by tonytran2015 (Melbourne, Australia)
This is the final part on using the Moon for finding direction and time. The surface features of the Moon can be used as a compass rose for Earth inhabitants.
Step 1: A Natural, Upside Down Natural Compass Rose
Near to full Moon the phase (waxing-waning) and horn-line methods are not accurate. Right at full moon they are not applicable. However at those times we may obtain directional information from the global map of the Moon using the colour and shade of its surface (soil) features. Since moonlight is only reflected light from the Sun and is not intense and we may look at the Moon's surface for the features.
We have to identify the features of the Moon associated with Lunar own rotational poles, so that the Moon can be placed and aligned on an upside down compass rose aligned for the rotation of the Earth.
Each of us may have have different individual visualization (or a simplified picture) of the Moon to orientate its poles on such compass rose. My own visualization for the shades on the Moon is a small lion licking the face of a kneeling monkey and it is drawn on the Moon in the title figure.
Step 2: An Oscillating Core for a Compass Rose.
Figures: The Moon appears to oscillate with a period of 27.3 days.
Consider that compass rose an UNDERNEATH view of a normal compass rose and you can use it for finding directions when it is high in the sky. (The leading side of the Moon, with a lion visualization, is on our West and its trailing side, with a monkey visualization, East). However the North of the Moon is the North pole of Lunar rotation axis and it makes an angle with the axis of the Earth, the angle sometimes reaches 23.5 + 1.5 = 25 degrees. Imagine that you can walk on the Celestial equatorial plane and the Lunar axis is planted on it at an angle of 90-25 degrees and you go around it once every 27.3 days.
Looking at that inclined Lunar axis, you will see that axis alternatingly tilted to your right hand then to your left hand. Looking from the earth, the axis of the Moon appears to oscillate clockwise and anti-clockwise (with amplitude equal to the lunar orbit angle, which requires complex calculations, and can be up to up to 25 degrees ) as the Moon orbits around the Earth. This compass rose only gives correct orientation when the Moon is made oscillating inside it ! The North of the Moon is aligned to 0 degree only when the Moon goes through its maximum or minimum value of Lunar declination (at furthest distance to the Celestial equator). When the Moon crosses the Celestial equator, the angle between Moon axis and Celestial axis is highest in absolute value..
So we have a natural compass rose but we must remember that Moonscape features does not easily give accurate direction and the Moon oscillate inside our Earth aligned compass rose between up to +25 and -25 degrees as well as tilling its poles toward or away from us. The title figure of this article is made for the reference, mean orientation of the Moon, when its axis is at right angle to the line of view and its equator is aligned to 90-270 degree marks of the graduation ring. Users intending to use the compass rose on any full Moon should check the orientation of the surface features against the East West directions (given by Waxing-Waning rule and by adjusted horn line method) two or three nights prior to the full Moon. Otherwise an uncertainty of up to 25 degrees should be allowed with this compass rose.
Step 3: Lunar Navigation Requires a Combination of Methods
Figure 1: Moon phase chart for a Solar declination of (-20) deg (South). Figure 2&3: Panoramic view of the travel of the Moon.
Navigating by the Moon becomes easier when we do it nightly on consecutive nights and keep records from previous nights. At half-Moon times we can use the Waxing-Waning rule and my improved horn-line method (given in p2) to draw the Celestial axis line on the Moon then record the position of the horn-line on the featured surface. At full Moon times we use Lunar surface features with the angle for the Moon obtained previously from the 3/4 Moon nights.We have to remember that the horn-line rotates almost steadily about each full-Moon.
Alternatively, the if we form the habit (when we have to navigate) of daily recording the direct measurements of Lunar declination, from the Moon and the Celestial pole (by either stars at night or the Sun before Sunset), we have accurate values of Lunar declination. The Moon and its declination can then replace the Sun in my method of determining direction and time (reference ). The accuracy is further improved if we combine the knowledge of our latitude, the phase and elevation angle of the Moon to predict its trajectory for the night (therefore we already have had an initial estimation of the North-South direction).
After the North-South direction has been found it is easy to tell time from a full Moon as the Moon is trailing the Sun by about 12 hours.The estimation is more accurate if we apply extrapolation to our own records of Moon rises and Moon sets on previous nights. When there is no Moon, we have to use stars and that will open new topics.
With lots of switchings among methods, the navigators may find that finding direction and time via the hidden Sun as given in reference  the simplest.
. tonytran2015, Finding North direction and time from the Moon, Instructables,
https://www.instructables.com/id/Finding-North-dire... posted on Jun 9, 2015.
. tonytran2015, Finding North direction and time from the Moon, p2: using the horn line, Instructables,
https://www.instructables.com/id/Finding-North-dire... posted on Jul , 2015
. tonytran2015, Finding North direction and time from the Sun using bare hands, Instructables, https://www.instructables.com/id/Find-North-direct... posted on 2015 may29.