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Astro*Dictionary by Michael Erlewine





2 articles for "Invariable Plane"

Invariable Plane [Astro*Index]

An imaginary plane, passing through the center of mass of the Solar System perpendicular to the total angular momentum vector of the system.

Its position relative to the ecliptic is specified by its node (N) and inclination (I) as follows:

N = 106°35'01" + 3452"T
I = 1°34'59" + 18"T

where: T is measured in Julian centuries (of 36525 days) from 1900.

See also: ♦ Barycenter ♦ Ecliptic ♦ Node
Invariable Plane [DeVore]

The Solar System possesses two fixed planes: that of the Solar Equator; and the Invariable plane — a central plane of the Solar System discovered by Laplace, which, passing through its center of gravity at a mean inclination of about 1°35' to the Ecliptic, is independent of the mutual perturbations of the planets. The inclination of the orbits of Venus and Mercury to the Solar Equator, slightly more than 3 degrees, is less than that of the other planets. Since these are the two closest planets to the Sun, the Solar Equator can be considered as their reference plane. The Earth's inclination to this plane, of slightly more than 7", is exceeded only by that of Pluto. The Ecliptic, the Earth's plane of revolution around the Sun, intersects the Solar Equator in the middle of Gemini and Sagittarius, at which points the Earth has no heliographic Latitude North or South. However, the values of these inclinations and the longitudes of the planetary Nodes along this plane are all variable due to motions of the orbits themselves with respect to the other great reference plane of the Solar System: the Invariable Plane — so-called because its position remains unaltered by any forces within the system. In this plane the combined angular momenta of all the planets is a maximum. There are two classes of disturbances in the normal undisturbed elliptical motion of the planets in their orbits in space: periodic perturbations and secular perturbations. Periodic perturbations are deviations due to the gravitational pulls of the planets on each other. However, after the planets have revolved a considerable number of times, and thus have been in all possible relations to each other, these periodic perturbations cancel each other. A famous example is the long period inequality in the motions of Jupiter and Saturn, which shifts their positions by a degree or so- one forward and the other backward — in a period of about 918 years.

Actually their recurrence cycle in the fixed Zodiac — 46 conjunctions distributed nearly evenly in all 12 Signs of that Zodiac — is about 913-1/2 years, but the inequality lengthens this to 918 years. Therefore the periodic perturbations are determined by the second order recur- rence cycles of the planets in the fixed Zodiac. However, at the end of such a cycle of fluctuation the distorting effects have not been completely cancelled out, and small remaining residues show up in what are termed the elements of the planets' orbits. As a result of this residue, the nodical line at which the orbit plane of each planet intersects the invariable plane, is displaced backward, in a precessional motion of the whole orbit plane. In addition, the inclination of the orbit plane to the invariable plane is slightly decreased or increased. A third effect is a shift in the position of the major axis — longest axis of the orbital ellipse. This shift may be either forward or backward, but it is more likely to be forward for all of the planets except Venus. Finally the shortest axis of the orbital ellipse — the minor axis which crosses the major axis at the center of the ellipse — increases or decreases its length; i.e, the eccentricity of the ellipse becomes greater or less.

Two great masters of celestial mechanics, Lagrange and Laplace, demonstrated that while there are periodic fluctuations in the lengths of the major axes there are no secular perturbations — long-term oscillations. Since the duration of a planet's revolution around the Sun depends on the major axis alone, this means that except for minor short-term fluctuations the periods of the planets are constant. They further demonstrated that the inclinations and eccentricities oscillate within narrow limits which are never exceeded, thus preserving the stability of the Solar System. Finally they showed that the orbit planes precess backward along the invariable plane, while most of the major axes revolve forward-spending briefer periods in actual retrograde motion. Only the major axis of Venus spends more time revolving backward than forward. Thus the Solar System, through an intricate process of mutual adjustment, maintains its basic configurations of orbits, and its stability. As one planet de- creases its eccentricity and inclination, one or more orbits must at the same time be increasing their eccentricities and inclinations: whereby the total amount of eccentricity and of inclination to the invariable plane remains constant! This has been termed the Magna Charta of the Solar System. The late Ernest W. Brown showed that the effects of resonance could not have been great enough within the past hundred million years to have destroyed this stability; nor would it be in the next hundred million years.

