thesis on the visibility of crescent-5

8/22/2019 THESIS ON THE VISIBILITY OF CRESCENT-5

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Chapter No.5

APPLICATIONS

Durin8 rhls work lt ls obs€oed thar since th6 Babytontan eE flt recenty a

nomber ol pr.diction crltsrta, mathehatic.t .s we as obsewational. were

developed ro detemln€ whon the new tunardesc€nl woutd beflrsr seen tor a

gtven

rocataon. as tho fist appea.ance ot new tunar crescent marks tho beginning ot a

new month in obseryarionat tunar catendaE thele crireria and modets are

sagnirrca.t fo, calendaicat purposes_ wh€ther an actuat obsrya ohat tuna,

carendar, like the tstamlc Lunar catendar, ui izes lh.se crireria tor arangtng its

carendar of not rhe36 c.trerta provtd6s a €uidance for both teslhg an evtdenco otcrescenl si8lting by common peopte and tracing down ihe dares ot a catendar jr

hErory where app.opriate dates are not we recoded. Ttus the main uti ty oi theprediction c terta tor the eartiest visibiny of new crescent ts to regutate thoobsefr atlon.l lunar catendaf .

Although ftrst order approximations, rike Anrhmetc LunarCatenda, thar areoased on lh6concept of LeapyeaFand rh6 averag6 mooon or rhe Moon fave beenin use, Nluslims hEve been to owing dctuat si€htng o, crescenls ar teast tor themonrhs of fas n8 (Ramazan) and pitgnmage (z hajjah), the acruat moion oi theMoon varies grea y due to vartous tactoB whtch causo rne obseryarionat catendarlo be ditfered froh the arithmelc c6t6trdar.rh6 Catendars if based on a prediction

c lerlon llko thar otya op or ihe one devoloped In this work are rhe cto56t to rheob*patlonat catendai In this chapter, wecohp6rethese carendaBwith th€ a.tualobseryatronat catend6r in pracrice In paktstan tor th6 years 2ooo ro 2OOz, ft tsfound rhst

on avorage 93.7% obseryadons ,16 ac@rdtng to rho yalop,s o_v6tue

t72



criterion or our s-value (or Q&K) cnterion. The disagr.ededt ls lhe resull ot eilher

the bad weather du.lo whlch the.ew lonarcr6cent could not be slghted 6nd th.

lunar nonlh b68an one day lare, or too opilmjsrlc clalms ol obse atloh and tho

Lunarmonthbeganonedayearllerthanpredlcted.

Funher, In ihls work another aoollcarlon ol these models is consldered. Tnls

is lhe use ot lhese modelsto dwelop a compui.tional roolro detemlnethe lenglh

of cesce.t from cusp to cus!. flie n€w lun.. c.scent as well as crescent on next

few evenan$ b obsened io bs shorter tha. its rheoreli.ar length Le. 180 degree

IromonecusDlotheother.Anumberoialrho6haved€scribedthereasonsforthe

shortenln€ of the obsenBd crescent (Danlon, 1932, Schaefer, 1991, McNally,

1943). However, Jew have atlempted devislng a mathemallcal technlque lo

delenino the exrenr of rhis shorrening ol rength ot crescent. On the basis ol one

pafamelef dlleia ee have used cresent ot minimum visible widlh as limil on lhe

le.$h or .re$enr and devrs6d a simple rechnlque to calculate lr. The chapter

beginswilh a desc ption ofthesme.

5.1 LINCTH OF LUNAR CRESCENT

Ihe hct,lld rltc nc\v luhlrclesor appcds stroncr llEn 180. terA r.islnornldt cenlrics. Il wns Denj.h wlD fi^r savc rn exptturarnr for the pbenoneion (Dor.ru_

lt32&1936)andalributcdi(o$etunarteniincloseto$ecuspsMcN! yanribuluda

dillerenl reNon snh tis pbenom€ion disadine Danjon\ hlpo$esis (McNa y, 198:t).

