Halachah 1 – Different Opinions About the Length of the Solar Year
The Rambam explains that there are different opinions among the sages regarding the exact length of the solar year. Some Jewish sages calculate it as 365 days and 6 hours, meaning 365¼ days. Others say it is slightly less than that. The Rambam notes that non-Jewish scholars, including Greek and Persian astronomers, also disagreed about this matter.
Halachah 2 – Calculating the Four Tekufot
According to the opinion that the solar year is 365 days and 6 hours, every nineteen-year cycle leaves a remainder of 1 hour and 485 parts, as explained earlier. Each season, or tekufah, is separated from the next by:
91 days, 7 hours, and 30 minutes.
Once one tekufah is known, the following tekufot can be calculated by repeatedly adding this amount.
Halachah 3 – Defining the Four Tekufot
The four tekufot mark the sun’s entry into four major seasonal points:
- Tekufat Nisan: when the sun enters the beginning of Aries.
- Tekufat Tammuz: when the sun enters the beginning of Cancer.
- Tekufat Tishrei: when the sun enters the beginning of Libra.
- Tekufat Tevet: when the sun enters the beginning of Capricorn.
The Rambam also gives the starting point for the calculation: in the first year of Creation, Tekufat Nisan occurred 7 days, 9 hours, and 642 parts before the molad of Nisan.
Halachah 4 – Calculating Tekufat Nisan by the Nineteen-Year Cycle
To calculate Tekufat Nisan for the first year of any nineteen-year cycle, one counts how many complete cycles have passed since Creation. For each completed cycle, one adds 1 hour and 485 parts. After converting parts into hours and hours into days, one subtracts 7 days, 9 hours, and 642 parts. The remaining amount is added to the molad of Nisan of the first year of that cycle, and the result gives the time of Tekufat Nisan.
Halachah 5 – Calculating Tekufat Nisan for a Specific Year
To calculate Tekufat Nisan for a specific year within a cycle, one adds:
- 1 hour and 485 parts for every completed nineteen-year cycle.
- 10 days, 21 hours, and 204 parts for each completed year within the current cycle.
After subtracting 7 days, 9 hours, and 642 parts, and removing full lunar months from the total, the remaining amount is added to the molad of Nisan. This reveals the date and time of Tekufat Nisan for that year.
Halachah 6 – The Fixed Times of the Tekufot
According to this calculation, the tekufot can only fall at certain times of the day or night:
- Tekufat Nisan: at the beginning of the night, midnight, beginning of the day, or midday.
- Tekufat Tammuz: at 7½ hours or 1½ hours, either by day or night.
- Tekufat Tishrei: at 9 hours or 3 hours, either by day or night.
- Tekufat Tevet: at 10½ hours or 4½ hours, either by day or night.
This creates a fixed repeating seasonal pattern.
Halachah 7 – Finding the Weekday of Tekufat Nisan
To determine the weekday and hour of Tekufat Nisan, one counts the complete years that have passed since Creation, removes groups of twenty-eight years, and calculates the remainder. For each remaining year, one adds 1 day and 6 hours, then adds 3 days because the first Tekufat Nisan of Creation occurred at the beginning of Wednesday night. After dividing by weeks, the remainder reveals the weekday and hour of Tekufat Nisan.
Halachah 8 – Example of Calculating the Tekufah
The Rambam gives an example using the year 4930 from Creation. After removing complete twenty-eight-year cycles, one year remains. Adding 1 day and 6 hours, plus the additional 3 days, places Tekufat Nisan on Thursday night, six hours into the night. From there, each following tekufah is found by adding 91 days, 7 hours, and 30 minutes. The Rambam also explains that if one calculates the date of Tekufat Nisan within the month, one may need to add one, two, or three days to align the result with the weekday of the tekufah. If more than that is required, it indicates an error in the calculation.
Chapter Theme
Chapter 9 explains how the Jewish calendar calculates the solar seasons, known as the tekufot. While earlier chapters focused on lunar months and the molad, this chapter shows how the solar year is tracked so the calendar remains aligned with the seasons, especially to ensure that Pesach occurs in the spring.