What really happens when Earth turns? The rotation of Earth describes periods that are measured in days. The solar year is 365.242 days long, the lunation period 29.53 days long, and so forth.
Extracted from Matrix of Creation, page 42.
Earth orbits the Sun and, from Earth, the Sun appears to move through the stars. But the stars are lost in the brightness of the daytime skies and this obscures the Sun’s progress from human view. However, through observation of the inexorable seasonal changes in the positions of the constellations, the Sun’s motion can be determined.
The sidereal day is defined by the rotation of Earth relative to the stars. But this is different from what we commonly call a day, the full title of which is a tropical day. Our day includes extra time for Earth to catch up with the Sun before another sunrise. Our clocks are synchronized to this tropical day of twenty-four hours (1,440 minutes).
about how the cardinal directions of north, south, east and west were determined, from Sacred Number and the Lords of Time, chapter 4, pages 84-86.
Away from the tropics there is always a circle of the sky whose circumpolar stars never set and that can be used for observational astronomy. As latitude increases the pole gets higher in the north and the disk of the circumpolar region, set at the angular height of the pole, ascends so as to dominate the northern sky at night.
Northern circumpolar stars appearing to revolve around the north celestial pole. Note that Polaris, the bright star near the center, remains almost stationary in the sky. The north pole star is constantly above the horizon throughout the year, viewed from the Northern Hemisphere. (The graphic shows how the apparent positions of the stars move over a 24-hour period, but in practice, they are invisible in daylight, in which sunlight outshines them.) [courtesy Wikipedia on “circumpolar star”, animation by user:Mjchael CC-ASA2.5]
Therefore, the angular height of the pole at any latitude is the same angle we use to define that latitude, and this equals the half angle between the outer circumpolar stars and the pole itself. For example, Carnac has a latitude of 47.5 degrees north so that the pole will be raised by 47.5 degrees above a flat horizon, while the circumpolar region will then be 95 degrees in angular extent.
It is perhaps no accident that the pole is called a pole since to visualize the polar axis one can imagine a physical pole with a star on top, like a toy angel’s wand. The circumpolar region is “suspended” around the pole like a plate “held up” by the pole. Therefore, a physical pole, set into the ground, can be used to view the north pole from a suitable distance south (i.e., with the pole’s top as a foresight for the observer’s backsight). Such an observing pole would probably have been set at the center of a circle drawn on the ground, representing the circumpolar region around the north pole. This arrangement, a gnomon,* existed throughout history but usually presented as part of a sun dial.
This series is about how the megalithic, which had no written numbers or arithmetic, could process numbers, counted as “lengths of days”, using geometries and factorization.
My thanks to Dan Palmateer of Nova Scotia for his graphics and dialogue for this series.
The last lesson showed how right triangles are at home within circles, having a diameter equal to their longest side whereupon their right angle sits upon the circumference. The two shorter sides sit upon either end of the diameter (Fig. 1a). Another approach (Fig. 1b) is to make the next longest side a radius, so creating a smaller circle in which some of the longest side is outside the circle. This arrangement forces the third side to be tangent to the radius of the new circle because of the right angle between the shorter sides. The scale of the circle is obviously larger in the second case.
Figure 1 (a) Right triangle within a circle, (b) Making a tangent from a radius. diagram of Dan Palmateer.
Figure 1 (a) Right triangle within a circle, (b) Making a tangent from a radius.
This series is about how the megalithic, which had no written numbers or arithmetic, could process numbers, counted as “lengths of days”, using geometries and factorization.
My thanks to Dan Palmateer of Nova Scotia for his graphics and dialogue for this series.
This lesson is a necessary prequel to the next lesson.
It is an initially strange fact that all the possible right triangles will fit within a half circle when the hypotenuse equals the half-circles diameter. The right angle will then exactly touch the circumference. From this we can see visually that the trigonometrical relationships, normally defined relative to the ratios of a right triangle’s sides, conform to the properties of a circle.
A triangle with sides {3 4 5} demonstrates the general fact that, when a right triangle’s hypotenuse is the diameter of a circle, the right angle touches the circumference.
The number of days in four years is a whole number of 1461 days if one approximates the solar year to 365¼ days. This number is found across the Le Manio Quadrilateral (point N to J) using a small counting unit, the “day-inch”, exactly the same length as the present day inch. It is an important reuse of a four-year count to be able to draw a circle of 1461 days so that this period of four years can become a ouroboros snake that eats its own tale because then, counting can be continuous beyond 1461 days. This number also permits the solar year to be counted in quarter days; modelling the sun’s motion within the Zodiac by shifting a sun marker four inches every day.
A useful set of links to 4 recent posts about the Great Pyramids recording the length of different latitudes in the northern hemisphere. Further commentary will soon be forthcoming to better integrate these posts.
