Good approximation to solar declination by a watch face

Good approximation to solar declination by a watch face

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.53).

#solar declination, #watch face, #multi-dial watch face, #Solar navigation, #find North, #time, #survival.

The value of solar declination is needed for accurate determination of North direction and time using a divider or a watch (references [1], [2]). Good approximation to solar declination is required by the methods to produce accurate results in cold temperate zone and arctic zone. The required value of solar declination can be simply obtained using only a watch face or even the drawing of a watch face on the ground.

1. Method

solar-declination-by-a-watch-face

Figure: Determining solar declination using a watch face. (The lines SOLAR DECLINATION Its rough estimate is required for Fine Alignment of the watch are to be ignored.)

Draw the dial of an upside-down watch face as a small sub-dial of a watch face (on its 3 o’clock side) as in the figure. The radius of the sub-dial should be close to the length of 4 minutes markings on the rim of the main dial.

The four numbers 6, 9, 12, 3 on the rim of the upside-down sub-dial correspond to 21/6, 23/9, 21/12, 21/3 respectively. They are the dates on the calendar. Your current date gives a point on the rim of this sub-dial.

Project the point of your current date horizontally onto the rim of the main dial. The angle from the direction of 3 o’clock to that of a main long hand pointing to the projected point is equal to the angle of solar declination.

The angles from the Northern and Southern Celestial poles to the Sun are just the angles from the 12 o’clock and 6 o’clock directions respectively to that of the above main long hand.

2. Applications to survival situations

Most multi-dial watches and chronograph watches already have sub-dials made with the sub-dial radius being close to 4 minute length on the rim of the main dial. This method can be conveniently applied to any such watches having their sub-dials on either the 3 o’clock or 9 o’clock side.

When having no actual watch face, you can draw a watch dial and a sub-dial on the ground to determine solar declination.

Accurate value of solar declination improves the accuracy of the determination of North direction using a divider or a watch (references [1], [2]) when the Sun has low altitude in the cold temperate and arctic zones.

References:

[1]. tonytran2015, Finding directions and time using the Sun and a divider., Additional survival tricks, survivaltricks.wordpress.com, https://survivaltricks.wordpress.com/2015/05/06/finding-directions-and-time-using-the-sun-and-a-dividing-compass/, posted on May 6, 2015.

[2]. tonytran2015, Finding accurate directions using a watch, Additional survival tricks, survivaltricks.wordpress.com, https://survivaltricks.wordpress.com/2015/05/19/finding-accurate-directions-using-a-watch/, posted on May 19, 2015.

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Simple determination of East Asia lunisolar New Year

Simple determination of East Asia lunisolar New Year

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.49).

#East Asia New Year, #lunar New Year, #lunar leap year, #lunar leap month, #lunisolar calendar, #Vietnamese New Year, #lunar calendar.

When traveling to or working with East Asia countries Westerners are sometimes puzzled by their Calendar and long New Year festivals which vary from year to year on the Western Calendar.

This blog gives simple explanation to Westerners the rules of East Asia Lunisolar calendar which is based on Celestial observations and has been designed to give season information to users.

To easily understand this article, readers are advised to first read the simple summary on stars in the sky [1] to know the declination, right ascension and the date of a star.

Simple calculations [2] shows that each lunar month is 29.530 days. Two lunar months has a length of 59.06 days. The lunisolar calendar used in China since ancient time has had Winter solstice falling on the 11th month of the year since more than 2000 years ago, since 113BC (Han Dynasty II p.38 [3]) .

The solstice point (the point from ecliptic most South of the celestial equator) is moving slowly in the sky and is currently opposite to 90 degree Right Ascension.

1. New Year time is just a convention.

A lunisolar year can be made to start at any of its seasonal point, the point can be in the Winter or in the Summer. It all comes to a matter of convention. For example, the Burmese lunisolar calendar has its New Years starting when the Sun enters the constellation Aries.

For East Asia lunisolar calendar making, there are two major alternatives for determining its New Years as in the following.

