Halachah 1 – A More Precise Length of the Solar Year
According to one opinion among the sages, the solar year is slightly less than 365 days and 6 hours. Its length is calculated as 365 days, 5 hours, 997 parts, and 48 moments. A “moment” is one seventy-sixth of a part. According to this more exact calculation, the solar year exceeds the lunar year by 10 days, 21 hours, 121 parts, and 48 moments. Unlike the earlier calculation, this system leaves no extra remainder after each nineteen-year cycle, because the solar years and the lunar calendar cycle align more closely.
Halachah 2 – The Length of Each Tekufah According to This Calculation
According to this more precise solar-year calculation, the time between one tekufah and the next is 91 days, 7 hours, 519 parts, and 31 moments. Once one tekufah is known, the next tekufah can be calculated by adding this amount, just as in the earlier seasonal calculation.
Halachah 3 – Tekufat Nisan in the First Year of Creation
According to this calculation, Tekufat Nisan in the first year of Creation occurred 9 hours and 642 parts before the molad of Nisan. The Rambam adds that in every first year of each nineteen-year cycle, Tekufat Nisan will likewise occur this amount of time before the molad of Nisan.
Halachah 4 – Calculating Tekufot Within the Cycle
Once Tekufat Nisan of the first year of a nineteen-year cycle is known, each later tekufah is calculated by adding 91 days, 7 hours, 519 parts, and 31 moments. This process is repeated from season to season until the end of the cycle.
Halachah 5 – Calculating Tekufat Nisan for a Specific Year
To find Tekufat Nisan for a particular year, one first determines how many complete years have passed in the current nineteen-year cycle. For each completed year, one adds the yearly solar-lunar difference of 10 days, 21 hours, 121 parts, and 48 moments. After converting moments into parts, parts into hours, and hours into days, one subtracts 9 hours and 642 parts. The remaining amount is reduced by lunar months, and whatever is left is added to the molad of Nisan for that year. The result gives the exact time of Tekufat Nisan according to this calculation.
Halachah 6 – Why This Calculation Was Used for Leap Years
The Rambam writes that it appears to him that this more precise tekufah calculation was the one used by the Great Beit Din when deciding whether to intercalate the year. Since leap years were declared in order to align Pesach with the spring season, the court used the more accurate calculation of the solar year rather than the simpler calculation of 365 days and 6 hours.
Halachah 7 – Both Tekufah Calculations Are Approximate
Even this more precise calculation is still only approximate, because both tekufah systems are based on the sun’s average motion rather than its exact true position. In actual astronomical terms, Tekufat Nisan may occur about two days earlier than the time produced by either of the two calculations. Thus, these methods provide a structured calendar calculation, not an exact measurement of the sun’s true position.