McNall) proved rhar lh€ tcngrh ofrhc shadoss ctose to $€ hrnar cNp ond fic d.panolcoflunar suiface IoD beins pertecr spherc coutdnl,jimiiish rtre brignllrss oflhe regions

ofcresent close ro cusps lo bc rhe caNc ol rhe phenomenon. IIe arribured ttrc tength

shorlcdng ofcNscent to lbe,.seing afeca,due lo $e turbrlcDe of lne ,rhosplrere.

McNally has also developed a limula for calcutalnlg te knBh of rhc desceDl, Larcly

Sull (Sulta., 2005) has anribured 0E shortening of lengtn of crcscenr duc to the

Blackwell Conr.st Threshold (Btackwclt, 1946) and has d€leloped

Iforhula

loc.lcurale ciesenfs lcngrh. W. have aho devctopcd a sinpte &chniqne tor catcul.ring

173



l.nglh of new lum ccscenl (Qucshi and Khrh, 2007). In the fouowins we reprcduce

this cflorr wilh slighr nodiilcation md a codection,

Schrrer cjecred McNall! s expldaion on $e bais or his Yiw thar rhc

shonening oflhe cr{ent length is situply b.ca6c oflh€ sharP d*line offie brigntn€ss

of rhe cr€scenr clo* ro rhe cusps ( SchaelTer, 199 ! ). Usins rh. dcudte dodel of Hatl@

(llapk , 1984) for calcularing rhc surface brighhcs ollhe cesnt Scbaetrer claims that

Daljon\ collected obse aions anJ his own n€* dara fic tbe nodel Howewr, nenhet

Danjon nor Schaefer have sneecsred a ddhod lor calculaling cacehl ldg$ Hapk€t

rDdcl nat be accurat for $eoreical setling rclatcd lo thc clongalion ofrhe M@n bul as

frr as the obscryed cresc€nls are conconcd dEre oughl lo be a depanur€ frod snooth

relarion berween elongation and lhe crescenl lcngth. Thc tason we co.sider n baFd on

obsenarions ofsone norning and {enihs cesccDh.

ltosl of the edly desfiption of the phononen, concenuated on rclatine it to the

plEs (or dongation) of the Moon ihal is gcnet lly th€ !e6on b.hind the Phenonenon

As rhc clongalion increass rne lengrh of rhe cesccnl fronr cusp to cusP k€eps ioc€Ning

Nhich a connon obseryalion. The nathemalicd dc*riprion ol lhe phenomenon'n

lems

ufdeficicncy arc. br Daijon Nd !ho\t to bc incoftd bv McNallv Hosev€r. e or€r

esrimrrcd limil oo rh€ ninimu \idlh of visibl. cEse (2 to 6 arc seconds) bv

VcNJlly le ro ren .mdll"dlu* lbr DJnjotr Liilil lhe d*np'ion due lo McNallv i:

logicall, souDd so is $at of Suh dd bolh rcsulkd in$ tcchniques for calculatng

hDglh of se$oa. HoNerer bolh llcNally dnd Sullan hrve nol reponed lhe aptlicalion

of rlEn desription o. lh€ Ecorded hisloricll dria found in lii€iatuE (Yallop 1998.

Schaeffer l99l elc ). Accordinglo Danjon, d desctibed by F.l@hiet al

si,(a) = st(.) cot(@) (5'l l)

Wh.c $e @ PQ = o is fie deli.icncy at in fiS l (Fatoobi e|' Al" 198) a is rhe

elongltion dd o i5 half the cccenl l€nElh tr apP€6 rhal Dojon tr*d lhe Sine

t14



fomulE. by Nunins sphdicEl 6gL at Q to b. idr egle McNallv rejeded Dmjoo s

dSmcnt ed 6ing fou-Pafl fomuh adiv6 .l:

(5.1)

Nlserically, for small ddgtes d sd a thee is onlv . muejn't dillemce b'lsFn lhe lso

Esults. Generally thc .lonsation (4) cd be cahulaled and the cre$ent l'nrth (2o) is

obede.!. e the rw fomuls 6 b. LPd lo find fi' dclici'ncv arc' Hosder' ro

calcul.rc the c6..1 lenelh nonc of these @ be ued- McNally daetoPs a fomula fot

angula! rpdlion 9 ftoD a cusp in tems ofclescent width R d:

I

SinE

,=f!1.'to"l2t )

(5.r r)

nininum lisibl. *id$ n.sured ih ddid dn€cdon'wtv

lron dE

disc. Thercforcthe logh of th€ ce*ent h€ oblaits is l8O0 _ 29

whde r h th€ sdldidetd of tbe Moo[ md

Usiry (he Blackqell $rcshold con(6t Sutan (sultan 2oo5) adres at tlE

ninimun vhibG *id$ (in |ems of didetcr of rh' smalld eqlival€nl Blackselr

(Bhckstll, 1946) di*) of c@enl ar Frigee dd apoge al his l@rion of ob$Parion'

Tbe fomula rhal hc deleloped for calculali'8 thc crc$61 lenglh rsi

o.l4)

-T *t't Rl

o5



l2t +w \{5.1.5)

wirh w is the dim€ter of e snallsr visible .quivalent Bl&kqcll dnc and l/ h cental

widtholrhecre$e.t. (5.1 5) is$ecorsted fomof (1.5)inQureshi a Knan(Qutshi &

Kian, 2007). Sultd.onside6 minimum diameter of Blacliwell dGc lo bc 0.14 alc

minucs Nho the Moon b near peris€e md 0.16 m ninul€s wh€n the Mmn is n.or

The presenl $ork is based on rhe obseNalion or the last (old) rcsceit oD

February 26,2006. Duling this obsenation rhat sGned from lhc bcginhing ofnorning

oviliglr rill \ell past sutrie, il was noriced rhar for rhis 48 holrs Mon. noE tlrn 2?

dcFcs aMy ton lhe sun ftc ce$ent l€n8fi srancd ro derede \rith lhe rising suD

simihr obsnalion on Mdch 28'' shen lhe aee of Moon wds dound 3l tous !.d

arolnd 18.5 degrees asay lron rhe sun. rhe cdscenr leneth d*leased nrorc npidly qi(h

d(E6ing co.ra$, The l.n rine thb ciescent wJs $en lvilhou optical aid well at$

sunriF s?s less lhd 90 dege* in l€ngh. Tso dtys later n€w cc$enl with agc 27 6

hols ar 15 degees a\ey fom lhe sun Nas olsned till setling Close lo lhe lDtiab

though rhick humid a(mosphde the crcs€nt lenglh Ms aganr obscrved to bed4rcsnrg

Thee obsFations cleaily demonslrare thai lheF isnuch notc 1o b€ expload abolr lhe

phcnohenon ol shonening of cc$ent lcngth apan fom tlapke s .c€urate model thrl

shows detendoce ofcB*cnt lcnsth on clongalion tlone.

TherefoE, inrhis qorl,lo besin si$ qecoisidera simPl. seodeuical model ior

rhe ce$e.r. fu model dFsibes the phenoncnon of shortnine of lcn8lh that depends

on th. aclual seniSiaocLr of lh. Moon d *ll a the rclaliv. alliiude (ARCV) of th€

csc.nl o\fr tftal sky. This is denved fro,n thc sinste pmnct.t (q-vatue or !!al!c)

crilerion of edlie$ visibiliry or cre$ent (chapler 4) fld is bascd on th€ facl thai

whe.cve! rhe widlh (o' btigb$e$) of cF*c clos to cusp is below lhe mininuto

vhiblc c€nrnl widrh (or b ghtn6, or rh. dcscent the vhol€ l.hsth or ccscent wirh

t76



s.lld width eould nor b. visibl.. Applying ou mod.l on lhe rc@ded vbibihv rnd

iNisibiliiy dala lvaitablc fic ldgth ofcEsenl in 4ch ce is calculaiql Thc calcnlaled

lenSrhs of c$en1 @ al$ omParcd wih thc obseded leheths dd wi$ thc lengds

catculsred uing fodlls (t.1.3) de b McNally md (s.1.4 & 5 1 5) due b Slltan. ln

cs ofusing McNally's fomuh AA is @nsidded liom lhe cilerioD used in lhis work&d for Sul|!n's fomula the ninimM width or Bl&kwll disc (,) it 66ideEd b be in

the d.ge 0.14 alc minul€ io 0.16 arc Finut€ and dep€nds on the dislane b.tqeen Eanh

