Halachah 1 – Finding the Double Distance
To calculate the moon’s true position, one first calculates three things for the night of visibility:
- The moon’s mean position at the time of visibility.
- The moon’s mean anomaly.
- The sun’s mean position.
Then one subtracts the sun’s mean position from the moon’s mean position. The remainder is called the distance between the sun and moon. This distance is then doubled, and the result is called the merchak hakafol, the double distance.
Halachah 2 – The Range of the Double Distance
The Rambam reminds us that all these calculations are only for the purpose of determining whether the new moon can be seen. On a night when the new moon could be visible, the double distance will always fall within a specific range: from 5 degrees to 62 degrees. If the number is outside that range, it does not fit the conditions of a normal visibility calculation.
Halachah 3 – Adjusting the Mean Anomaly Based on the Double Distance
The double distance determines how much must be added to the moon’s mean anomaly. The Rambam gives a scale:
- Around 5 degrees: add nothing.
- 6 to 11 degrees: add 1 degree.
- 12 to 18 degrees: add 2 degrees.
- 19 to 24 degrees: add 3 degrees.
- 25 to 31 degrees: add 4 degrees.
- 32 to 38 degrees: add 5 degrees.
- 39 to 45 degrees: add 6 degrees.
This adjustment begins the process of converting the moon’s mean anomaly into a corrected anomaly.
Halachah 4 – Continuing the Adjustment Scale
The Rambam continues the same scale for larger double distances:
- 46 to 51 degrees: add 7 degrees.
- 52 to 59 degrees: add 8 degrees.
- 60 to 63 degrees: add 9 degrees.
After applying the proper addition, the result is called the maslul hanachon, the corrected anomaly.
Halachah 5 – Using the Corrected Anomaly to Find the Moon’s True Position
Once the corrected anomaly is known, one checks whether it is less than or greater than 180 degrees.
- If it is less than 180 degrees, subtract its correction from the moon’s mean position.
- If it is greater than 180 degrees, add its correction to the moon’s mean position.
The result is the moon’s true position at the time of visibility.
Halachah 6 – When No Lunar Correction Is Needed
If the corrected anomaly is exactly 180 degrees or exactly 360 degrees, there is no correction. In that case, the moon’s mean position at the time of visibility is also its true position.
Halachah 7 – The Correction Table for the Moon’s Corrected Anomaly
The Rambam gives the correction values for the moon’s corrected anomaly. For example:
- 10 degrees gives a correction of 50 minutes.
- 20 degrees gives a correction of 1 degree and 38 minutes.
- 40 degrees gives a correction of 3 degrees and 6 minutes.
- 80 degrees gives a correction of 5 degrees.
- 100 degrees gives a correction of 5 degrees and 8 minutes.
- 150 degrees gives a correction of 2 degrees and 48 minutes.
- 170 degrees gives a correction of 59 minutes.
- 180 degrees gives no correction.
These values are used to adjust the moon’s mean position into its true position.
Halachah 8 – Corrections Above 180 Degrees and In-Between Values
If the corrected anomaly is greater than 180 degrees, one subtracts it from 360 degrees and uses the correction value for the remainder, just as was done for the sun. If the anomaly falls between two listed values, one estimates the correction proportionally according to its place between the two numbers.
Halachah 9 – Example of Calculating the Moon’s True Position
The Rambam gives a full example for the beginning of Thursday night, the second of Iyar in the reference year.
The calculation begins with:
- The sun’s mean position.
- The moon’s mean position at the time of visibility.
- The moon’s mean anomaly.
The sun’s mean position is subtracted from the moon’s mean position, giving the distance between them. This distance is doubled, producing the double distance. Based on that double distance, 5 degrees are added to the moon’s mean anomaly, producing the corrected anomaly.
The correction for that corrected anomaly is then found and subtracted from the moon’s mean position, because the corrected anomaly is less than 180 degrees. The result is the moon’s true position, which the Rambam gives as being in Taurus, around 18 degrees and 36 minutes.
Using this method, the true position of the moon can be calculated for any future visibility time.
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