An Astro-Archaeological Analysis: The Tall Gnomon of Guo Shoujing (PPT slides)
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Vance Tiede
Astro-Archaeology Surveys
Presented at the SEAC Conference, Malta, 22-26 September 2014
An Astro-Archaeological Analysis: The Tall Gnomon of Guo Shoujing
Diffusion of Astronomy
“The investigation of the transmission of mathematics and
astronomy is one of the most powerful tools for the
establishment of relations between different civilizations.”
“[Unlike] stylistic motives, religious or philosophic
doctrines, …astronomical methods…require for their
transmission the direct use of scientific treatises.” Neugebauer, The Exact Sciences in Antiquity (NY: Dover, 1957), 1.
Tall Gnomons: Precision Without a Telescopic Lens (cf. Needham 1959, 296)
Tycho Brache Uraniborg
1500 Ulugh Beg
Samarkand
1437
Guo Shoujing Gaocheng
1276
Nasir al-Din al Tusi Maraghe
1262
Sawai Jai Singh II Jaipur
1727
Tall Gnomon of Nasir al-Din al-Tusi محمد بن محمد بن الحسن طوسی
Maraghe Observatory, Persia N 37⁰ 23’ 45”, E 46⁰ 12’ 33”, 1262 AD
Yuan Luni-Solar Calendar Reform of 1280 AD
The Yuan Emperor Khubilai Khan “ …has specifically
commanded us to carry out a reform and set in order a
new astronomical system. For this purpose, we have
newly made a Simplified Instrument and Tall Gnomon and
have arrived at constants based on observations using them.
We have carried out research on seven items:”
1. Winter Solstice;
2. Year Surplus;
3. Tread of the sun;
4. Travel of the moon;
5. Crossing entry [timing the lunar nodes on the ecliptic];
6. Angular extensions of the lunar lodges…; and
7. Sunrise, sunset, day and night marks [Venus/Stars?]….”
(Guo Shoujing, in Siven 2009, 282-286)
Guo Shoujing Scaled up the 8-chi Gnomon 5-fold
Standard (8-chi tall) Gnomon
Tall (40-chi) Gnomon:
8-chi x 5
“Kuo lengthened
the eight ch’ih
pendicular into
forty ch’ih, thus
greatly increased
the accuracy in the
calculation of the
summer and
winter solstice.”
Tung Tso-pin 1937, 128erp
Water Channel:
- Levels
- Reflects
Seasonal Shadows at the
Tower for the Observation of Stars &
Standard for the Measurement of the Sky, 1276 AD Gaocheng, Henan Province, China
34° 24’ 8.73” N, 113° 8’ 26.23” E, DigitalGlobe/Google Earth imagery
27 Dec 2009, est. 1100L 2 Jul 2014 28 Apr 2009
Summer Spring
Winter
Tower for the Observation of Stars
& Standard for the Measurement of the Sky Gaocheng, Henan Province, China 34° 24’ 8.73” N, 113° 8’ 26.23” E, 1276 AD
(cf. Krupp 1983,60)
Midwinter 27 Dec 2009
est. 11:00 Local
Astro-Archaeological
Research Questions
1. Why is Guo Shoujing’s Tall Gnomon’s 128-chi horizontal
template scale (kuei-piao) 40% longer than required to
measure the shadow of the Midwinter Sun (-23.5ᵒ dec)?
Midsummer Moon Major SS (-28.5ᵒ dec)?
Other?
2. Was the Latitude of Guo Shoujing’s solar shadow observations at
Gaocheng (N 34.4°) or Beijing (N 39.9°); and
3. Can a “Virtual Field Check” of the Yuan Dynasty hao length of
“about 0.03mm” (Mercier 2003, 195) refine the limit of shadow
resolution marked on the Template Scale?
(Han Dynasty hao = 0.024mm).