Jupiter, the most massive of all the planets, has an orbital inclination to the Invariable Plane which never exceeds 0°28', nor ever less than 0°14'. Its current value is about 0°21'. Furthermore, the Nodes of the Jupiter and Saturn orbits on this plane are never separated from each other by much less than 180°; hence these two planets largely determine the position of the Invariable plane — especially Jupiter. According to Stockwell, the mean period of their common precession is 49,972 years. Similarly the perihelion ends of the major axes of the orbits of Jupiter and Uranus never get much less than 1800 from each other. The common mean period for a revolution of their major axes (line of apsides) is 348,700 years. Thus Jupiter is the "flywheel" which balance the Solar System, a perfect symbol of justice and law.

The Earth's orbit — the ecliptic — an never have an inclination to the Invariable plane in excess of 3°6'. The value on January 1, 1850 was 1°35'19.376" - the figures are taken from Stockwell's "Secular Variations of the Eight Principal Planets," in the "Smithsonian Annual Contributions to Knowledge," Volume 18, 1872. According to him the maximum eccentricity of the Earth's orbit is .0693888; the current value .0159. The period of the orbital precession of the Ecliptic on the Invariable Plane is indeterminate, since the minimum inclination of the Ecliptic to that plane is 0°0'0". Similarly, the minimum Eccentricity is also 0, hence the mean period of motion of the line of Apsides is also indeterminate.

LeVerrier, the discoverer of Neptune, and Stockwell, calculated the position of Earth's perihelion, one end of the line of apsides, over a period in excess of 4,000,000 Years. By counting the number of times the line of Apsides revolved within that period, one gains a good estimate of its period in the present Mahayuga. This Maha- yuga of the Hindus is a period of approximately 4,320,000 years, in which they say all of the planets recur at nearly the same position. The astronomer Stuart showed that this is correct and that the period is 4,319,936.8663 years: at the end of which Mercury, Venus, Earth, Mars, Jupiter and Saturn return to 2 position in the Fixed Zodiac about 20° behind where they started. He found this also applied to the "new" planets, Uranus and Neptune; and that an increase in the period of Pluto of only one part in 100,000, or 0.001 per cent, will also bring it into recurrence. It would appear that in the present Mahayuga the mean period of revolution of the Earth's apsides is about 115,000 years from LeVerrier's figures, and about 110,000 from Stockwell's somewhat more accurate figures: and the average period of revolution of the major axis of the Earth's orbit must have a mean value of approximately the same order of magnitude: i.e., 110,000 to 115,000 years.

In the present cycle both of these periods are near minimums, since the eccentricity and inclination of the Earth's orbit are decreasing to minimum values. In the current cosmic Era the length of the Planetary Precession and rotation of the Line of Apsides will be from 72,000 to 75,000 years. The minimum inclination will be reached in about 20,000 years and the minimum eccentricity about 26,000 A.D., one cycle of general Precession after Christ. The last Stationary position of the Perihelion-Stationary-Direct after several thousands of years of retrogressive motion — was about 26,000 years before Christ: again one cycle of the general Precession.

The relationships of these cosmic cycles to the time of the Christ is indeed remarkable, and tends to confirm the belief that a new cycle of general Precession then commenced. Furthermore at that epoch the Nodical line of Ecliptic and Invariable Plane was at right angles to the Nodical line of Ecliptic and Equator — the Equinox — thus making a Cross! The position of the Nodical line of the Planetary precession in the Moving Zodiac was 16°14'6.00" Cancer-Capricorn on January 1, 1850. The present position of the Perihelion end of the Line of Apsides — where the Earth is nearest the Sun — is about 11° Capricorn, i.e., the position of the Sun on or shortly after January 1 of every year (deviation due to Calendar variation or Leap Year effect). Thus it appears that we commence our year at what after all is astronomically the most logical time.

