Modern use of old astronomical observations - Chinafverbunt/iac2011/china.pdf · Modern use of old astronomical observations China Frank Verbunt Astronomical Institute, University

Modern use of old astronomical observationsChina

Frank Verbunt

Astronomical Institute, University of Utrecht, Netherlands

July 7, 2011

Frank Verbunt (Astronomical Institute Utrecht) Modern use of old astronomical observations July 7, 2011 1 / 37

Outline

1 Introduction

2 Astronomical use of ancient observationsChange of obliquityRotation of the EarthSupernovae and neutron starsNon-Keplerian motion of cometsVarying colours of stars

3 Historical use of ancient observationsDating the Shang dynastyDating the Xia dynasty


Introduction: General literature on Chinese astronomy

Science and Civilisation in China,Joseph Needham, 1959, Vol.3Sect. 20; 1965, Vol.4.2 Sect. 27j.Beautiful books in which muchmaterial is made available. Sufferfrom lack of astronomical expertiseand a strong tendency ofover-interpretation; should be readcritically.

The shorter science and civilisationin China, Colin Ronan and JosephNeedham, 1981, Vol.2 Sect.2.Popularized abbreviation: moreaffordable and less time consumingto read.

SourcesAncient Chinese data thatare used for modernpurposes are

official dynastichistories

provincial chronicles

discovered in modernexcavations (e.g. ofgraves)

Specific literature is citedwith each topic.


Introduction: Transcription

GeneralChinese is transcribed indifferent systems:

English: devised by Wade(1859) and modified byGiles (1892)

French: devised byCouvreur (1902) of theEcole Françaised’Extrême-Orient

Modern: Pinyin approved(1958) and adopted(1979) by the ChineseCommunist government

These lecture notesThese lecture notes keep thetranscriptions from the cited references.Laplace published before a system wasofficially adopted.Needham uses Wade-Giles (but writesh for aspiration ′).

modern Giles Needham LaplaceXia Hsia HsiaZhou Chou Chou TscheouQi Ch′i Chhi


Introduction: The Chinese daycount

The Chinese daycount hasten stems (top to bottom),and twelve branches (left toright), each subsequent dayhas the next stem and thenext branch. Thus, only 60of 120 possiblecombinations are used.


Ancient observations: Change of obliquity

Cassini 1740Cassini compared oldmeasurements of theobliquity with a linearinterpolation

he assumed that the smalldifferences betweenEratosthenes, Hipparchosand Ptolemy reflect theiraccuracy

he then concluded that theevolution of the obliquity isnon-uniform

History of obliquity: Cassini


Perturbing effects: parallax and refraction

When an object P isobserved from O , its position must be corrected for two effects:

1 parallactic correction: to obtain the angle at which the object is seenfrom the center E of the earth, the correction is given by angle OPE,and depends on the location of O . O depends on time of day, and onlongitude, latitude on Earth. The parallax of P is defined as the angleEPL , i.e. radius of the earth divided by distance to P.

2 refraction: due to refraction of the light in the earth atmosphere, anobject is seen higher above the horizon. The correction is angleO ′OP (exaggerated in the figure).



Gnomon shadowsTo determine the obliquityfrom gnomon shadows,correction for refraction andparallax are required.

In 1811 Laplace re-analyzedancient reports of gnomonshadows, many fromGaubil’s (1809) report on oldChinese astronomy, toconvert hem to ancientobliquities.

He compared the results withhis theory. They agreed.

History of obliquity: Laplace



Different transcriptions

in Laplace/ in Needham:Gaubil:

Tcheou-kong Duke of ChouLieao-hiang Liu HsiangTsou-tching Tsu Chhung-ChihLitchun-foung Li Shun-FêngEbn-Jounis Ibn YunusCocheou-king Kuo Shou-Ching

ReferencesA. Gaubil, Connaissance duTemps 1809, p. 382

P.S. Laplace, Connaissance duTemps 1811, p. 429 (= OeuvresComplètes XIII, p. 51; Laplaceuses decimal degrees: 400 toa circle, 1=100′, 1′=100′′)

J. Needham, 1959, Scienceand Civilisation in China 3, p.289

Laplace Oeuvres Complètes on the web: goto www.gallica.bnf.fr andsearch for Laplace oeuvres completes


Ancient observations: Rotation of the Earth

Earth-Moon angularmomentum

The total angular momentumin the Earth-Moon system isconserved

Currently, the Moon recedesfrom the Earth at 3.82 cm/yr;hence the orbital angularmomentum increases

To be compensated by aslow-down in the rotation ofthe Earth, the day mustlengthen by 2.3 ms/cy.

