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