Halachah 1 – Why Calculate the Moon’s Direction?
The Sages taught that when examining witnesses, Beit Din would ask:
“To which side was the moon inclined?”
Because this question formed part of witness interrogation, the Rambam explains how to calculate it. He notes, however, that this calculation is not essential for determining visibility itself and therefore presents it only in an approximate form.
Halachah 2 – The Zodiac Is Tilted Relative to the Celestial Equator
The path of the sun through the zodiac does not lie on the celestial equator. Instead, it is inclined toward the north and south.
- One half of the zodiac lies north of the celestial equator.
- The other half lies south of it.
This inclination is the basis for understanding the moon’s apparent direction in the sky.
Halachah 3 – Aries and Libra Are the Crossing Points
The zodiac crosses the celestial equator at two points:
- Beginning of Aries
- Beginning of Libra
Therefore:
- Aries through Virgo lie on the northern side.
- Libra through Pisces lie on the southern side.
Halachah 4 – The Maximum Inclination
Starting from Aries, the zodiac gradually rises northward until Cancer.
At the beginning of Cancer, the zodiac reaches its greatest northern distance from the celestial equator:
23½ degrees (approximately).
From Cancer it returns toward the equator until Libra.
Likewise:
- From Libra it moves southward.
- It reaches maximum southern inclination at Capricorn.
- Then it returns toward Aries.
Halachah 5 – The Equinoxes
Because Aries and Libra lie exactly on the celestial equator:
- The sun is neither north nor south when located there.
- It rises exactly due east.
- It sets exactly due west.
- Day and night are equal throughout the inhabited world.
These are the equinoxes.
Halachah 6 – Every Zodiac Degree Has a Measured Inclination
Every degree of the zodiac possesses a certain northern or southern inclination.
The maximum possible inclination is approximately:
23½ degrees
at Cancer and Capricorn.
Halachah 7 – Table of Zodiac Inclinations
The Rambam provides a table:
| Zodiac Degrees from Aries | Inclination |
| 10° | 4° |
| 20° | 8° |
| 30° | 11.5° |
| 40° | 15° |
| 50° | 18° |
| 60° | 20° |
| 70° | 22° |
| 80° | 23° |
| 90° | 23.5° |
These values are used to determine how far north or south a zodiac position lies.
Halachah 8 – Interpolating Between Values
As with earlier astronomical tables, values between the listed entries are estimated proportionally.
For example:
- 5° corresponds to roughly 2° inclination.
- 23° corresponds to roughly 9° inclination.
The same method applies throughout the table.
Halachah 9 – Extending the Table Beyond 90 Degrees
Once one knows the inclinations up to 90°, all other values can be calculated by symmetry:
- Between 90° and 180°
- Between 180° and 270°
- Between 270° and 360°
just as was done previously with lunar latitude calculations.
Halachah 10 – Determining the Moon’s Position Relative to the Celestial Equator
To determine how far north or south of the celestial equator the moon actually appears:
- Calculate the zodiac inclination of the moon’s true position.
- Calculate the moon’s latitude.
- Determine whether each is north or south.
If both are in the same direction:
- Add them together.
If one is north and one is south:
- Subtract the smaller from the larger.
The result gives the moon’s distance from the celestial equator.
Halachah 11 – Example
For the example used throughout these chapters:
- The moon’s zodiac position has about 18° north inclination.
- The moon’s latitude is about 4° south.
Since they are in opposite directions:
18° − 4° = 14°
Therefore the moon is approximately:
14° north of the celestial equator.
The Rambam again notes that this is only an approximate calculation, because it does not affect the actual visibility decision.
Halachah 12 – Determining Where the Moon Appears in the Sky
After knowing the moon’s distance from the celestial equator:
Near the Equator
If the moon is on or very near the celestial equator:
- It appears approximately due west.
- Its illuminated side faces directly east.
North of the Equator
If the moon lies north of the equator:
- It appears between west and northwest.
- The crescent tilts somewhat toward the south.
South of the Equator
If the moon lies south of the equator:
- It appears between west and southwest.
- The crescent tilts somewhat toward the north.
The farther from the equator, the more pronounced the tilt.
Halachah 13 – Estimating the Moon’s Height Above the Horizon
Witnesses were also asked:
“How high was the moon?”
This can be estimated from the arc of visibility.
- A small arc of visibility means the moon appears low.
- A large arc of visibility means the moon appears higher above the horizon.
Thus, the greater the arc of visibility, the higher the moon appears to observers.
Halachah 14 – Conclusion of the Hilchot
The Rambam concludes that he has now explained all the calculations needed for:
- Determining moon visibility.
- Examining witnesses.
- Understanding the astronomical basis of sanctifying the new month.
He explains that he gathered these methods so that a student can find everything necessary within the Torah’s framework and not need to search elsewhere.
He closes with the verse:
“Seek from the Book of the Lord and read; not one of these shall be missing.”
(Isaiah 34:16)
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