A Gauquelin position describes where one celestial body sits along its own daily arc for a particular time and place. The scale has 36 sectors. It begins at the eastern horizon, passes the upper meridian, reaches the western horizon, and continues below the horizon back toward rising.
The four anchors
| Sector position | Sky event | Arc |
|---|---|---|
| 1 | Rising at the eastern horizon | Diurnal arc begins |
| 10 | Upper culmination at the meridian | Midpoint of diurnal arc |
| 19 | Setting at the western horizon | Nocturnal arc begins |
| 28 | Lower culmination at the meridian | Midpoint of nocturnal arc |
Each half of the daily circuit receives 18 equal divisions of elapsed semiarc. A sector therefore measures progress through local rising and setting geometry, rather than a fixed 10-degree slice of the zodiac.
The calculation
Let H be the body's signed local hour angle, φ the birthplace latitude, and δ the body's declination. The geometric semi-diurnal arc H₀ is the hour angle from upper culmination to either horizon crossing.
Above horizon: position = 1 + 18 × (H + H₀) / (2H₀)
Below horizon: position = 19 + 18 × (H − H₀) / (360° − 2H₀)
For the below-horizon expression, a negative hour angle is continued through 360 degrees when needed. The result is wrapped onto the continuous interval from 1 up to 37, where 37 returns to the rising point at 1.
Worked example
For 1 January 2000 at 20:00 local time in Manila (UTC+8, 14.6° N, 121° E), the Sun's apparent right ascension is about 281.2782°, declination −23.0327°, and local sidereal angle 41.4570°. Its signed hour angle is 120.1788° and its semi-diurnal arc is 83.6419°. The Sun is below the horizon, 18.9589% through its nocturnal arc:
That continuous position falls in sector 22. The fraction matters near a boundary: a rounded whole sector alone cannot show how close the body is to entering the next one.
True position and ecliptic projection
The calculator displays two variants. True planetary position retains ecliptic latitude and uses the body's actual apparent right ascension and declination. Ecliptic projection keeps its tropical longitude but sets ecliptic latitude to zero before converting to equatorial coordinates. The Sun usually changes little; the Moon and Pluto can differ more. The chosen variant appears as the main result and the other remains visible for comparison.
Recorded-time sensitivity
Sector positions turn with the local sky, so a clock error can change a whole-sector label. The calculator evaluates the same data ten minutes before and after the entered time and flags bodies that cross an integer boundary. That comparison measures sensitivity; it does not infer or correct a missing birth time.
High-latitude limit
If the formula needs an arccosine outside its real range, that body is circumpolar at the entered latitude: it does not have an ordinary geometric rise and set on that daily path. The calculator leaves its sector unavailable. It does not substitute a separate polar method. Refraction, observer elevation, parallax, and the visible edge of a disc are also outside this geometric center-of-body model.
Historical plus zones
The familiar plus-zone grouping covers sectors 36–3 around rising, 9–12 around upper culmination, 19–21 after setting, and 28–30 around lower culmination. “Plus” is a historical category name, not a statement that a placement is beneficial. Replication debates involve sampling, occupation classification, data handling, and statistical design beyond what a chart calculator can decide.
Definitions used here
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