ON A DIFFERENT NODE ....

COMMENTS ON VENUS TRANSIT PAIRS & NODE MOVEMENT

It was argued that the actual transit series of Venus (periodicity of transit pairs) is 243 years, not 251 years.

It was also argued that the line of nodes moves retrograde around the Sun instead of prograde (i.e. forward or in the direction of Earth's orbit).

The article "Venus Transits & Precession" explains the occurrence of Venus transit pairs and the mathematical relationship between the synodic cycle and Earth's 360-degree orbit period around the Sun. Calculations have shown that 157 mean synodic cycles are almost exactly time equivalent with 251 tropical years, whereas 243 sidereal years are not time equivalent with 152 mean synodic cycles. (299 mean synodic cycles would be almost equal to 478 sidereal years, but do not coincide with the occurrence of transits due to the motion of the nodes)

The following diagram illustrates the position of every fifth synodic period in a 360° circle (orbit); i.e. groups of 5 synodic periods are 2.2929...° apart. The table on the right shows each consecutive synodic position.

The table also includes a short list of transit pairs (e.g. 1518 CE to 2498 CE), which - in the linear progression of time - would occupy the synodic positions as indicated. A careful examination reveals how the 243-year transit series (152 synodic periods) is actually embedded in the 251-year "tropical" cycle (157 synodic periods), producing a pattern of +5, -10, +5, -10, etc. synodic periods. In other words, the degrees you add in 8 years you subtract in 243 years and return to longitude in 251 years (according to the motto "one step up and two steps down").

Based on the 360-degree tropical year one can easily calculate the "forward" migration of the line of nodes, which moves in synch with the mean synodic cycle. Assuming that the line of nodes remains situated exactly between transit pairs, the theoretical rate of node movement would be 32.88" per tropical year. Observations have shown that this rate is closer to 32.44"/year.

http://www.marco-peuschel.de/simtrans.pdf

If precession is caused by a wobble of the Earth's axis of rotation, the observed forward or prograde motion of the lines of nodes (e.g. Mercury, Venus, Mars) would merely be an "apparent" motion. Very accurate formulae exists that describe the "apparent" forward motion of the line of nodes (for Venus: +0.90112°/century or approx. 32.44"/year) relative to the dynamic equinox.

It seems, however, that the "real" retrograde motion of about -17.82"/year relative to inertial space (50.26"/year real motion of the equinox minus the 32.44"/year apparent motion of the nodes) is not well defined or expressed by a formula. Apparently, astronomers do not know from which inertial point of reference Venus' line of nodes has been observed to retrograde by about 17.82"/year or about -0.495°/century.

IF such a retrograde motion of Venus' line of nodes is a real motion with respect to the Sun and inertial space, it would have to exist regardless of precession; i.e. whether or not the pole (or the equator) of the Earth wobbles relative to the Sun. Precession (wobble) only affects the calendar date of when a transit occurs, but not the transit cycle itself or the direction of the observed motion of Venus' line of nodes.

An observer on Earth, recording the number of mean solar days from one transit to the next, will notice the forward migration of Venus' line of nodes (32.44" per year) as a real motion relative to the positions of the Sun and the Earth. Since precession does not affect the mean solar day (e.g. the observer's position on a fixed meridian), even a "geocentric" observer will not notice a retrograde motion of the line of nodes relative to the positions of the Sun and the Earth during Earth's 360-degree orbit around the Sun.

Transits occur as predicted regardless of the observed rate of the precession. Hence, the retrograde motion of Venus' line of nodes relative to inertial space is an apparent motion caused by the same celestial phenomenon that produces precession or the apparent motion of the sphere of the fixed stars - namely, the binary motion of our Sun.

In other words, the line of Venus' nodes moves forward with respect to the Earth and its orbital motion in a 360-degree tropical year, but appears to move backward in a sidereal year.

Astrophysicists have no plausible explanation for the orbital plane movement of (e.g.) Venus. Relying on standard Newtonian dynamics, they attribute the more than obvious resonance effects between Earth and Venus to Coincidence - the "God of Science".

In Einstein's universe, each object produces within a certain degree a curvature of its surrounding space. All moving objects (stars orbiting their companion, planets orbiting their sun, moons orbiting their planets etc.) cause an ever-changing yet harmonic pattern of interference in the curvature of space (as within the solar system). Observations show that such "perturbations" do not result in chaos, but rather produce resonance effects.

There is no reason not to assume that the same principle applies, for instance, to the orbital motions of Earth and Venus. In other words, the harmonious occurrence of Venus transit pairs is a natural result of the subtle and silent forces that govern motions in the universe.

© 2004 Sirius Research Group

August 7, 2004