Finding North direction and time accurately from the horn line of the Moon.

Finding North direction and time accurately from the horn line of the Moon.

by tonytran2015 (Melbourne, Australia).

Click here for a full, up to date ORIGINAL ARTICLE and to help fighting the stealing of readers’ traffic.

 

#find North, #finding North, #direction, #time, #Sun, #hidden Sun, #navigation, #survival, #Moon, #phase, #horn line, #half Moon,
Here I add two more steps to the common horn line method for the Moon to obtain more accurate North direction and time from its horn line. The modified method uses position of the Moon, shape (phase) of the Moon, solar declination and user’s latitude to work out North direction and rough local time.

1. Basic information on the Moon for navigation.

mooncrescent.jpg

moonshapesnangles4c.jpg

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. From the shape of the Moon, it is easy to say how late the Moon is trailing the Sun (new Moon trails by 0 degree and 0 hour, new half-Moon by 90 degree and 6 hours, full-Moon by 180 degrees and 12 hours, and late half-Moon by 270 degrees and 18 hours .). The shape and the position of the Moon allow some guessing of its trajectory for the night.

The Moon completes its orbit in space in 27.321 days, and it completes one full revolution on the Celestial sphere in that time. Its angular velocity on that sphere is 1/27.321 (rev/day) = 0.036601 (rev/day) .

The Sun apparent travel on the ecliptic takes 365.256 days. Its angular velocity on the elliptic is 1/365.256 (rev/day). The Moon revolves on the Celestial sphere faster than the Sun by an angular velocity of 1/((1/27.321)-(1/365.256)) = 1/29.530 (rev/day). When the Sun is one full turn ahead of it, the Moon will catch up, and they will be both in the same direction again on the Celestial sphere after a period of about 29.530 days. So the intervals between consecutive full Moons will be something like a pattern of (30days, 29days).

By keeping records of previous full Moon nights people know it is a WAXING or WANING Moon.

The simple Waxing-Waning rule is that the bright side of the Moon is on the West for waxing and East for waning Moon.

It is natural for people to desire to use the horn line, which is the line connecting the two horns of the Moon, to draw the North South direction. However it has been found that the intersection between the horn line and the horizon does not accurately give the North direction.

Here we find out the reasons for that inaccuracy and show a more accurate method of using Moon’s horn-line.

It may be easier for some readers to first read step 5 then come back to read steps 2, 3 and 4.

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

2. Estimating the current solar declination

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Estimating the current declination.

The whole Celestial spherical shell rotates around its two Celestial poles. The Sun moves slowly on that sphere on a great circle called the ecliptic. Its distance to the two opposite Celestial poles varies periodically, and its distance to the Celestial equator is call the declination of the Sun.

You can make a rough sketch of this declination from the principal values and estimate the declination for the current day.

3. The horn line is not easily transformed to the ground meridian line.

image

Figure: Panoramic view of the travel of a partial Moon in the sky. The Celestial axis is always at right angle to the path. This picture is for the winter, with the Sun in the other hemisphere and the bright side of the Moon tilts toward the ground. In the summer, it tilts toward the sky.

The horn line is at right angle to the plane containing the very slender triangle formed by the Earth, the Moon and the Sun but the Celestial axis is at angle of (90-23.5) degrees to that plane. So the horn line usually form an angle of that size to the Celestial axis.

Near to half-moons the horn line is easily defined, and it is also easy to see that the projection of the Celestial axis onto the half-moon makes with it an angle equal to solar declination.

On top of those complication, the Moon also has its own declination and an observer has additional difficulty working out the direction of the horn line as it is usually not at right angle to his line of view.

4. Twisting the horns of the partial Moon.

MoonShapesNAngles5C

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

At half Moon, it is possible to twist the horn line about the line of view to generate a line KL parallel to the Celestial axis. The amount of twisting is opposite to the declination angle of the Sun.
Similarly, when the angle Sun-Moon-Earth is about 90°+/-30° (=120° or 60°) the amount of required twisting is about 0.85*declination of the Sun.

The required twisting is varied with the phase of the Moon as in the following:

Half Moon requires twisting by full Solar declination,

15% or 85% bright area requires twisting by half Solar declination,

full or no-Moon requires no twisting.

Remember that if the Sun is into your hemisphere (in your summer) the bright side of the half Moon has to be twisted downwards (toward the Celestial equator) by an angle equal to the solar declination angle. The opposite should be done in your winter.

This correction here already causes a difference between the results from the old horn line method and the current method. There will be another difference caused by drawing the “spear line” parallel to Celestial axis in the next section.

Note:

The required twisting on the horns of the Moon varies sinusoidally with time and peaks to the values of minus/plus Solar declination when the Moon is half-full.

5. Finding North direction from a Celestial North South line seen on the Moon.

image

Observing a Celestial axis KML drawn on the Moon: U is observer, E center of the Earth, N terrestrial North pole, S terrestrial South pole, M Moon, UV local vertical, KL a line parallel to Celestial axis, EQ normal to plane UKL, UP a line parallel to Celestial axis. The red circle through U is the intersection between the plane UKL and the Earth’s surface.

Suppose that there is on the Moon M a line KL parallel to the Celestial axis, as illustrated in the figure. We draw a plane through the observer containing the line KL. On that plane UKL draw a line PU nearly in the direction of KL, descending into the ground at latitude angle.That is

(|angle /(PU,KL)| <90° ) and (angle /VUP = 90 deg. – latitude angle).

The line UP is then parallel to the Celestial axis, and its projection on the ground gives the local North South (meridian) direction.

