1,331. Calculating the Third Latitude

Hilchos Kiddush HaChodesh 17:10

After calculating the second latitude, you must adjust it to account for small fluctuations in the moon’s orbit. The size of the adjustment is as follows: If the moon is between the start of Aries or Libra and that constellation’s 20th degree, take two-fifths of the second latitude; if the moon is between the 20th degree of Aries and the 10th degree of Taurus, or between the 20th degree of Libra and the 10th degree of Scorpio, take one-third of the second latitude; if the moon is between the 10th degree of Taurus and its 20th degree, or between the 10th degree of Scorpio and its 20th degree, take one-quarter of the second latitude; if the moon is between the 20th degree of Taurus and its end, or between the 20th degree of Scorpio and its end, take one-fifth of the second latitude.

If the moon is between the start of Gemini and its 10th degree, or between the start of Sagittarius and its 10th degree, take one-sixth of the second latitude; from the 10th to the 20th degree of Gemini or Sagittarius, take 1/12 of the second latitude; from the 20th to the 25th degree of Gemini or Sagittarius, take 1/24 of the second latitude; from the 25th degree of Gemini to the fifth degree of Cancer or from the 25th degree of Sagittarius to the fifth degree of Capricorn, do not take anything because the moon’s orbit doesn’t fluctuate at these points.

From the fifth to the 10th degree of Cancer or Capricorn, take 1/24 of the second latitude; from the 10th to the 20th degree of these constellations, take 1/12 of the second latitude; from the 20th degree to the constellation’s end, take one-sixth of the second latitude.

From the start of Leo or Aquarius to that constellation’s 10th degree, take one-fifth of the second latitude; from the 10th to the 20th degree of these constellations, take one-quarter of the second latitude; from the 20th degree of Leo to the 10th degree of Virgo, or from the 20th degree of Aquarius to the 10th degree of Pisces, take one-third of the second latitude. From the 10th degree of Virgo or Pisces to the end of that constellation, take two-fifths of the second latitude.

This fractions of the second latitude that we have taken throughout this halacha are called a circuit of the moon.

Hilchos Kiddush HaChodesh 17:11

We already know whether the moon’s latitude is to the north or the south. If it’s to the north, subtract the circuit of the moon from the second longitude; if it’s to the south, add them. This only applies when the moon is between the start of Capricorn and the end of Gemini; If the moon is between the start of Cancer and the end of Sagittarius, then we do the opposite. When this is the case, if the moon's latitude is to the north, add the circuit of the moon to the second longitude; if it is to the south, subtract the circuit from the second longitude. The result of the operation performed on the second longitude is called the third longitude. If there is no fluctuation in the circuit, then there is nothing to take from the second latitude. In such a case, the second longitude will be used as the third longitude without any adjustments being made.