Periods

recovered from http://web.archive.org/

This document was prepared by Richard Heath as a letter for Nature magazine and submitted on 14th April 1994 but remained unpublished. For readers of the Matrix of Creation (2nd ed, Inner Traditions Press, 2004) it marks the discovery of a unit of time proposed and named the Chronon, as being 1/10000th of the Moon's orbit and also the difference between the sidereal and tropical day of the Earth. The paper also documents a discovery made, with Robin Heath, later to be documented in his books: that one can divide up the solar year by its excess over the eclipse year to reveal an 18.618:19.618 ratio between these years, and many other interesting numerical facts not mentioned in this place. The puzzle here is a connection between the rotation of the Earth, the solar year and the precession of the Moon's orbit which (a) may be explainable by science (b) appears to have puzzled Megalithic astronomers and (c) should puzzle us today. 

by Richard Heath and Robin Heath

We find that the Earth’s rotational day divides the year according to the 18.62 year cycle of the Lunar Nodes. From this we conclude that the Earth’s orbit, the Moon’s orbital precession and the Earth’s rotational velocity are most probably interconnected. The tropical solar year in days is factorised almost exactly by 18.618 times 19.618 and the Moon travels one ten thousandth of its orbit in the time difference between sidereal and tropical days.

We have been considering a range of numerical coincidences present in arithmetical and geometrical analyses of astronomical cycles involving the Sun-Moon-Earth system. There is an apparently lawful relationship concerning the Earth, Sun and Moon, one that is most unusual.

The Earth ‘s rate of rotation is directly proportional to the ratio of angular velocities of the Sun and the Moon ~ orbital nodes; as seen from Earth.

The reason why this fact has been hidden is that we use the day or the degree to manipulate the data concerning these phenomena and since the day is implicated in the above law it obscures the relationship and the degree changes the numbers to further obscure it.

We now refer to the angle traveled by the sun on the ecliptic in one day as a DAY. If we convert the Moon’s average daily motion of 13.176 degrees per day to DAYs per day we obtain 13.368 DAYS per day. This is the sidereal frequency per year because DAYS per day is also revolutions per year. This shows the virtue of using DAYS over degrees.

As there is not a great deal of familiarity with the terms used in describing Sun and Moon phenomena, we will recap some terms (see Figure 1). 

NODES nature1 500

  • The Moon crosses the Sun‘s path or ecliptic at two places, the lunar nodes.
  • Full or new moons occuring near a node produce solar or lunar eclipse respectively.
  • Whilst the Sun moves East day by day by about one degree, it precesses the Lunar Nodes in the opposite sense, i.e. retrograde. The Sun moves about 18.618 times faster than the precessing nodes.
  • Whilst the Sun returns to the same place on the ecliptic after one Solar Year, it will return to a given node after a shorter period an Eclipse Year. In Earth days, a Solar Year is 365.242 units long whilst an Eclipse year is 346.620 units long.

The Metonic Period is the 19 year anniversary of the Moon which dominates the  repetition of cyclic astronomical aspects in the sky. We know that the megalithic identified this period and others of similar length (the Saros and Nodal periods), because interrelated units of measure, especially the megalithic yard and royal cubit, can be found within monuments which recorded these periods as counted lengths.

How the Metonic Works

There is only numerical way to arrive at a system in which there is an anniversary between the sun, the moon and the stars over 19 years (as in the Metonic period), involving having a lunar orbital period (around the earth) which divides into the same period, in this case exactly 254 times.

    • 254 lunar orbits of (on average) 27.32166 days equals 6939.7 days
    • 19 solar years of 365.2422 days equals 6939.6 days and
    • 235 lunar months of 29.53059 days equals 6939.7 days

If the moon returns to the position of the sun after 19 years then the phase of the moon will be the same so that there will be 254 minus 19 equal to 235 lunar months in the Metonic observatory and it is in the nature of orbits which become commensurate with each other (as discrete, whole-number gravitational systems), to fall into such resonant relationships rather than chaotic ones.

Signature Ratios within the Metonic

Since the solar year, lunar orbit and month are synchronous, the excess of the solar over lunar year will form a near rational (i.e. integer) fraction of months or orbits, in that case an excess of 7/19 (0.368) lunar months.

    • The lunar orbit is 27.32166 days
    • The lunar month is 29.53059 days

Similarly, the excess of the lunar month over the lunar orbit become the rational and fractional ratio found between their frequencies within the 19 year Saros cycle, that is 254/235; which has the fractional part, reciprocated of 1/0.08085 = 12.368 which is then N for the N:N+1 triangle describing the orbit relative to the month, of the moon.

254-235-triangle 600

The stone age person had significant contact with the natural world and, with this, the sky. By night many bright points appear upon the black dome of the celestial sphere at night, as a fixed pattern, and the moon is then like a weaker version of the sun. Day begins when the sun appears on the eastern horizon (to define morning) and sets in the west (to define evening). It would therefore soon become clear, to stone age observers, that the starry points we now call stars move like the sun by rising in the east and setting in the west. 

HEXAD Megalithic Astronomical Framework

 

A six-fold hexad of three dimensions as they affected megalithic astronomers

Hyparxis (In Greek, ὕπαρξις) means 'essential nature' and is the Neoplatonic term for the summit, beginning, or hierarch of a hierarchy, as follows: The word is particularly used by the Neoplatonist, Proclus who uses it to mean "the summit of any nature, or blossom, as it were, of its essence."

Eternity is cyclic and often symbolized by the image of a snake swallowing its own tail, known as the Ouroboros (or Uroboros). The circle is also commonly used as a symbol for eternity, as is the mathematical symbol of infinity, \infty.

Time is the fourth dimension and a measure in which events can be ordered from the past through the present into the future,[1][2][3][4][5][6] and also the measure of durations of events and the intervals between them.