Declination

Meaning

Declination (written δ) is the angle between a body and the celestial equator, the Earth's equator projected out onto the sky. It works like latitude on a map: 0° on the equator, up to 90° at the celestial poles, counted north (positive) or south (negative). Together with right ascension, which is measured along the equator, it makes up the equatorial system of coordinates.

Astrologers usually work in a different system, the ecliptic one. Longitude (λ) is the familiar zodiac position, counted along the ecliptic, the Sun's yearly path, from 0° Aries. Ecliptic latitude (β) is the distance north or south of the ecliptic. The two systems use different reference circles. The ecliptic is tilted to the equator by the obliquity (ε), about 23°26′ today, so a planet with no ecliptic latitude at all can still have a large declination.

The conversion is [3]:

sin δ = sin β · cos ε + cos β · sin ε · sin λ

For a point on the ecliptic (β = 0), such as the Sun, the angles or a lot, this reduces to sin δ = sin ε · sin λ. The declination is then zero at 0° Aries and 0° Libra (the equinox axis) and greatest, equal to ε, at 0° Cancer (north) and 0° Capricorn (south), the solstice axis. So the Sun's declination runs through a yearly cycle from 0° at the March equinox, to about 23°26′ N at the June solstice, back to 0° in September and to about 23°26′ S in December. Because sin λ = sin (180° − λ), a degree and its antiscion always have the same declination.

Origin and history

Astronomy. Measuring positions from the equator is very old, since the equator is what the daily turning of the sky is centred on. In his commentary on Aratus and Eudoxus, Hipparchus (2nd century BC) gives many star positions in equatorial terms: declinations, or more often distances from the pole, and positions along circles parallel to the equator that amount to right ascension, though he does not use that name. Historians disagree about whether this adds up to a formal coordinate system [2]. Ptolemy's Almagest (2nd century AD) works out the arcs between the equator and the ecliptic (I.14) and tabulates them in a "table of inclination" (I.15): for each degree of the ecliptic from 0° Aries to 0° Cancer, how far it lies from the equator, which is the declination of that degree [1]. The table rests on his value of the obliquity, 23°51′20″ (I.12) [1] (see obliquity).

Astrology. Ptolemy's Tetrabiblos already reasons with equal declination without naming it: signs equally distant from a solstice are "of equal power" because the Sun in them makes days of equal length [4]. The use of a planet's own declination, latitude included, is set out by Placidus (1657), who renamed antiscia "parallels" and counted two bodies as linked only when their declinations are really equal [5] (see declination parallel). In modern astrology Kt Boehrer's Declination: The Other Dimension (1994), which gives special attention to planets out of bounds [6], is credited with a renewal of interest in declination in the 1990s [9]. Leigh Westin's Beyond the Solstice by Declination (1999) [7] and Paul F. Newman's Declination in Astrology: The Steps of the Sun (2006) [8] followed.

How it is used

• Parallels and contra-parallels. Two bodies at the same declination on the same side of the equator are parallel; on opposite sides, contra-parallel. See declination parallel.
• Out of bounds. A body whose declination is greater than the obliquity is beyond the Sun's farthest reach. See out of bounds.
• The Moon's cycle. The Moon's greatest declination in a month changes over 18.6 years. See lunar standstill.

Geocentric or topocentric. Declinations in astrology are normally geocentric, as seen from the Earth's centre. An observer on the surface sees the nearby Moon displaced by parallax, up to about 1° depending on where the Moon stands in the local sky [3]; for the Sun and planets the shift is tiny. Topocentric declinations matter for real moonrise positions, as at ancient monuments, but are rarely used in chart work.

On this site. The Declination panel works out geocentric declinations from each point's longitude and latitude and the chart's own obliquity (the true obliquity for the moment of birth). It covers the planets, the Moon's Node, the Ascendant and Midheaven (when the birth time is known), the seven Hermetic lots plus any lot you add by search, and the Behenian stars. It lists every declination, marks points out of bounds against the chart's obliquity (stars are not flagged), shows the Moon's reach for the year, finds parallels and contra-parallels within an orb of 0.25° to 1.5° (1° by default), notes whether each is also an antiscion or contra-antiscion, and draws everything on a declination strip. Progressions and Transits modes follow declination over time.

Examples

All figures use ε = 23.44°.

• 15° Gemini (λ = 75°) on the ecliptic: sin δ = 0.3978 × 0.9659 = 0.3842, so δ ≈ 22.60°, or 22°36′ N. The Sun is there in early June, close to its greatest declination.
• The Moon at 15° Gemini with 5° north latitude: sin δ = 0.0872 × 0.9175 + 0.9962 × 0.3978 × 0.9659 = 0.4627, so δ ≈ 27.56° N, well beyond the Sun's limit: out of bounds by about 4.1°.
• The same Moon with 5° south latitude has δ ≈ 17.63° N. The zodiac position is identical; the declination differs by almost 10°.
• 0° Aries has δ = 0°, but a planet there with 5° north latitude has δ ≈ 4.59° N.