1a. Why a 128-chi Template Scale?: Midsummer Major SS Moon (-29ᵒ dec) Venus? Bright Star (-32ᵒ to -38ᵒ dec)
Table 3. Tall Gnomon Minimum Declinations at Gaocheng & Beijing
OUTPUT: Program STONEHENGE (Hawkins 1983, 328-330)
#127
#122 delta d
Gno mon Tall Gnomon d decl Target -
Chinese Distance Height Location Astro-Target Declination decl Skyline
chi (m) (m) N Latitude on Skyline (deg/deg/radian)
84.7250 20.64500 9.75 Moon -29.3668401684 0.0007901684
SMAJSS -0.5125480518 0.0000137910
Gaocheng 15JUN1280
34.4°
128.0006 31.19 9.75 Venus ? -38.2400939269 6.4359772602
Min dec -0.6674155453 0.1123289938
111.2772 27.12 9.75 Moon -29.3664503563 0.0004003563
SMAJSS -0.5125412483 0.0000069875
Beijing 15JUN1280
39.9°
128.0006 31.19 9.75 Venus ? -32.7367236168 0.9326069501
Min dec -0.5713636134 0.0162770619
Lunar Magnitudes by Phase at Meridian Transit: Estimated Shadow/Reflection Visibility
(11 Dec 1300 – 10 Jan 1301 AD)
Lunar Magnitudes by Phase at Meridian Transit
11 Dec 1300 AD- 10 Jan 1301 AD Estimated
Phase Illuminated Visual Shadow/Refection
Day Name % Date Magnitude or Invisible
New 0 11-Dec -1.82 I
1 1% 12 -4.65 I
2 1% 13 -4.65 I
3 1st Crescent 4% 14 -6.73 R
4 8% 15 -8.03 R
5 15% 16 -8.97 R
6 23% 17 -9.69 R
7 32% 18 -10.29 S/R
8 1st Quarter 42% 19 -11.79 S/R
9 53% 20 -11.22 S/R
10 64% 21 -11.59 S/R
11 75% 22 -11.89 S/R
12 85% 23 -12.14 S/R
13 93% 24 -12.12 S/R
14 99% 25 -12.44 S/R
15 Full 100% 26 -12.48 S/R
16 99% 27 -12.44 S/R
17 94% 28 -12.32 S/R
18 87% 29 -12.15 S/R
19 79% 30 -11.92 S/R
20 69% 31 -11.65 S/R
21 59% 1-Jan -11.33 S/R
22 Last Quarter 49% 2 -10.97 S/R
23 39% 3 -10.17 S/R
24 29% 4 -10.07 S/R
25 21% 5 -9.49 R
26 14% 6 -8.77 R
27 8% 7 -7.84 R
28 Last Crescent 3% 8 -6.48 R
29 1% 9 -4.06 I
30 New 0% 10 -0.58% I
http://www.freegreatpicture.com/earth-star/full-moon-reflection-50358
1b. Venus: Thai Pei4 (Great White One)
• Visible in Day and Night:
• 3rd Brightest Celestial Object (mag. ≤ - 4.6)
• Casts Shadow Below: http://www.digitalsky.org.uk/venus/shadow-of-venus.html Above: Statis Kalyvas
http://astrobob.areavoices.com/2009/01/14/bask-in-her-radiance/
1c. Venus Min & Max Declinations (+23.5º +8º ≈ +32º dec)
(McCurdy 2005, 189)
.
Period of Absolute Extreme (+ 32 degrees) Declinations of Venus
http://nssdc.gsfc.nasa.gov/planetary/factsheet/venusfact.html
Period Siderial Synodic Absolute Absolute
Planet Earth Days Earth Days Earth Days Earth Years
Venus 224.701 583.92 - -
Earth 365.2564 - - -
Earth-Venus - - 47,924,345 131,207
1d. Venus Maximum Declination (+23.5º +8º ≈ +32º dec)
“According to the mathematical wizard Jean Meeus,
perihelion last coincided with the Northern
Hemisphere's winter solstice… in the year A.D. 1246.”
http://www.idialstars.com/jan2012.htm
http://skyscript.co.uk/forums/viewtopic.php?t=5201&sid=aa6afae25e1614c853a10d6640926621
1g. Venus Visible in Daylight Solar Eclipse
http://www.zam.fme.vutbr.cz/~druck/eclipse/Ecl1997r/Tse1997uw2/0-info.htm
o ₊
March 9
1h. Venus Meridian Transit: Daytime Naked Eye Observation
Recorded in the Shan Chű Hsin Hua (1340 AD)
Waxing Crescent Moon & Venus
Stellarium Planetarium (left)
Photo, 18 June 2007, 1553 UT, SW England (right) © Martin J. Powell, http://www.nakedeyeplanets.com/venus-conjunctions.htm
“ And indeed only nine days later, the
planet Venus ‘crossed the meridian.’ ”
A Meridian Transit of Venus was
recorded (2 September +1340) in the
Shan Chű Hsin Hua (New Discussions
From the Mountain Cabin) by Yang Yű,
a Co-signatory Observer in the Bureau
of Astronomy: “This was a very bad sign.”
