Declination parallel

Meaning

Declination is how far a planet is north or south of the celestial equator, the Earth's equator projected onto the sky. It works like latitude on a map: 0° on the equator, positive to the north, negative to the south. The Sun's declination swings through the year between about 23°26′ north at the June solstice and 23°26′ south at the December solstice. That limit is the tilt of the Earth's axis, the obliquity of the ecliptic. The planets stay close to the Sun's path, so their declinations mostly lie within the same band.

Two planets are parallel when they have the same declination on the same side of the equator, both north or both south. They are contra-parallel when they have the same amount of declination on opposite sides, one north and one south. Raphael says a parallel acts like a conjunction [4]. The contra-parallel is commonly compared to an opposition in modern reference works; the older sources cited here do not discuss it. Orbs vary and are small; about 1° is common, and it is this site's default.

Origin and history

The idea of places with equal declination is old. Ptolemy says that signs the same distance from a solstice are "of equal power", because the Sun in either gives equal days and nights and rises from the same part of the horizon, which is the same as saying they share a declination. Signs the same distance from an equinox lie on "equal parallels", one north and one south [1]. Al-Bīrūnī describes signs that turn "in the same parallel", such as Gemini and Cancer [2]. Lilly's antiscion rests on the same ground: degrees where the Sun makes days and nights of equal length [3]. These are all statements about degrees of the ecliptic, the Sun's path.

The parallel as a link between the planets themselves, using each body's actual declination, is set out by Placidus de Titis in his Tabulae primi mobilis (1657). What are commonly called antiscia, he writes, he calls parallels, since Ptolemy speaks of signs that describe the same parallels. He counts two bodies as parallel only when their declinations are equal, with their latitude taken into account: on the same side of the equator this is his primary or "beholding" parallel, and on opposite sides the northern one commands and the southern obeys [6]. He directs the Sun to such parallels in his timing methods, and he also defines "mundane" parallels measured by the daily turning of the sky [6]. Whether he was the first to use true declination in this way is not established here.

Raphael, writing in 1828, defines the zodiacal parallel as two planets with the same declination and gives it the effect of a conjunction. He credits Placidus as the first to define the related mundane aspects, which are measured by the daily turning of the sky rather than along the zodiac [4].

Kt Boehrer's Declination: The Other Dimension (1994) is a modern book-length treatment. Its publisher describes it as covering the astronomy and astrology of declination, with particular attention to planets out of bounds, above all the Moon [5].

How it is used

Parallels and antiscia. For a point on the ecliptic, declination depends only on its longitude: sin δ = sin ε · sin λ, where ε is the obliquity. The antiscion of λ is 180° − λ, and sin (180° − λ) = sin λ, so a degree and its antiscion have exactly the same declination: the antiscion is a parallel. The contra-antiscion is 360° − λ, whose sine is −sin λ, so its declination is equal and opposite: a contra-parallel. For the angles, house cusps and lots, which lie on the ecliptic, the mirror points and the parallels are the same thing. See antiscion and contra-antiscion.

Latitude breaks the match. Planets are not exactly on the ecliptic. With ecliptic latitude β the formula becomes sin δ = sin β · cos ε + cos β · sin ε · sin λ. The Moon can be up to about 5.3° off the ecliptic, Mars nearly 7°, Venus nearly 9° when it passes close to the Earth, and Pluto about 17–18° (greatest values seen from the Earth, 1900–2100, computed with the Swiss Ephemeris). Such a body can sit on another's antiscion without being parallel, or be parallel without any antiscion contact.

Uneven orbs. Declination changes fastest near the equinoxes and slowest near the solstices. Near 0° Aries, 1° of declination covers about 2.5° of longitude. Near 0° Cancer the Sun's declination barely moves: every ecliptic degree from about 13°41′ Gemini to 16°19′ Cancer lies within 1° of the maximum. So a 1° orb in declination is tight near the equinoxes and loose near the solstices.

Out of bounds. A planet whose declination is greater than the Sun's greatest (about 23°26′) is called out of bounds. Only a body with latitude can get there. The Moon at 0° Cancer with 5° of north latitude has a declination of about 28.4° north.

On this site. The Declination panel, in the Advanced layers section, gives the declination of each planet, the Moon's Node, the Ascendant and Midheaven (with a known birth time), the Hermetic lots (plus any lot you add) and the Behenian stars, in degrees and minutes north or south. It works out declination from each point's longitude, latitude and the obliquity at the moment of the chart. It lists every parallel and contra-parallel within an orb you can set (1° by default), says whether each is also an antiscion or contra-antiscion by longitude, and marks planets that are out of bounds. It can also follow declinations over time, by secondary progression and by transit. The Antiscia panel, listed just before it, checks each mirror contact and says whether it is also a true parallel or contra-parallel, and when it is not, names the points that lie off the ecliptic.

Examples

All figures use an obliquity of 23.44°.

• 0° Gemini on the ecliptic: sin δ = sin 23.44° × sin 60° = 0.3978 × 0.8660 = 0.3445, so δ ≈ 20.15° N. Its antiscion, 0° Leo (120°), has sin 120° = sin 60°, so the same 20.15° N: a parallel.
• 10° Taurus (14.81° N) and its contra-antiscion 20° Aquarius (14.81° S): a contra-parallel.
• The Moon at 15° Leo with 5° north latitude: sin δ = 0.0872 × 0.9175 + 0.9962 × 0.3978 × 0.7071 = 0.3602, so δ ≈ 21.1° N. A planet on the ecliptic at its antiscion, 15° Taurus, has δ ≈ 16.3° N. The antiscion contact is exact, but the two are about 4.8° apart in declination: not a parallel.
• The same Moon with 5° south latitude has δ ≈ 11.6° N, about as far from 16.3° on the other side.