The minimum eccentricity of the Earth's orbit, at about 29,900 A.D., will be the smallest minimum since the greatest maximum, about 850,000 B.C., showing a great cycle, governing all planetary eccen- tricities in the Solar System, of a duration of approximately 1,750,000 years. According to Madame Blavatsky's "Secret Doctrine" it was around 850,000 B.C. that the first and most serious cataclysm destroyed most of the continent of Atlantis, at the start of what she terms the Fifth Root Race. As a cataclysm by Water, this suggests that the next cataclysm may be by Fire, and will occur about 25,900 A.D., at the start of the Sixth Root Race. Since she maintains that each Root Race has 7 Sub-races and each of these in turn 7 Family Races, there should be 49 Family Races in a Root Race or Lifewave. She also states that the period of a Family Race was that of the general Precession, a little under 26,000 years — although the Root Races overlap, in that a new one commences before an older one has run its course. It is easy to show that the Precession which ended with Christ was the end of the Fifth Family Race of the Fifth Subrace of the Fifth Root Race: making 33 Family Races or Precessions since 850,000 B.C. Therefore the present Sixth Family Race, of the present cycle of Precession, may be considered as a bridging cycle out of which both the Sixth Sub-Race and the Sixth Root Race will in the next cataclysm approach their start around 25,900 A.D.

The foregoing is not put forward dogmatically, but as an interesting explanation of the significance of these long cosmic cycles. The implication is that the present cycle of Precession is a bridging cycle between two great Lifewaves (Root Races), and thus has extraordi- nary importance; that it commenced with Christ and the cosmic Cross formed by the Equinoxes and the Line of the Planetary Nodes; and that the significance of the Crucifixion is essentially cosmic, and the Mission of the Christ one of initiating the great Precessional cycle of Transition from the Fifth to the Sixth Lifewave. It is a notable fact that on April 1, 25 A.D. (Julian Calendar), when Jesus was 30 years of age and at the start of his mission, according to a consensus of historical researches, there was a Great Cardinal Cross, wherein Uranus in Cancer at its Node on the Invariable Plane opposing Neptune in Capricorn at its Node on the Ecliptic, was in cross relationship to Saturn in Aries at its Node on the Equator opposing Jupiter in Libra — all the Nodes on the three basic planes which at that time were forming the cosmic cross. In addition there was a Full Moon in Libra with the Sun in Aries, Mars in Aries also in the Cross, and at its Node on the Ecliptic. Pluto was in early Sagittarius; and Mercury and Venus were retrograde in the last decan of Pisces — the Sign of Christianity and of the traditionally first of the 12 Ages into which the Precessional cycle is customarily divided. Thus through the crossing of orbit planes, the Nodes, this Planetary Cross shows a remarkable relationship to the Cosmic Cross made at that time by the Equator, Ecliptic and Invariable planes.

This full discussion is warranted on the basis that this date marks the blending of all the chief cycles which affect the Earth, and the significance of the cosmically-indicated Crucifixion of Christ, which could never before have occurred in the two-billion-year history of the Earth. A third Cross is found to be involved, if one considers the four consecutive Solar eclipse paths which passed over Jerusalem and Bethlehem, both before and after the life of Jesus. The total Eclipse of July 4, 336 B.C. at 6.3° Cancer; the total Eclipse of April 2, 303 B.C. at 7.5° Aries; the annular Eclipse of January 5, 29 B.C. at 12.6° Capricorn; and the annular Eclipse of October 4, 590 A.D. at 13.2° Libra — all Julian dates. These form a Cross in their positions on the Ecliptic (Zodiac), the positions in near-agreement with the Zodiacal places of the four chief major planets on April 1, 25 A.D.: Uranus, at 10.1° Cancer; Neptune, at 13.8° Capricorn; Saturn, at 4.8° Aries; and Jupiter, at 15.4° Libra - all calculated from Schoch's Tables by Ralph Kraum. Thus the Planetary Cross activated the Eclipse Cross (zodiacal), and the drama of the ensuing Crucifixion was enacted in Jerusalem where the four eclipse-paths had crossed and were to cross (Geographical), while both in turn were the projection of the basic evolutionary Cosmic Cross of the three funda- mental planes which signified the commencement of the most vital cycle of Precession (both planetary Precession and general Precession), within the period of two Lifeways (transition from one to the other)-which is about 100 general Precessions or 2,570,000 years: the period of a double Polar Inversion. — CHARLES A. JAYNE, Jr.

See also: ♦ Barycenter ♦ Ecliptic ♦ Node


Astro*Index Copyright © 1997 Michael Erlewine


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