[cf. Schlegel (5), p. 635; Chavannes (1),
vol. 3, p. 374] Needham et al. 1954, 419)
1i. Venus Visible in Daylight: Transiting the Sun
http://www.theatlantic.com/infocus/2012/06/the-2012-transit-of-venus/100313/
AP Photo/Michael Probst
Kolobrzeg, Poland Reuters/Ali Jarekji
Amman, Jordan Reuters/Jim Urquhart
Salt Lake City, Utah
5 June 2012
5 June 2012
5 June 2012
1j. Venus at Solar Transit With Shadow Definer or Helioscope
http://www.youtube.com/watch?feature=player_detailpage&v=H9zXMpijpME
Yokohama Science Center, 8 June 2004 by Itsuo Inouye, AP
Bright Star, Sun, Moon & Venus: Meridian Transit Reflection (mag < 1.5, + 32⁰ dec, 1300 AD)
http://www.incredibleindiaphotogallery.com/2010/07/weekend-travel-to-almora-kausani-baijnath-jageshwar-nainital/dsc_0961/
Meridian Transit Bright Stars (+ 32 dec, Mag. < 1.5, 1300 AD), Sun, Moon & Venus
Hawkins & Rosenthal 1967 http: //en.wikipedia.org
MT SAO Star
Decl. Beijing or Catalog Visual Greek (Latin) Chinese
deg Gaucheng Number Magnitude Name Name
38.3 G 699 0.14 α Lyrae (Vega) 織女 (Weaving Girl)
22.90 B/G 536 0.24 α Boötis (Arcturus) 大角 (Great Horn)
15.28 B/G 380 1.34 α Leonis (Regulus) 轩辕十四 (Fourteenth Star of Xuanyuan)
14.84 B/G 168 1.06 α Tauri 畢宿五 (Fifth Star of the Net)
7.25 B/G 745 0.89 α Aquilae 河鼓二 (River Drum Two)
7.00 B/G 224 0.10 α Orionis (Betelgeuse) 参宿四 (Fourth of Three Stars)
6.78 B/G 291 0.48 α Canis Minoris, Procyon 南河三 (Third Star in Southern River)
-9.25 B/G 193 0.34 β Orionis (Rigel) 参宿七 ( Seventh of Three Stars)
-15.97 B/G 257 -1.58 α Canis Majoris (Sirius) 天狼 (Celestial Wolf)
-28.21 B/G 248 1.43 ε Canis Majoris 弧矢 ( Bow and Arrow)
-33.24 G 867 1.29 α Piscis Austrini 北落師門 (North Gate of Military Camp)
+/- 23.5 B/G -26.74 Helios (Sol)
+/- 28.5 B/G -12.74 Selene (Luna) 月
+/- 24.5 B/G -4.60 Aphrodite (Venus) 金 星 (Great White One)
2a. Solar Observations: Gaocheng or Beijing?
“…[T]here is still the common
impression, even with some
serious historians, that the
solsticial shadow observations
listed by Guo Shoujing were
made at Yangcheng [Gaocheng]
in Henan….. Dong Zuobin made
it clear that the observations
listed by Guo Shoujing were
made in Beijing. ”
(Mercier 2003, 191-192, cf. Krupp 1983, 60-61)
2b. Yuan Shih Solar Observations: Beijing, not Gaocheng
Table 2. Yuan Shih Dec & Tall Gnomon Locations
OUTPUT: Program STONEHENGE (Hawkins 1983, 328-330)
#122 #127
d delta d
Gno mon Tall Gnomon Yuan shih Tall Gnomon dec Sun MT -
Chinese Distance Height Location Sun dec Sun dec dec Gnomon
chi (m) (m) N Latitude Date (deg & radian) (deg & radian)
12.35274 3.01 9.75 22.6947 17.2480 5.4467
Gaocheng 30May+1279 0.3010 0.0951
34.4°
76.74293 18.70 9.75 -23.5368 -28.0586 4.5218
14Dec+1279 -0.4897 0.0789
12.35274 3.01 9.75 22.6947 22.2681 0.4256
Beijing 30May+1279 0.3887 0.0074
39.9°
76.74293 18.70 9.75 -23.5368 -22.5552 -0.9817
14Dec+1279 -0.3937 -0.0171
3a. Shadow Definer & (sub-mm) Resolution?
