Finding North direction and time using the hidden Sun via the Moon

by tonytran2015 (Melbourne, Australia)

Finding North direction from the Moon cannot not be as accurate as from the Sun. There are many causes for this:
1/- The Moon does not always rise on the principal East (at 90 degree of the compass rose).
2/- We cannot work out by heart the Moon’s declination (up to +/- 5.1 degrees to the ecliptic, and 23.5+5.1 degrees to the Celestial equator ).
3/- We cannot easily work out when the Moon reaches its highest elevation angle at its meridian time. The Moon does not often cast strong shadows for shadow sticks to work.
Here I describe my new method to find out North direction and time with improved accuracy. The method uses shape and position of the Moon, solar declination and user latitude to work out the position of the hidden Sun, then work out North direction and approximate local time with an accuracy of 30 minutes. Literally, the user can work out North direction and the local time with his bare hands.
I have field tested this method and I have relied on it for many years.

1. Basic information on the Moon for navigation.

 

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Figure 1: Moon phase chart. Figure 2: A crescent Moon may not align itself to the terrestrial East or West horizon points (see texts).

The Moon is a satellite of the earth. Everyday Moon-rise and Moon-set time is retarded by about 50 minutes. This allows the Sun to travel further on its journey every subsequent night. Therefore after full moon the partial bright side stays on the East (trailing) side and dark crescent appears on the West and dark area gets fatter daily until the whole moon is dark. Similarly, from new Moon a bright crescent appears on the West and grows fatter and bright area gets fatter daily until full Moon is reached. However the bright and dark sides of a partial Moon rarely point accurately to East or West directions.

Figure 2 of this section shows a crescent Moon on the Celestial sphere. The horizontal great circle represents the horizon of the observer. The inclined great circle represent the Celestial equator and the arrow through the center of the sphere represents the Celestial axis. The circle parallel to the Celestial equator is a constant declination circle being the trajectory of the Moon during the hours. The two intersection points of the two great circles are the terrestrial East and West points of the horizon. This picture shows that the crescent Moon may point its bright to dark line far away from the terrestrial East or West points when there is a combination of high declinations of both the Moon and the Sun on the same side of the Celestial equator.

Each Lunar (Moon) cycle begins with the Moon being visible as a thin bright arc in the sky (called a New Moon), trailing the Sun by less than one hour. After Sunset this thin Moon is seen bright on the West until it sets. On subsequent days, the Moon is more and more behind the Sun, its position shifts gradually towards the East and the Moon remains for longer and longer duration in the night sky till full Moon day. After full Moon day, the Moon (now called a Late Moon) becomes thinner and thinner and is seen risen in the East in the night, it remains visible in the sky after Sunrise, and travels ahead of the Sun. On subsequent days, its lead on the Sun gradually reduces. Near the end of the cycle, the Moon is visible as only a thin bright arc rising in the East for less than one hour before Sunrise and after Sunrise it can still be seen leading the Sun by that same amount of time. At the end of the Lunar cycle, the Moon sends no reflection of Sunlight to Earth and is too close to the Sun to be visible in the day sky.

Keeping diaries of past days of full and new Moon helps people know where their time is in the current cycle, and so they know whether the leading (West) side of the Moon should be bright (new to full Moon) or dark (full to new Moon). Fortunately, the users of my method described here do not have to refer to any such records of the Moon.

It is interesting to note that Buddhist East Asians use lunar calendars and observe fastings at new and full Moon. From their calendar and their fasting festivals , they already know whether the Moon is waxing or waning. This may help explaining why they are good at finding North direction using the Moon.

CAUTION 1: The bright to dark line of the partial Moon can point far away from the terrestrial principal East or West directions.

CAUTION 2: The horn line of the partial Moon can point far away from the terrestrial principal North or South directions.

 

 

2. Moon shapes giving Moon-Earth-Sun alignment.

The various shapes of the Moon under various angles of lighting by the Sun are given in the illustration picture. The Moon goes through this cycle every 29.5 days. The picture is drawn for the principal values of the angle of Moon-Earth-Sun. The picture allows determination of the direction of the Sun from the shape of the Moon.
The angle Moon-Earth-Sun will be more accurately known if the navigator is in the habit of directly measuring and recording it before Sunset (few hours earlier) whenever the Moon is seen during day light.