&d th. Mmn obtained using simpl. lined inieQolalion

Irvi€wofQueshi & Khan (QuEshi & Khan,2007) tlre bLishrn€s ofcfsenr ar

displacement vfrcn a cusp is gvei bY

8.. = tF...Cdv tr -cos t)+

sh* t G th€ radius of Moon, F. is fie mdimun nux of sunlight

olVoon.l islhc 'ePar-rionberqecn lhe Sunand

'teMoon in our

the lutu suface dd X B th€ disldc. of the M@n ftom the Eanh'

lhe cescenl at angular sepaElion V fom lhe cusP is eivcn bv

lV,r, =rcosWll CosE) = tl ccatv

(5.r.6)

(5.!.7)

whc t/. is lh. width of fie cdnr i! lne diddle ln bolh the* €quttioc !' vari6 lmh

oo ro 9Oo alo.g fie lenerh of rhe cFscent frcn centE ro a cusp respeclverv

For rhc develop'nen( ofanv nodel thai dcsibes $e ni'inun Po$ibl' sidlh rhtt

cd bc visiblc lttrough naked eve one requi.es 10 s'ek guidance fron $e aclual

obedalioN. ln $e history of *idtjficatlv rcponcd obeNation of thc srv voug

cr.sent Moon, lh€ ecord is that due lo Pi.rce od February 25' 1990 (eporled bv

s.h!.fd ad Yatlop) Thc cl€*nt he claift |o have sn wirh narcd ev' B jusl 14 E

houB and ils widrh wa3 O 18 dc minut€ Amonesl'll

rfie'*oded

ob*flalios lh'

t11



siglling of such a youg ed rhin cesc.nr wb n€vd rcpon.d- In lhe norlel $ar is

developed in this sork thc losct limil ofihe *idth ofvisibl. ctsent is considered ro be

o.l8 aE minut€. However this ninimum is not th€ abelule ninimm for all c6@nls for

all posible el ile altitudes (ARcv). I. fiis work *e consider rhh ninimun of 0. 1 8

. arc-ninutcs of crcscenl width shen fic Elaliw dinulh. DAZ of $cM@n is

aomd

rlr r.larir. alliiudc ARcv gives lhe q-lalueof_0.22. Y.llop s ditedon (4 2 3) for $n q-

,1R(y =9 6311-6J226W +0 7319 t'i2 ol0ls,t/3 6'18)

Thc values of ARCV accordinglo lhis *iteion giving $e q_rdlue equal to '0 22

Nould ield ! difcre lotr€rlihiion lhc visiblc width olthe crescenr' Tbis is causcd bv

dilTriem relarivc dzinulhs DAZ FoT lh. lasl posibl' ARCV (4o) th€ *id(h ol lbe

iNisibk ae$erl Nould bearcund 108 alc{cconds $at occur dl a large valucofDAZ ln

\i.\r ol diis $ilcrion ihi nininud {idth of lisible cr€$eol for @v ARcv is Gm'd tr-

and s te *esent isjusi invisible for$is{idth:

(tIa)

Whqrc l'l. is tlE tlmrclical enlEl sidlh of he ces'enr and 4costl is $e r€duced

rvidth al aogte V Irom lhe center of $e de$ent'/-

n dre sidth r€duced bv the chnve

ahnude ARCV li ordcr thal soEe pan ol dsenl is visibl€ 4(!'rvl > l'l' ar sonc

\alue V = Vn'llrus

thc eftstive visibtewidlh of$e ce$cnl tor v nnsing fon 0" ro

(5.1.r0)

Th. brishlness of crescenl falls sha4lv s 0 approaches 900 - t th' aclul visible reidrh

of cE$.nt at any val!.of

V m6rtE less tbd d€ e'onetic valu€ of vidh eiven bv

equatioh (5.1.8) Therefore rhc etr6tiv' v6ible width siven bv (5 1 10) is justiced

178



IE it ir ma dly lh koglh of.ilsc.d 6d nodo! htr lh. vilibL with of {tt*.al

b! lo diminjrl rlso. Wh@\tr lhc cr.rcdt it ilviliblc'n

vi.w of (5.19) 4r'bs to

c*v-fr=r (5.1.Il)

I!.ll oOE qscr. ia vi.r6e lb .tleI it vit'bL ia sftlth tl to'E'rgh

!'n Dlrt

dilh!6l!.cc..ttti3ncv.r!d.conDldc 180!irlcrgh Tbu!'tV=V.

