Tuesday, January 31, 2017

SPX vs 24th Harmonic of Mercury's Right Ascension

Mercury is the closest planet to the Sun, and named after the god of commerce, travel, and thievery in Roman mythology, the counterpart of the Greek god Hermes who also guides the souls to the underworld. Mercury is the Celtic god Lugus, the Germanic god Wotan, the old Indian god Rudra, later known as Shiva, associated with magic, poetry, and warfare. In ancient Babylon Mercury was the god Nabu, the divine scribe and god of wisdom. To the Egyptians Nabu was Tehuti, rendered by the Greeks as Thoth. Nabu was one of the major gods of Egypt and personified the principle of reason. However, Thoth had no connection with the planet Mercury until the Greeks introduced astrology to Egypt, where the planet was regarded as belonging to the god Set, while Thoth presided over the Moon. Finally Hermes Trismegistus seems to be the syncretic combination of Hermes and Thoth.  

Mercury was attributed a divine messenger due to the fast speed across the sky. Mercury attains Inferior Conjunction with the Sun (nearest approach to Earth) every 115.88 Earth days (= average Synodic Period), but this interval can range from 105 to 129 Earth days due to Mercury's eccentric orbit. Its period of retrograde motion as seen from Earth can vary from 8 to 15 days on either side of inferior conjunction. This large range arises from the planet's high orbital eccentricity. Mercury's axis has the smallest tilt of any of the Solar System's planets (about  1⁄30 degree), and its orbital eccentricity is the largest of all known planets in the Solar System. At aphelion, Mercury is about 1.5 times as far from the Sun as it is at perihelion. Because both Mercury and Earth are moving in elliptical orbits, the maximum elongation angle varies from one orbital revolution to another (HERE).

The Celestial Equator is the plane formed by the daily rotation of the Earth around its own axis. It is inclined to the Ecliptic at 23°26’. This angle changes very slowly. The position of a celestial body, e.g. Mercury, is measured with reference to the plane of the Earth’s equator. The Geocentric Equatorial Coordinate System is projecting the Earth's equator onto the celestial sphere (forming the celestial equator) with a primary direction towards the vernal equinox, and a right-handed convention. Hence the Right Ascension (in hours, minutes and seconds) is the angle of the planet in the Equator plane (RA), and the Declination shows how the planet is inclined to the Equator. 


In the above chart Mercury's Synodic Period of 105 to 129 days was divided by 24 (1 Synodic Period = 360° / 24 = 15° = 24th Harmonic). Therefore one oscillation of the Cosinus of Mercury's Right Ascension between -1 and 1 (= 15h) takes 4 to 5 Calendar Days, and considerably longer during the retrograde periods.