3: Direction of the Sun from the Moon

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The line joining the two horns of the Moon is always at right angle to the plane of Sun, Earth and the Moon. Draw a half-line from you to the Moon and extending far past the Moon. Imagine the Sun is at the far end of this half-line. Swing this half-line in the direction of the bright side (at right angle to the line joining the two horns) of the Moon to have the angle of Moon, Earth and Sun giving a matching shape for the brightened part of the Moon. The half-line then gives the direction of the Sun.
Alternatively, you can think of placing a sphere between you and the Moon, and a torch is is used to shine on the sphere and the torch is placed in various directions until it gives a partially brightened sphere similar to the current Moon shape.

4. Finding North direction and time.

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With the direction of the Sun known, the technique given by my previous blogpost “Finding North direction and time using the Sun and a divider” [1] can be applied to find North direction and local time.
The selection rule of right or left hand placement of CA in “Finding North direction and time ising the Sun and a divider” has been generalized.

The generalization is:
(Northern latitudes with rising Sun or Southern lat. with setting Sun) ==> CA on the left of CB,
(Northern latitudes with setting Sun or Southern lat. with rising Sun) ==> CA on the right of CB.
The time for rising Sun here is from 0hr to 12hr (AM) and time for setting Sun here is from 12hr to 24hr (PM).
The rest of that method applies to the hidden Sun to give North direction as well as time.

I have tested and found that this method goves direction accurately and easily. The additional benefit is that it also gives approximate time.

Reference
[1]. tonytran2015, Finding North direction and time using the Sun and a divider, http://www.survivaltricks.wordpress.com/, 06 May 2015.

PREVIOUS SURVIVAL blogs

Navigating with an AM MW radio receiver, posted January 17, 2017The Scorpius constellation, posted January 8, 2017, The Orion constellation., posted December 26, 2016, Rice as emergency food.Using GPS in off-grid situationsSlide Sky-Disks with grid masks showing azimuths and altitudesSlide Sky-Map for displaying tropical stars.

Click here for my other blogs on  divider43.jpgSURVIVAL

Click here for my other blogs on  divider43.jpgSURVIVAL

Click here go to Divider63D400 Home Page (Navigation-Survival-How To-Money).

 

Finding North direction and time using the Moon surface features

by tonytran2015 (Melbourne, Australia)

#find North, #direction, #time, #Moon, #surface features, #natural compass rose, #navigation, #survival

This article shows how to use the Moon for finding direction and time.
The surface features of the Moon can be used as a compass rose for Earth inhabitants.

1. An 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.

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Figure: The surface features of the Moon is used as the core of a compass rose.

2. An oscillating core of the compass rose !

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Figure 1: Moon as an oscillating core of a compass rose.

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Figure 2: Moon as an oscillating core of a compass rose.

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Figure 3: Moon as an oscillating core of a compass rose.

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 alternately 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.

3. Lunar navigation needs a combination of methods.

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Figure 1: Moon phase chart for a Solar declination of (-20) deg (South).

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Figure 2: Panoramic view of the travel of the Moon. MoonRosePathFigure 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 [3]). 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 [1] the simplest.

 

References

[1]. tonytran2015, Finding North direction and time using the hidden Sun via the Moon,https://survivaltricks.wordpress.com/2015/07/06/finding-north-direction-and-time-using-the-hidden-sun-via-the-moon/, posted on July 6, 2015

[2]. tonytran2015, Finding North direction and time accurately from the horn line of the Moon. https://survivaltricks.wordpress.com/category/moon-horn-line/
posted on August 12, 2015

[3]. tonytran2015, Finding North direction and time using the Sun and a divider, http://www.survivaltricks.wordpress.com/, 06 May 2015.

 

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Navigating with an AM MW radio receiver, posted January 17, 2017The Scorpius constellation, posted January 8, 2017, The Orion constellation., posted December 26, 2016, Rice as emergency food.Using GPS in off-grid situationsSlide Sky-Disks with grid masks showing azimuths and altitudesSlide Sky-Map for displaying tropical stars.

Click here for my other blogs on  divider43.jpgSURVIVAL

Click here go to Divider63D400 Home Page (Navigation-Survival-How To-Money).