2. Simple rules.

MoonShapesNAngles5C

Figure 1: Phase of the Moon. A new Moon is the Moon with a thin white crescent on its leading edge (top right corner of the picture) which is first visible right after sunset on the Western horizon.

If the calendar makers want their people to have simple and clear rule on the start of a New Year, they can define the New Year starting on the Second New Moon after Winter Solstice day.

This would be easy for ordinary people and people in remote areas to work out their two last (11th and 12th) lunar months of the year, and have enough time to prepare for the New Year festival.

3. Precision rules with uniform determination of months.

polrnorthq2c30.jpg

Figure: Inversion map of the Northern Celestial 3/4-sphere. The non-concentric circle is the ecliptic and winter solstice is its most distant point from the North pole (on the left of the North pole).

The Eastern Asia lunisolar Calendar requires each of its lunar month has a characteristic star in the sky to match with the seasons. There are 12 chosen characteristic stars. A lunar year has either 12 lunar months (normal year) or 13 lunar months (leap year). Any lunar month not containing any of those 12 chosen characteristic stars is called a leap month and is named after its preceding month.

Each Lunar month begins with a New Moon and ends before the next New Moon.

If the Calendar Makers insist on astronomical precision with uniform determination of months then they can define each month having to contain a star at regular spacing of Right Ascension, that is 11th month having some star of 90 degree R.A. on the meridian line at midnight on one night of the month and so on [4], [5].

Therefore they would require that

11th month has a star of 90 degree R.A.,
12th month has a star of 120 degree R.A.,
1st month has a star of 150 degree R.A., (Regulus of Leo has 152.05° R.A., 12° decl.)
2nd month has a star of 180 degree R.A.,
3rd month has a star of 210 degree R.A.,
4th month has a star of 240 degree R.A., (Delta Scorpii has 240.22° R.A., –22.60° decl.)
5th month has a star of 270 degree R.A.,
6th month has a star of 300 degree R.A., (Altair of Aql has 297.7° R.A., 8.85° decl.)
7th month has a star of 330 degree R.A.,
8th month has a star of 0 degree R.A.,
9th month has a star of 30 degree R.A.,
10th month has a star of 60 degree R.A.,

any month that has no star in the above list is called a leap month bearing the same name as its preceding non-leap month. Therefore it is hard for ordinary people to know the beginning of the Year.

4. Most probable choice.

I would think that the ancient Calendar makers chose the first alternative rather than the more difficult second alternative.

The second alternative also has an additional complication that there is a precession of Equinox at a rate of 360 degree per(approximately) 25,920 years. In 2000 years the Winter Solstice has moved by 27.7 degrees (about one month). Chines Calendar Makers would have noticed it and saw the need for adjustment had they chosen the second alternative but I could not find any literature about that kind of adjustment.

It is most likely that Chinese Calendar Makers had chosen the first alternative. Their choice may have had influence on Calendar Makers of neighboring countries.

If East Asian Calendar Makers chose the easy rules of for determining New Year day then the 1st month of any East Asian New Year would contain a star that has a date of 18 February(= 21 December + 59.06 days), 59.06 days after Winter Solstice. That would come to a simple rule for star watchers (for the current configuration of Earth orbit):
The New Year starts on the second new moon after Winter Solstice day and the first lunar month of the lunisolar calendar should have a star of 18 February (= 21 December + 59.06 days) of Right Ascension of nearly 152 degrees (near to that of Regulus of Leo) on its meridian at midnight.

The second through to the tenth months of the lunisolar calendar have been anchored to seasons by requiring each to have a star chosen as specified in section 3. If bright stars of approximate Right Ascensions are chosen instead, there would only be more or less leap months repeating the name of the preceding months. The choice of bright stars of approximate Right Ascensions may also have been influenced by superstition and politics.

It is common to find references to Festivals of First Full Moons of the years (Tết Nguyên Tiêu) in ancient Chinese historical texts but it is not easy to find references to Festivals of First New Moons ( Tết Nguyên Đán) in those ancient texts.

