Astronomy college course/Saros cycle

Organization
This page will begin with a History section that links the Ecliptic, the Saros cycle and the Antikythera mechanism.

pages that need to be rewritten ASAP
The following subpages to Orbital mechanics exist and will be organized in a few days
 * Astronomy college course/Saros cycle/Saros/Quiz_1
 * Astronomy college course/Saros cycle/Saros

Resources that are already linked to wikipedia and should be moved with great care
Ecliptic Antikythera

Topics for quiz 1
223 synodic months    = 223  &times;  29.530589  &asymp; 6585.32  days (lunar phases)

242  draconic  months  = 242  &times;  27.212221  &asymp; 6585.35  days (line of nodes)


 * The synodic month is the time between two consecutive new moons, i.e., when the Moon passes the Sun in during it's monthly transit through all the constellations of the zodiac.
 * The draconic month marks two passages of the Moon through the line of nodes, i.e., when the Moon is in the plane defined by Earth's orbit around the Sun.

An eclipse can only occur


 * The anomalistic month marks successive perihelion's of Moon's elliptical orbit.  At perigelion, the Earth-Moon distance is at a minimum, and the Moon's orbital speed is at a maximum.  (But due to the rotation of the Earth, the Moon's apparent motion in the sky (from east to west) is at minimum on that day).

Topics for quiz 2
There seems no end to the complexities and patterns regarding cycles of eclipses. For reference, we note a few of them.

Anomalistic and sidereal months
From Orbit_of_the_Moon:
 * 223 synodic months    = 223  &times;  29.530589  &asymp; 6585.321  days (lunar phases)
 * 242  draconic  months  = 242  &times;  27.212221  &asymp; 6585.357  days (line of nodes)
 * 239  anomalistic  months   = 239  &times;  27.55455  &asymp; 6585.537  days (closest to Earth)
 * 241 sidereal months  = 241  &times;  27.321662  &asymp; 6584.521  days (orbit relative to the stars)

The anomalistic month marks the duration between consecutive perihelions, i.e., when the Moon is at it's closest approach. The Moon's proper motion is also governed by cycle, and the Antikythera mechanism contained a pin gear for the Moon's motion to model this effect. The matching of the Saros cycle to nearly 239 anomalistic months causes successive eclipses of the Saros cycle to endure for similar lengths of time. We also see that 241 sidereal months misses the cycle by one day, meaning that the stars are somewhat close to their original position with respect to the Moon on the next Saros. Finally, the fact that the Saros is within about 11 days of a year ensures that consecutive Saros eclipses will occur in roughly the same season.

Inex cycle
An even more precise cycle is the Inex cycle cycle:
 * 358 synodic months =358 &times; 29.530589 =10571.951 days
 * 388.5 draconic months = 388.5 &times; 27.212221 =10571.948 days