Figure 2. Shadow Definer (ying fu) Design; Observing Table; Pinhole Principle; & “7chi” Mark of the Template Scale (Siven 2009, 188, 190); http://web.calstatela.edu/faculty/kaniol/a360/yingfu1.htm;
http://hua.umf.maine.edu/China/astronomy/tianpage/0022MingGnomon6471w.html
3b. Yuan Dynasty hao-millimeter Linear Conversion
Table 1. Yuan znang/chi - Metric Linear Unit Converter
Given
Starry
Night Pro Plus 6 Meridian
Calculated
Stone Declination Declination Transit
Feature chi meter feet block ( ° ' ) (decimal °) (LMT)
Height: Gnomon Bar 40.0000 9.75 31.98 na
Length: Template Scale 128.0000 31.19 102.30 36.00
Length: Stone Block 3.5556 0.8664 2.84 1.00
4.1039 1.00 3.28 0.87
Date, Latitude, Location 1.0000 0.24 0.80 0.28
30 May +1279, +39° 54’ 12.3695 3.01 9.89 3.48 +22° 41.68' 22.69466667 12:24:00
14 Dec +1279, Beijing 76.7400 18.70 61.33 21.58 - 23° 32.21' -23.53683333 12:27:15
Chinese Units zhang chi cun fen li hao Meter
zhang 1 10 100 1,000 10,000 100,000 2.400000
chi 0.1 1 10 100 1,000 10,000 0.240000
cun 0.01 0.1 1 10 100 1,000 0.024000
fen 0.001 0.01 0.1 1 10 100 0.002400
li 0.0001 0.001 0.01 0.1 1 10 0.000240
hao 0.00001 0.0001 0.001 0.01 0.1 1 0.000024
Conclusions 1. The 128-chi Template Scale Length was capable
of measuring Meridian Transit (MT) shadows of:
Sun, (Full/Gibbous) Moon, & Venus at Solar
Transit (8-year cycle); and reflections of
(Crescent) Moon, Venus & Bright Stars (+32ᵒ dec,
visible magnitude < 1.5).
2. The solar observations of Guo Shoujing in the
Yuan Shih were made near Beijing, not Gaocheng.
3. Yuan Dynasty hao = 0.024mm Han Dynasty hao.
Future experiment could confirm the hao as the
Limit of Sun shadow resolution of a Tall Gnomon.
References 2Hawkins, Gerald S. 1983 Mindsteps to the Cosmos, New York: Harper & Row. Kelly, David and Eugene F. Milone 2005 Exploring Ancient Skies: An Encyclopedic Survey of Archaeoastronomy. New York: Springer. Krupp, Edwin C. 1983 Echoes of the Ancient Skies: The Astronomy of Lost Civilizations. New York: Harper & Row. Liu, C. Y 1987 “A Research on the Implication of Zhang-Chi in Ancient Chinese Astronomical Records,” Acta Astronomica Sinica, 28:4, 402. http://adsabs.harvard.edu/abs/1987AcASn..28..397L Maspero, Henri 1939 “Les Instruments Astronomiques des Chinois au temps des Han,” Mélanges Chinois et Bouddhiques, vol. 6 (1938-9), 183-370, McClure, Brude and Deborah Byrd 2014 “Venus brightest in mid-February for all of 2014,” EarthSky (February 14) http://earthsky.org/human-world/venus-brightest-greatest-brilliancy-greatest-illuminated-extent#why McCurdy, Bruce 2005 “Venus Vignette,” Journal of the Royal Astronomical Society of Canada, 99:187-189 http://adsabs.harvard.edu/full/2005JRASC..99..187M Mercier, Raymond 2003 “Solsticial observations in thirteenth century Beijing.” SCIAMVS, 4:191-232. Needham, Joseph et al. 1986 Heavenly Clockwork, Cambridge: Cambridge University Press. 1954 Science and Civilization in China, III (Astronomy), London: Cambridge University Press. Odenwald, Sten 008 “Ancient Elipses in China” http://sunearthday.nasa.gov/2009eclipse/ancienteclipses.php Sivin, Nathan 2009 Granting the Seasons: The Chinese Astronomical Reform of 1280. New York: Springer. Shen, K’ang-shen; Crossley, John N.; Lun, Anthony Wah-Cheung; Liu, Hui 1999 The nine chapters on the mathematical art: companion and commentary. Oxford University Press. Tiede, Vance 2010 “Astronomical Orientation of Pyramid Tombs in North China,” Historical Astronomy Division, AAS Meeting, Washington, DC. https://www.academia.edu/3462054/Astronomical_Orientation_of_Pyramid_Tombs_in_North_China Tung Tso-Pin (Dong, Zuobin, 1895-1963), Lin Tun-Chen & Kao Phing-Tzu 1939 周公測景臺調查報告 Chou Kung Tshê Ching Thai Thiao Chha Pao Kao [Zhou gong ce jing tai diao cha bao gao] Report of an Investigation of the Tower of Chou Kung for the Measurement of the Sun’s (Solsticial) Shadow, Com. Press Academia Sinica), Chhangsha. UNESCO 2010 “Report of the decisions Adopted by the World Heritage Committee at its 34thSession (Brasilia, 2010),”Decision: 34 COM 8B.24, 215-216. http://www2.astronomicalheritage.net/index.php/show-entity?identity=17&idsubentity=1
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