Historical eclipsesAssume constant recessionspeed of 3.82 cm/yr, computethe orbit of the Moon backwardsin time, and from this the timesof eclipses

From a constant deceleration inthe rotation of the Earth,compute at which time thelocation on Earth was on theline center-of-Mooncenter-of-Sun, i.e. observed theeclipse

Adapt deceleration until itmatches



Parameters of the Earth-Moon system

Table: Measured parameters of the Earth and Moon system. Note that on shoulduse the sidereal day, 86164.1 s, and the sidereal month, 27.32166 d, for thecomputation of the angular velocities of the Earth and of the lunar orbit. Datamainly from Dickey et al. 1994 Science 265, 482.

parameters of the Earth and MoonEarth Moon

mass M = 5.9734 1027 g m = M/81.33radius R = 6.37103 108 cm r = 1.7379 108 cmangular rotationvelocity Ω = 2π/(86164.1 )s ωm = ωdimensionless ang.momentum radius rg,e =

√0.331 rg,m =

√0.394

current orbital parameterssemi-major axis a = 3.8440 1010 cmderivative a = 3.82 cm/yrangular velocity ω = 2π/(27.32166 d)eccentricity e = 0.05490



EquationsTotal energy:

E = −GMm

2a+

12

IΩ2 (1)

Change in energy:

E =GMm2a2

a + IΩΩ (2)

Angular momentum:

J = Mm

√Ga

M + m+ IΩ (3)

Equations c’tdJ is constant, hence an change inΩ implies a change in a. Changein angular momentum

J = 0 =Mm

2

√Ga

M + maa

+ IΩ

(4)Eliminate a from Eq. 2:

E = IΩ(Ω − ω) (5)

where ω ≡√

G(M + m)/a3.Thus, E sets the time scale.



Historical eclipses

data selected from Stephenson 1997

Rotation of the EarthThe overall slow-down isdetermined by the oldestChinese and Babylonianeclipse observations

It is 1.7 ms/cy, significantlysmaller than the predictedvalue of 2.3 ms/cy

The cause is not known.Change of form of Earth afterIce age, i.e. I < 0? (Dickey etal. 2002)



ReferencesF.R. Stephenson, 1997,Historical eclipses and Earth’srotation, C.U.P. collects the datacritically

F. Verbunt, 2002,www.astro.uu.nl/∼verbunt/onderwijs/binary/earth.pdfgives simplified theoreticaldescription, and references tomodern research

Babylonian record of eclipse of136 BC


Ancient observations: Supernovae and neutron stars

History of the Sung Dynasty; translations Duyvendak 1942In the 1st year of the period Chih-ho [1054], the 5th moon, the daychi-ch’ou [July 4] [a guest star] appeared approximately several inchessouth-east of T’ien-Kuan [ζ Tauri]. After more than a year it graduallybecame invisible.

On the date hsin-wei [April 17, 1056] the Chief of the Astronomical Bureaureported that from the 5th moon of the 1st year of the period Chia-yu [June9 to July 8, 1054] a guest star had appeared in the morning in the easternheavens, remaining in T’ien-Kuan, which only now had become invisible

It was visible by day, like Venus; pointed rays shot out from it on all sides;the colour was reddish-white. Altogether it was visible for 23 days


HST-mosaic of Crab Nebula



Crab nebula and pulsar1921, Lundmark: M 1 = Crabnebula close to position of1054 guest star

1928, Hubble: expansion ofCrab nebula started around1054

1934, Baade & Zwicky:supernova results fromformation neutron star

1937, several popularjournals: guest-star 1054was supernova

Energy equationCollapse of white dwarf with massM = 1.4M to neutron star ofradius R ' 10 km releases

E ∼GM2

R∼ 5 × 1046J (6)

amply sufficient to explainsupernova energetics



Theory: Pacini 1967A rotating dipole magnet in vacuoradiates energy according to

Lm = −2B2

o R6Ω4

3c3(7)

This derives from loss of rotation:

Erot = IΩΩ (8)

Equating the two, and withΩ ≡ 2π/P we obtain (in cgs)

B2 =3Ic3

8π2R6PP (9)

Age of neutron star

With P ≡ dP/dt , we can separatevariables t and P in Eq. 9, andintegrate to find the age t of theneutron star as

t =P2 − Po

2

2PP'

P

2P≡ τc (10)

where the last equation holds whenP Po , i.e. the period now ismuch longer than the initial periodPo . τc is called characteristic age.



Crab nebula and pulsarStaehlin & Reifenstein 1968discover pulsar in Crabnebula

period: P = 0.0331 s

period change:P = 4.224 × 10−13 ss−1

hence: B ∼ 1012 G, ageabout 1200 yr

if t = 1969 − 1054, thenPo ' 0.016 s

Conclusionsneutron stars are born insupernovae

the initial rotation period isvery short (∼ 20 ms)

the magnetic field is veryhigh (∼ 108 Ts)

Eqs. 7-10 are OK



SN 1181

after Stephensen & Green 1999 Astronomy & Geophysics 40, 2.27

The Chinese textIn the Comprehensive History ofCivilisation by Ma Duanlin, wefind:In the 8th year, sixth month, dayjisi [6 Aug 1181], a guest starappeared. . . On the day jiaxu [11Aug] the guest star guarded the5th star of Chuanshe.The accurate indication of ‘the 5thstar’ allows unambiguousidentification with the supernovaremnant 3C 58 (i.e. the 58thsource in the 3rd Cambridgecatalogue of radio sources)


Slane et a. 2004 ApJ 616, 403

SN 1181andpulsar

pulsars measured with ROSAT, assumed that age t = τc

Cooling of neutron starsthe Chinese give us a realage

X-ray observations give(upper limit to) temperature

the pulsar in 3C58 is coolerthan standard theory (solidline) predicts.



Historical lightcurves indicate Tycho and Kepler were type I



Radio image of Kepler SNR X-ray image of Kepler SNR

APOD 16 Jan 2007



Properties of Type IFrom the lightcurve, we now thatKepler’s supernova was a type I.From the radio and X-rays, weconclude that no neutron star wasformed.From the X-ray spectra, we candetermine which chemicalelements a type I supernovaproduces.We can use these results to testthe theory of supernovae.

Expansion of Kepler SNRBy comparing images of differentepochs, we can determine theexpansion.

Hughes (1999) comparesX-ray image from 29 Sep1979 and 10 Mar 1997

the later image is (4.5±0.5)%larger

a fit to R = tn, with to=1604,gives n = 0.93 ± 0.09,compatible with freeexpansion



LiteratureThe founding articles areJ. Duyvendak, 1942, PASP 54, 91N. Mayall, J. Oort, 1942, PASP

54, 95The best book is Historicalsupernovae and their remnants,F.R. Stephenson & D.A. Green,

2002, Oxford U.P.

ReferencesK. Lundmark, 1921, PASP 33, 225E. Hubble, 1928, ASP Leaflet 1, 55W. Baade, F. Zwicky, 1934, Proc.

Nat. Acad. Sci. U.S.A. 20, 259(and 254)

F. Pacini, 1967, Nature 216, 567D. Staelin, E. Reifenstein, 1968,

Science 162, 1481J. Hughes, 1999, ApJ 526, 298


Ancient observations: Non-Keplerian motion of comets

Non-Keplerian effectsThe elliptical orbits of comets aroundthe Sun change because of

gravitational influence ofplanets, in particular Jupiter

the rocket effect caused byasymmetric mass loss from thecomet

Computations of perturbations of theorbit by these effects can be verifiedby comparison with observations ofearlier passages of periodic comets,as noted by the Chinese andBabylonians.

Literature: Halley’s cometChinese observations andcomputed orbit

T. Kiang, 1972 The pastorbit of Halley’s comet,Mem.Soc.R.astr.Soc. 76,27-66

Chang et al., 1985,Nature 314, 587.

An early Babylonianobservation

C. Walker, 1985 Nature314, 576



Babylonian tabletsBM 41462The comet which previouslyhad appeared in the east inthe Path of Anu in the area ofPleiades and Taurus, to thewest [. . . ] and passed along inthe path of EaBM 41628[. . . in the path] of Ea in theregion of Sagittarius, 1 cubit infront of Jupiter, 3 cubits hightowards the north [. . . ]

Comparison withcomputationsStephenson et al. 1985,Nature 314, 587 discovered,translated and dated thesetablets, and compare themwith orbits for Halley computedbyYeomans & Kiang 1981

MNRAS 197, 633Landgraf 1986 A& A 163, 246



After Stephenson, Yau & Hunger 1985, Nature 314, 587.


Ancient observations: Varying colours of stars

Claims for variationsWith a certain regularity articlesappear which claim that a certainstar had a different colour (than itscolour in modern times) whenobserved by ancient Chines,Babylonians, Romans or Egyptians.Examples are Sirius and Algol.Careful analysis of the ancient textsinvariably has shown that there is noreliable evidence for colour changesof naked-eye stars in historic times.E.g. some ancient texts describeSirius as red, but other texts aswhite.

LiteratureExamples of good discussionsof claims of colour changesare

on Sirius: Rob van Gent,1989, Observatory 190,23; S. McCluskey, 1987,Nature 325, 87

on Algol: Rob van Gent,1989, Space Sci. Rev. 50,372


Historical use: Dating the Shang dynasty

Literature for early ChinaShang Civilization, Kwang-ChihChang, 1980, Yale University Press:an excellent (according to experts)and very readable (according to me)general book on the Shang.Cambridge History of Ancient China,1999, C.U.P. eds. M. Loewe and E.L.Shaughnessy: excellent and veryreadable, but extremely expensive.

