.5° | 3 sec | 10 sec | 30 sec | 90 sec |
Krakow Lat: 50.05° | 3 sec | 13 sec | 93 sec | N/A |
London Lat: 51.5° | 4 sec | 16 sec | N/A | N/A |
Vilnius Lat: 58.68° | 13 sec | 47 sec | N/A | N/A |
Anchorage Lat: 61.2° | N/A | N/A | N/A | N/A |
N/A indicates that the sun does not get this far below the horizon at this time of the year due to the high latitude of the location. See Why Some Zmanim Never Occur for more details. |
While the above question is interesting from an academic perspective, the measurements above show a negligible difference between calculating at the equinox VS the equilux for most locations and zmanim. The difference in calculating zmanim up to 16.1° alos / tzais on the equinox vs the equilux isn’t significant until the 30 second difference at the 72-minute zman. Since this is typically calculated as 16.1° lechumra, there is no difference at all for this zman. The less commonly used 19.8°, has an up to 90 second difference (at the latitude of Montreal). The ~11.5° misheyakir times start showing a difference at high latitudes. This is not significant even as far north as London but becomes significant at the 58.68° latitude of Vilna (Vilnius) since it reaches 47 seconds.
Observations on Degree Based Calculations
- The commonly used 16.1° time is a slightly rounded chumra for both the equinox and equilux. The actual numbers are 16.04° and 16.08°.
- The 19.8° zman mentioned by many calendars and seforim is calculated at the equinox where it is 19.784° and not equilux where it is 19.848°. It should possibly be rounded up to 19.9° lechumra to account for the equilux calculation.
- The misheyakir 11.5° times are a slight kula since both the equilux (11.442°) and the equinox (11.424°) calculations show a sightly later time.
- As noted above, the degree-based calculations were done using the more accurate Jean Meeus / NOAA algorithms. Seforim printed in the past did not have access to the newer algorithms and typically used the USNO algorithm, but as seen below, there is only a trivial difference between the algorithms.
Zman | Equinox | Equilux |
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USNO | NOAA | USNO | NOAA |
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30 Min | 7.203° | 7.199° | 7.208° | 7.205° |
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50 Min | 11.432° | 11.424° | 11.449° | 11.442° |
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72 Min | 16.055° | 16.04° | 16.092° | 16.08° |
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90 Min | 19.804° | 19.784° | 19.865° | 19.848° |
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Notes: