Planetary Periods, or Cycles

The mean symbolical periods of the various bodies are the length of time between two successive conjunctions of that body with the Sun at the same geocentric longitude, i.e, falling on the same day of a year. In other words the Sun in its apparent annual revolution forms conjunctions with each of the other bodies as viewed from the Earth, each successive annual conjunction with the same body taking place at an advanced point in the Zodiac. After a time these conjunctions themselves form a cycle of conjunctions, beginning on approximately the same degree of the Zodiac, or days of the year. The length of this cycle with reference to a particular planet constitutes the planetary periods. These are:

Moon: 19 years, the Cycle of Meton (q.v.).

Mercury: 79 years, with an inconstant mean advance of 1°37' each cycle.

Venus: 8 years, with an inconstant mean advance of 1°32' each cycle.

Mars: 79 years, with an inconstant mean advance of 1°34' each cycle.

Jupiter: 83 years exact.

Saturn: 59 years, with a mean advance of 1°53'

Uranus: 84 years, with a mean advance of 40'

Neptune: 164 years, 280 days; a mean annual motion of 2°10'54"

Pluto. 247.7 years, with a mean annual motion that, because of the extreme ellipticity of its orbit, varies from 1° in Pisces through Gemini, to 2.5° in Virgo through Sagittarius.

Ptolemy cites these time-measures as follows: Moon 4y, Mercury 10y, Venus 8y, Sun 19y, Mars 15y, Jupiter 12y, Saturn 30y. Those moderns who use his system add Uranus 90y, Neptune 18oy, Pluto 360y. Lilley alters this, as regards the Moon to 25y, and Mercury to 20y; others assign 27y to Mercury.

By means of these periods one is able to arrive at a rough approximation of a planet's position at a given date in a year for which an ephemeris is unavailable; as follows:

Example: To determine the longitude of Uranus on October 15th, 1672 (new style), add multiples of 84y and subtract the mean advance. To do this in one operation: assume any year in this epoch, say 1902. From this subtract 1672. This gives an interval of 230 years. Divide this by 84; the result, 2 periods and 62 years. Subtract 62 from 1902, which gives the year 1840: two Uranus periods subsequent to the desired date. To illustrate: the longitude of Uranus, as perceived in the ephemeris for 1940, on October 15th, is 17°09' Pisces. The 40' advance, times the two periods, is 1°20'. Subtract this from 17°09' and you have 15°19' Pisces as the longitude of Uranus on October 15th, 1672 (N.S.).

These and additional periods, arranged in tabular form for reference use, are as follows:

* Unusually exact. # Not an eclipse cycle. (a) Inconstant mean advance.

The three outer planets are usually computed by other methods: either (a) the first return, in even years, with a plus or minus correction showing excess over 360 degrees; or (b) the net mean annual motion.

*Mean annual advance, based on mean precession.