Glossary X
At a lunar backsight where permanent or temporary ancillary extrapolation gear has been set up there should be a length preserved between major stones which is the 4G for this site. This 4G represents, on the ground, the lateral distance an observer must move in order to 'shift' the Moon through the declination range K. K is the change in the Moon´s position during the 24 hours preceding a standstill. At a Major Standstill it is 46.5 arc minutes and at a Minor Standstill 30 arc minutes. See also- K, ANGULAR DISPLACEMENT, EXTRAPOLATION PROCEDURE, LUNAR STANDSTILL.

Megalithic Lunar Astronomy

Alexander Thom amassed a great deal of hard evidence for the existence of a megalithic calendar of 16 'months' or intervals. This evidence was astronomically gained from careful surveys of many sites. During this experience his attention had been drawn to a number of major stone settings which appeared to indicate the rising or setting points of the Moon at it's furthest extremes. The Moon reaches it's monthly declination extremes,- furthest north and furthest south- two weeks apart, with one complete cycle every month. The Sun takes six months to travel between it's extremes, the solstices and twelve months to complete one cycle.

Lunar Standstills

The Sun is regular in it's cycle. The position of the solstices changes very slowly. In 4000 years these have moved less than half a degree of declination,- 27 arc minutes.

		Lunar_Standstills
The four limiting positions of the lunar orbit.
The Moon however has more complicated extreme positions. The extremes themselves are moving up and down the horizon with a semi- period of 9.3 years and a complete cycle of 18.6 years. Thus there are two limiting declinations for the lunar extremes. These are termed Major and Minor Standstill positions. It takes 9.3 years to move from one to the other. The explanation for this movement is that the entire orbit of the Moon is precessing slowly with a period of 18.6 years. As the lunar orbit is inclined at an angle of more than 5 degrees to the plane of the Earth's orbit we see the Moon move through twice this declination shift from major to minor standstill positions. In 1800 B.C. the declination of the Moon at a Major Standstill was close to 29 degrees whilst the declination for a Minor Standstill 9.3 years later would be near 19 degrees.

		Standstills_horizon
The four limiting positions of the lunar orbit as seen on the eastern horizon.
It is only at these times the megalithic astronomers could resolve and differentiate the several small libations in the lunar orbit

Observing limitations of horizon astronomy

With the equipment available to Bronze Age astronomers it would be impossible to accurately measure the position of the Moon in it's orbit at any point other than the standstills. This is due partly to the high rate of change in declination over 24 hours but also to the problems raised by several minor discrepancies in the regularity of the orbit. None of these minor cycles can be sorted out and quantified at any other time than at a Lunar Standstill


Stake setting at a lunar extreme


		Stake_setting
The Moon is 'brought down' on the same foresight on three consecutive nights and stakes placed- M for Monday, T for Tuesday and W for Wednesday. If the observer also takes a step backwards each night the resultant stake settings will describe a parabolic curve. Here can be applied the knowledge of the properties of sagitta/arc/chord to this curve to refine the observation and locate the exact standstill position and time in retrospect.
Management of the simple phenomenon of parallax is the basis of quantifying movement of a celestial object when rising and setting on the horizon.
A distant object- the Moon- will appear to move in the same direction as a mobile observer with relevence to an object in the foreground- the horizon. The relationship is strict but in proportion to the length of the alignment to the foresight on the horizon.
For an alignment length of 8.8 kms an oberver may 'move' the Moon across a horizon mark by it's own diameter-half a degree-with a step-aside progression of about 224 metres.
For an alignment of 29 kms the step-aside needed to make an angular displacement of the Moon of half a degree will be nearer 800 metres.


Observing limitations of horizon astronomy


		Fig.1.1
Megalithic Lunar Observatories p.14. Fig.1.1
By stepping-aside the observer can bring the Moon down on the same foresight each night and set a new stake. When the extreme has past there will be a curve of stakes upon which extrapolation methods can be employed to calculate, in retrospect, when the extreme had occurred.
A.Thom. Preface: megalithic lunar observatories 1971.
"It was only natural that a people looking critically at the setting Sun would use the same observing method on the Moon. But here they found a much more complicated motion. They would see that it was only at the standstills that anything like repeatable results could be obtained. But the rapidity with which the Moon passes through the monthly declination maximum set them a serious problem, namely that of extrapolation. Did they solve this problem by first making it geometrical? If they tried the effect of stepping back each night as shown in Fig. 1.1 they would have been able to apply their knowledge of the geometry of the flat arc. We know how much time they must have spent on the problem at numerous observatories throughout the country, and it would be strange indeed if they had not somewhere tried out this method of avoiding confusion as the stake position moved first one way and then the other. This method would show the constancy of what we have called the sagitta (G), and would have led to the method of finding G at any site with sufficient clear ground."


Angular displacement by step-aside

The moving stake positions Thom refers to are the nightly setting of markers which are the positions an observer had to adopt in order to view the Moon rising/setting on the same foresight as the night previously. By the simple phenomenon of parallax these stake positions would assume a line along the ground. If, as Thom thinks likely, a step backwards was taken each night, then the line must describe a parabolic curve which would be a true representation of the path of the Moon at the turn around of it's orbital extreme.