Chinese traditionAccording to old Chinesehistories, the first three Chinesedynasties are

Xia 2100-1600 BCShang 1600-1100 BCZhou 1100-770 BC

The Zhou dynasty iswell-documented, but in the early20st century it was thoughtpossible that the Shang and Xiadynasties were purely mythical.



The Shang dynasty is real!This changed when it was found that manyof the names from the list of Shang rulers inhistorical texts also occur in texts engravedon bronze vessels and oracle bones fromthe time before the Zhou dynasty.In the 1920s spectacular excavations foundvery large and rich graves, presumablyfrom Shang kings and their wives. Theseexcavations also lead to the finding ofmany bronze vessels (many thousands)and oracles bones (∼ hundred thousandfragments), in an archeologicallydocumented setting, i.e. datable to Shangtimes without any doubt.



Oracle bonesThe texts of the oracle bones, whencomplete (as rarely is the case)contain the name of the King forwhom the prognostication wasmade, the day in the 60-day counton which this was done, thequestion asked, and the answerderived from the cracking (afterheating) of the bone. Typical oraclebones are shoulder bones fromlarge animals (cow, buffalo), andplastrons from turtles.

Lunar eclipsesOn oracle bones from King WuTing we find references to five lunareclipses, on days 9, 20, 22 (inmonth 8), 31, and 56/57 (in month13) in the sixty-day count.Example:On day ji-chou, divined. Pininquired: the ensuing yi-wei offerwine and millet to Tsu Yi? The Kingmade the prognostication andstated: ‘There will be misfortune:there will not be rain’. Six dayslater, in the evening-night of dayjia-wu, the moon eclipsed.



Dubbs 1951: If we assume1 Wu Ting must have reigned

somewhere in the period1400-1000 BC

2 the day count wasuninterrupted from earlyShang to present (we know itis uninterrupted from Zhousince about 841 BC)

3 the Chinese days run frommidnight to midnight already inShang times (as they areknown to do from Zhou andlater)

then we concludeDuring the 59 y reign of Wu Tinglunar eclipses occurred on theabove-listed day-counts.One eclipse must have startedbefore and ended after themidnight that separated day 56from day 57, in month 13.This leaves only one or twopossibilities, depending on

assumed changes in lunarorbit and length of day

details of the interpretation ofthe texts



Bamboo AnnalsIn 281 AD the Chinese discovered,in the grave of a ruler who died 296BC, a historical text, now known intwo rather different versions, as theBamboo Annals.In it we find references to

a gathering of the five planetson one location in the sky

the location of Jupiter in theconstellation Quail Fire when1. the Zhou received theheavenly mandate 2. the Zhoudefeated the Shang

Example text:King Wen was at Feng. The lordsof the nine regions all came. Thefive planets gathered in lodgehouse no. 4. In the 42nd year ofKing Wen, Jupiter was in QuailFire, therefore King Wen changed itto the First Year of Receipt of theMandate and began to stylehimself ‘King’.



Calculations by Pankenier 1981According to astronomicalcalculations this gathering ofplanets (which recurs every 516years) occurred in constellationCancer, on May 28, 1059 BC, ajia-zi day, i.e. day 1.Pankenier suggests that the Zhouleader who conquered the Shangin 1047 (again on a jia-zi day) setthe calendar to have started 12years earlier, at the time of theMandate indicated by the planetarygathering.

Luoyang, 1059 BCE, May 28



A problem. . .According to the Annals, thegathering of planets occurred in1071 BC; not in 1059 BC. . . .Pankenier argues (quite plausibly,in my view) that this is due to laterefforts to date the event, theresults of which were theninterpolated in the old texts.Not everybody agrees:www.stanford.edu/∼dnivison/KunYi.html

Conclusion from AstronomyThe results of the work both byDubbs and by Pankenier lead to achronology in which the conquest ofthe Shang by the new dynasty of theZhou occurred in the 11th century,probably close to 1050-1045 BC.

ReferencesH. Dubbs 1951, T’oung Pao 40, 322D. Pankenier, 1981, Early China, 7, 1


Historical use: Dating the Xia dynasty

Calculations by Pankenier 1981The Xia dynasty lasted 517 y!A gathering of planets occurred inconstellation Sagittarius, at the endof 1576 BC. Five planets weretogether early november in theevening sky; four of them still weretogether when they became visiblein the morning sky in December.Was this the Mandate for the Xiadynasty?

Luoyang, 1576 BCE, Dec 16


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Modern use of old astronomical observations - Chinafverbunt/iac2011/china.pdf · Modern use of old astronomical observations China Frank Verbunt Astronomical Institute, University