This is a brief introduction to the astronomy involved in planetary cycles. The ‘Cycles of History’ book contains a fuller description.
ASTRONOMY: SOLAR SYSTEM AND PLANETARY POSITION CALCULATIONS
Our Solar System is located in the Milky Way galaxy, a barred spiral galaxy with a diameter of about 100,000 light-years containing about 200 billion stars. Our Solar System consists of the Sun and its planetary system of thirteen planets or dwarf planets, their moons, and other non-stellar objects. It formed approximately 4.6 billion years ago from the collapse of a giant cloud of gas, dust and ice.
The principal component of the Solar System is the Sun, a G2 main-sequence star that contains 99.86 percent of the solar system’s known mass and dominates it gravitationally. The Sun’s four largest orbiting bodies, the gas giants, (4 of the 5 outer planetary bodies covered by this book) account for 99 percent of the remaining mass, with Jupiter and Saturn together comprising more than 90 percent.
The planets revolve around the Sun in elliptical orbits. That is, if you were to look down on the Solar System, you would see each planet trace out an ellipse (moving counter-clockwise) as it goes around the Sun. Unfortunately, every body in the Solar System pulls gravitationally on every other body, the strength of the pull depending on mass and distance. This means the orbits are not actually pure ellipses, but have minor deformations as the planets are pulled back and forth, in and out. Astronomers call these little jogs “perturbations”, and calculating them has been a major effort for centuries. Computers have allowed unprecedented speed and accuracy in these calculations.
Planetary positions for the aspect tables in this book were calculated using the Jet Propulsion Laboratory (JPL) export ephemeris DE406. This ephemeris, released in 1998, is one of a series of models of the Solar System produced by JPL consisting of data which allows computers to find positions, velocities and accelerations of major Solar System bodies. Jet Propulsion Laboratory (JPL) is a federally funded research and development center and National Aeronautics and Space Administration (NASA) field center located in Pasadena, California, managed by the California Institute of Technology (Caltech) for NASA.
The JPL ephemeris is the result of a massive multi-body numerical integration run (the most accurate method of calculating positions). The position files resulting from the numerical integration were too large for easy distribution, so they were abstracted to a series of coefficients of Tchebychev polynomials, which took less space (though even so the DE406 ephemeris takes 190 Megabytes). The numerical integration of course included all of the planets, as well as some of the larger asteroids. The asteroid belt occupies the orbit between Mars and Jupiter, between 2.3 and 3.3 Astronomical Units (each AU = 150m kilometres) from the Sun. It is thought to be remnants from the Solar System’s formation that failed to coalesce because of the gravitational interference of Jupiter.
Asteroids range in size from hundreds of kilometres across to microscopic. All asteroids except the largest, Ceres, are currently classified as small Solar System bodies (often called Minor Planets) The asteroid belt contains tens of thousands, possibly millions, of objects over one kilometre in diameter. Despite this, the total mass of the asteroid belt is unlikely to be more than a thousandth of that of the Earth.
The calculations for the book were done in the uniform time used by astronomers. The heliocentric XYZ positions output by the JPL routines were converted to geocentric Celestial Longitude and Latitude in the ecliptic of date (the tropical zodiac), and the aspects were calculated using Celestial Longitude only. Finally the astronomical times of the aspects were converted to dates in the appropriate calendar – Gregorian after October 15, 1582 and Julian before that.
Note that the book includes Pluto, even though the IAU (International Astronomical Union) reclassified it as a “Dwarf Planet” in 2006. This change of status was and is somewhat controversial and most non-astronomers still call Pluto a planet, as they have since its discovery in 1930. It is still the 10th most massive body observed directly orbiting the Sun – its mass may end up equalling that of Eris, currently estimated the 9th most massive. The NASA New Horizons spacecraft, due to fly past Pluto and its biggest moon Charon in 2015, will provide more information, and perhaps help distinguish Pluto from the four other bodies currently classified as dwarf planets.
ACTUAL & SCHEMATIC PLANETARY CYCLE DIAGRAMS
With planetary cycles both planets are moving at different speeds around the Sun counterclockwise. As they make their 90 degree, 180 degree and 270 degree aspects to each other both their positions relative to the Sun in each case are quite different. However the distance of one from the other still moves from 0 degrees through 180 degrees and round to 0 degrees again – and it is this we are interested in. The diagrams below illustrate the Actual cycle between the planets Jupiter and Saturn and the Schematic one we follow on this site.
Source: Nick Anthony Fiorenza