When the Moon is high in the sky and the plane UKL is steeply inclined to the local horizontal, the last condition is the satisfied by

( angle /MUV < angle /MUP ) and (angle /VUP = 90 deg. – latitude angle).

The line UP is then parallel to the Celestial axis, and its projection on the ground gives the local North South (meridian) direction.

For Southern latitudes draw UP’ close to the direction of LK (PUP’ is a straight line).

6. On the ground view of the horn line method.

image

Figure: Finding out North direction more accurately using horn line.

On half-Moon nights, when the angle Sun-Moon-Earth is 90°, twist the horn line by the declination of the Sun to generate on the Moon the line KL parallel to the Celestial axis, and similarly, when the angle Sun-Moon-Earth is about 90°+/-30° (=120° or 60°) the amount of required twisting is about 0.85*declination of the Sun.

When properly carried out, the plane UKL always makes with the horizontal plane an angle not less than the latitude angle. The line KL is the observer’s view of the Celestial axis. All lines co-planar to UKL generate the same view to the observer! Draw a “spear line” PU co-planar to UKL and spearing the ground at an angle equal to latitude angle. The spear line PU so obtained is then pointing exactly along the Celestial axis, towards the lower Celestial pole. The projection of PU onto the ground gives the terrestrial North-South line. North direction is then found.

When the Moon is high in the sky and the plane UKL is steeply inclined to the local horizontal, the lower end U of the spear line is nearer to the line KL than its upper end P.

Note:

The intersection line between the plane PKL and the ground surface is generally NOT in the North-South direction unless the observer is on the terrestrial equator circle. The drawing of the spear line PU cannot be by-passed in this method.

7. Summary of steps in this method.

moonsungreatcircle.jpg

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MoonShapesNAngles5C

wpid-wp-1439376905855.jpeg

To apply this method, the navigator has to go through all the following steps:

a. Working out the ROUGH (+/- 45 degrees) principal North-Sout-East-West directions, from the Waxing-Waning rule and the knowledge that the horn line direction is being close to an RA arc,

b. Estimating the Solar declination for the current time of the year,

c. Working out the proportion of Solar declination used for twisting the horns of the Moon from the Moon phase,

d. Twisting the horns of the Moon by the required angle and waving a stretched arm along the adjusted horn line to establish the plane through the Earth, Moon containing the direction of the Celestial axis,

e. Drawing a spear line inside that plane, inclined by latitude angle, aligned roughly to the ROUGH direction of the lower Celestial pole to establish its exact direction, and

f. Projecting the Celestial axis onto the ground surface to obtain the terrestrial North-South direction.

New users to this method should initially only use it as a double check for another method using the position of the hidden Sun, given earlier as part 1, in a previous Instructables article [2]. The agreement between the two methods would make users confident on their results.

8. Avoiding hasty and perilous conclusions when using the horn line.

image

Figure: A rare (or not so rare?) failure of the simplistic, traditional horn line method. The horn line intercepts the horizon near to the terrestrial North (wrong by 180 degrees!) in a place in Northern hemisphere. The traditional horn line rule really requires amendments.

At latitude less than 28 degrees, the horn line may point to Northern skyline at high Moon although most of the times it points to Southern skyline ! There is a peril of being sent astray by 180 degrees for unreserved navigators.

At high Moon the horn line only gives North South direction near to equinox times ! The error can be due East or West by the declination value of the Sun.

If the steps for using this method seem to be too complex, the Moon navigators may have to accept reduced accuracy from the Moon and use only Waxing-Waning rule in combination with the stars to navigate !

There is a third part to this topic, with the title “Finding North direction and time using the Moon p3- Moon surface features”.

Conclusions:

It is possible to work out accurately North direction from the horn line of the Moon.

The twisting of the horn line and the drawing of the spear line PU are two additional steps of this modified method.

References

[1]. Tristan Gooley, How to navigate using the Moon, the natural navigator,
http://www.naturalnavigator.com/find-your-way-using/moon, accessed 2015aug12

[2]. 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

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Finding North and time by stars. Posted on August 28, 2015

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

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

by tonytran2015 (Melbourne, Australia).

Click here for a full, up to date ORIGINAL ARTICLE and to help fighting the stealing of readers’ traffic.

(Blog No.006).

#find North, #finding North, #compass, #direction, #time, #Sun, #hidden Sun, #navigation, #survival, #Moon, #phase,

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.

image

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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 fasting 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

image

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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.

image

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divider43.jpg

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 gives 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.

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Navigating with an AM MW radio receiver, posted January 17, 2017, The Scorpius constellation, posted January 8, 2017, The Orion constellation., posted December 26, 2016, Rice as emergency food., Using GPS in off-grid situations, Slide Sky-Disks with grid masks showing azimuths and altitudes, Slide Sky-Map for displaying tropical stars.
, posted on 2018 July 10

Find North By Fingers

Finding North direction and time accurately from the horn line of the Moon. posted on August 12, 2015. This is my novel technique.

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Finding North direction and time using the Moon surface features. Posted on July 1, 2015.

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, posted on

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Finding North direction and time using the Moon surface features

Finding North direction and time using the Moon surface features.

by tonytran2015 (Melbourne, Australia).

Click here for a full, up to date ORIGINAL ARTICLE and to help fighting the stealing of readers’ traffic.

#find North, #finding North, #compass, #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.

MoonShapesNAngles5C

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

tiltedhornlinec2.jpg

Figure 2: Panoramic view of the travel of the Moon.

MoonRosePath
Figure 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, 2017, The Scorpius constellation, posted January 8, 2017, The Orion constellation., posted December 26, 2016, Rice as emergency food., Using GPS in off-grid situations, Slide Sky-Disks with grid masks showing azimuths and altitudes, Slide 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).

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