How did our Moon get to be up there? Astronomers are now on their fourth theory about this, and I don't reckon they should be allowed any more! Each theory is a bit less credible than the one before. First, they had an early Earth splitting in two, with Luna emerging from the Pacific Ocean. That lasted quite a while, but eventually it was deemed that there wasn't enough angular momentum in the system for it to have happened. Instead, Luna had to be captured, drifting in from outer space. That seemed OK, until the Apollo visits to the Moon in the 1960s; they then realised how very difficult it was to get into an orbit where capture took place, or to imagine a nearly-circular orbit resulting from capture; but also because a few key similarities were found, between earthly matter and Moon rock. So, instead, the 'accretion' theory developed whereby debris orbiting the Earth somehow congealed into Luna. But, debris impacting together would tend to slow down, and so drift nearer to Earth, whereas Luna is rather far away and gradually receding from us. So finally they have developed a big-impact model, BLAM! with some passing asteroid or whatever, and Luna somehow emerges. Pull the other one. 

Luna is far enough away from Earth not to be held within its gravity field, and this is paradoxical: other planets hold their satellites closer, bound firmly within the hold of their gravity pull, whereas Luna is always more strongly pulled by the Sun than by Earth. For this reason astronomers properly call it a 'companion planet' rather than a satellite. Also, Luna orbits in a plane all of its own, differing from any other in the solar system, tilted at five degrees to the ecliptic. If Luna properly 'belonged' to the Earth, i.e. had spun off from it, one would expect it to orbit in Earth's equatorial plane.

As the Moon moves from its furthest to its nearest approach each month, from apogee to perigee, it draws about 12% nearer to the Earth, and this causes the tides to grow, on average, thirty percent larger.  We can here sense the delicate balance involved in the Moon's position, for, were it just several percent closer to us, huge areas of land would regularly become flooded. The Moon meets the Sun twelve times in one year, giving this all‑important number for the division of the circle: twelve divisions of thirty (days/degrees) express a kind of 'ideal' structure here, while the figures average out at twelve and a third lunar months of 29.5 days each. Were it a mere few percent closer to Earth, there would be 13 months in most years leading to an unimaginably different mathematics. Once again, we may feel the subtle balance whereby Luna's orbit is, as it were, just right.

Now and then, glows light up on the lunar surface. They may spread across a crater floor: red or purple, or sometimes brilliant white for a moment, and teams of astronomers patiently log them as they shimmer across its surface. (2) One is short of an explanation for these, as Luna is supposed to have been volcanically dead for aeons. The glows often occur, as Patrick Moore helpfully observed, on the shores of lava seas.

After the Apollo missions, we were assured that moon-rock was bone-dry, and even that all moon-rock was un-hydrated, i.e. there had been no water in its chemistry. Even pure iron was found, non-oxidised, which can never happen on Earth. Then, later on, water-vapour clouds were detected over its surface, and how did they get there? Ice was then found at its poles and future missions may use this as a source of oxygen and water (3). So, like most things about our Moon, the theory is rather paradoxical.

Synchrony of the Saros:

The Saros Cycle is quite mysterious, because, as with the Metonic cycle, there is no reason why it should exist. We can view it as an ultra-high precision coincidence. It is the key to the pattern of eclipses between Sun and Moon. Solar eclipses wind themselves in long chains around the Earth, their basic link being the Saros of 18 years, 10 or 11 and one-third days.

Several cycles have to come together for a repetition of a similar eclipse.  The phase of the Moon has to be the same, either full or new, making the Saros an integer number of lunar cycles. The lunar nodes have to coincide with the phase, to fulfil the primary condition for an eclipse to happen, which is the alignment of the phase and node cycles.

Above: Eclipse tracks over one Saros cycle of 18 years. The 12 eclipses whose paths of totality are shown belong to one family, determined by the law of Saros.  The displacement in latitude and longitude can be clearly seen.

To have an eclipse which looks the same, the Moon must be the same distance away from Earth: if it's further from Earth ‑ near apogee ‑ it will appear smaller in relation to the Sun, and won't cover the whole solar disc. So the phase of the apogee/perigee cycle has to remain the same.  The Sun also changes its apparent size  with the season of the year, because in summer and winter it's further or nearer as Earth goes round it in an ellipse.  It would seem, then, that there are four cycles which have to come together to get the same eclipse happening again.  How often would these four cycles come together, the three monthly cycles and one yearly?  Thousands of years, maybe?   It turns out to be only eighteen years, which is most odd, and it works at six-figure accuracy.

Synchrony of the Saros cycle:

Phase (Synodic) cycle:   29.5306 x 223 = 6585.32 days =18 years, 11 1/3 days

Nodal (draconic) cycle:   27.2122 x 242 = 6585.35 days =18 years, 11 1/3 days

'Apogee‑perigee' cycle:   27.5545 x 239 = 6585.52 days =18 years, 11 1/2 days

The sidereal cycle also recurs approximately, so that links in a Saros-chain move only ten degrees along the zodiac, each eclipse. The Saros pattern of eclipses moves one-third around the world each time, because of the extra third of a day; and so the eclipses will tend to reappear at a similar geographic position, even three of them ‑ that is, 54 years.

There are two other 18‑19 year cycles, the Metonic cycle and the node (or, 'nutation') cycle.  The Metonic cycle computes the calendar, i.e. says where the Full Moons fall each year.  It happens that the lunar period of 29.5 days goes very exactly into 19 years: in that period it comes back to the same position. The Saros and Metonic cycles are not lunar cycles as such, whereas the lunar-node rotation period (called, 'nutation') is a true lunar cycle.  In 18.6 years the axis of the nodes move once around the zodiac, and this gives the eclipse seasons of the year as it moves through the four seasons. These are presently (2005) in April and October, when eclipses happen.

The Metonic cycle chimes on the 19th, 38th, 57th etc. birthdays, when the Sun and Moon will stand at the very same degrees as when you were born, and also in the same houses. The Jewish calendar is based on this, counting through nineteen years; twelve years as 'normal' with twelve lunar months, plus seven with the extra lunar month added in, to make a thirteen-month year. Thus, we can say that there are 12 7/19 lunar months per solar year.

(1)   - A Theloar et al., Variation of the Human Menstrual Cycle through Reproductive life Int Jnl fert 1967 12 p77

(2) - This project was conducted by the Lunar Section of the British Astronomical Association.

(3) :- http://nssdc.gsfc.nasa.gov/planetary/ice/ice_moon.html

As well as water being totally absent from the Moon-rock samples, low boiling-point elements such as sodium and potassium were also depleted from Moon-rocks, while high melting point metals were more abundant. More recently water has been found around the Moon's south pole, a realm in permanent shadow which never gets sunlight. This has given new hope to the dream of a colony on the Moon.

Earth has a mean diameter of 7,920 miles, the Moon 2,160 miles (radius 1,080 miles). Start by drawing a horizontal line length 4. With compasses and ruler divide the line in half and then half the halves; now a vertical length of 3 can be swung up and so a 3-4-5 triangle made. From here progress as shown in the top part of the diagram. Circles representing the Earth and the Moon can now be drawn with over 99.9% accuracy. The circle represents Heaven, the square represents Earth. With π as 22/7 a heavenly circle passing through the centre of the Moon has a circumference of 44 - the same length as the perimeter of the earthly square around Earth. Thus the Earth squares the circle of Moon.