Invariable
Plane. 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 913½
years, but the inequality lengthens this
to 918 years. Therefore the periodic
perturbations are determined by the second
order recurrence 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 decreases 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 180º 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 - can 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
Mahayuga 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 a
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 eccentricities 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 extraordinary 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
fundamental 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.
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