References

[1]. tonytran2015, Finding North and time by stars ,survivaltricks.wordpress.com, https://survivaltricks.wordpress.com/2015/08/28/finding-north-and-time-by-stars/

[2]. tonytran2015, Finding North direction and time accurately from the horn line of the Moon, survivaltricks.wordpress.com, https://survivaltricks.wordpress.com/2015/08/12/finding-north-direction-and-time-accurately-from-the-horn-line-of-the-moon/

[3]. Sima Qian, Records of History by the grand historian (translated by Burton Watson), Qin Dynasty, Han Dynasty I (Rev. Ed.) and Han Dynasty II (Rev. Ed.), the Res. Cent. for Transl. The Chinese Univ. of Hon Kong and Colubia Univ. Press, Hong Kong and New York, 1961. Han Dynasty II p.38 showed that in 113BC, month 11 has the solstice.

[4]. Helmer Aslaksen, The Mathematics of the Chinese Calendar, http://www.math.nus.edu.sg/aslaksen/calendar/chinese.shtml, accessed 19 Jan 2017.
[5]. Ho Ngoc Duc, Thuat toan am lich (in Vietnamese), https://www.informatik.uni-leipzig.de/~duc/amlich/calrules.html, accessed 19 Jan 2017.

Added after 2018 April 06:

There are 24 nearly equally spaced, designated (by East Asian Astronomers) marker points on the Ecliptic called “Solar terms” in “Chinese English”. The position of the Sun relative to these markers tell its progress along the Ecliptic and the season in the year. Any leap month is inserted such that the Sun does not go far from its expected positions for the month [6].

star map mercatorx1p6

Figure: The wavy line in this Mercator map of the sky is the Ecliptic. The Sun travels on it. There are 24 marker points on this line used by East Asian Astronomers to quantify the position of the Sun on this line.

References (cont.)

[6]. https://en.wikipedia.org/wiki/Solar_term

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Finding time to Sunset with bare hands

Finding time to Sunset with bare hands

by tonytran2015 (Melbourne, Australia).

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

#bare hands, #determine, #find, #find North, #time, #Sunset, #Sunrise, #time to Sunrise, #time to Sunset.

Finding time to Sunset with bare hands (Blog No. 11).

There are times when you have no watch or when it is not practical to carry a watch (such as when going for a swim in the sea) and you need to know the time from Sunrise or to Sunset. This time can be determined reasonably accurately using only your bare hands.

1. Hand postures

image

Figure. Hand posture for determining time to Sunset in the Northern hemisphere.

Cup your hand as if about to hold water. Position the wrist to have the thumb on top with four fingers horizontal and close together. Then stretch your arm, keeping all fingers at right angle to the stretched arm. Stand with your chest facing the Sun but DO NOT LOOK INTO THE SUN. Interpose the bent fingers on your stretched arm between the Sun and your aiming eye on the same half of your body. Twist the stretched arm to have the bent fingers forming with the horizon an angle equal to the local latitude angle and the contact line between middle finger and ring finger being on the same plane with the Celestial axis (Tilting the fingers from the horizontal by an angle equal to latitude angle is close enough).
The Sun will travel at right angle to your fingers to its setting position on the horizon .
Count the finger widths from the Sun to its setting position. Each finger width is about 1.5 degrees distance and is equal to 1.5×4 = 6 minutes of time to setting on equinoxes or is equal to 6.6 minutes of time to setting on solstices.
(At solstices, the length of the trajectory of the Sun is only (6.24radius)x cos(23.5degrees), so each 1degree of length corresponds to 4.4minutes of time).
For example, four finger widths to setting point gives 4×1.5×4 minutes of time to setting at equinoxes or 4×1.5×4.4 minutes of time to setting at solstices.

2. Notes

1/- In the Northern hemisphere the Sun moves to the right (North) when setting.
2/- In the Southern hemisphere the Sun moves to the left (South) when setting.
3/- The Sun is between the middle and ring fingers if any small gap between them let through strong rays of light.
4/- Your finger width on your stretched arm may sustain an angle different from 1.5 degree. You need to check it against the diameter of 0.5 degree of the rising or setting Moon.
5/- In Northern hemisphere, the Sun rises to the right (South).
6/- In Southern hemisphere, the Sun rises to the left (North).

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