(5.r.r2)

Tladc i. (51.12) ||,! i! ! ddr.. of Idf l!! l6€tt of ih' cr'!c'dt $ itll lt' iol'l

lcogth oflh. ctelcai k Sivcn bY:

(t.l.lr)t;rr*"CY'*)

D

mt



'I}lus $e ae$c len$h cd be dalualed whelever $e fieoelical sidlh lr'

€xcecds the mi.ioM width ,/, visible acording b YalloPt q'lalue ctn'rion oi our s_

value criterion, for $. palticular lalues of ARCV In $c Fis 5. l l the *8nent [D or

AC is the ninimm width lil- at dv ARCV inlisibl€ according to Yallop's cliterion

The scgnenl AB is rhe thorcdcal widlh ltl" at fie cenrE of fie cresccr! Alsngular

spaBrion vr from tbc centre olc€sent ED equh4(nrl/" 'lheefore the ponnt on

rhe ouler linb oi rlc cresceni tbal las dguhr separaion fon cerrc geal$ ihan

s. = ZDOA should noi be visibl€ TIE lisiblc cls€ then crtnds fom D o D' @d

has letrBlh 2!rn. One should nole lhal Nheneve! ttl" (nininum vhible wid$ accordnr8 b

Yallop s nitrion) is Srearer tan ttlq ($coetical widtb) {5 1 13) can nor bc sed ind the

cresceDi isnotlisible, ie iihas m lengdr'

The tr1odel developed nl this Nork lo cotrlpute tlB lenglhoflhe crcsccnl hrs been

applied lo a nuobc. ol ob*rvalions lepon'd in IneralE (Schaeffd 1984 Ylllop'

1998) Tbe resuls foi ihe crescenl length against lhe elongatio' also kno*n as irc of

lighl orARCL,ae ptscnled in lable 51 1and in Fig t'l2 Tlre loBlhs mcalculaFd

by scleciing lhc nnrinum vhiblc Nidrh Vn of dcscenl foi tlrc valLE ofARcv 'c'ordrgb {t.1.8) in rh€ elerv ca* and ihen usnrg (5 1 13)

The colunns or rhe hble 5 l ' I sllow rhc darc ot ob*ivirion thc @dinares of

rhe lcatioD of obseryer (Ldlilude and longitud€ Fspeclilclv) tbe rclatilc umull)

PAZ). rlre dladve .hnude (ARCV)'r:d

lhe clon8alion (ARCL) of $e Moon at lhc be'(

rinc ofobstvalion. lbllowcdbv setr1i_didetr and lhc cental widh ol cr'scnl in arc

ninules. rlt 4_valu., lhe niDimum cF$enl sidlh viiihle at lbe rclatile alritude

c.lculated lom (5.1 8) and finallt the cE$e'r lensth cdlculared usiie (5 1 11) Thetablc

is aFmged in chmnotogi@t or<lr of ob$mtio's dd co't'ains onlv Pai of th€ conPlele

data s€l lhat hs b€en used for conpaine mod'ls for carli esl crescenl siehting in pe!'ous

180



200

F 180

fi reo

3ro

Erai rooo80

i;@

=aoM

0

20 30

E mno

tig- 5. | ,2: Crlgn Lcogll! tr' vdi.Ii@ dE ARCV

Tlr! Fi8 5 1 2 slD{! lhai lh. nbdioel ctdid bdwen ct!*4t lcntlh 'd lhc

ctdgltion h not snolh s Eporr.d bv sd|Itrcr on {E b$i! of H@k''t mdcl Th'

tui! r.rlds fd tl 5 N (i) dE cr.rc.nt hngth ha to bc tff"t'd bv dE ElihMoon

dist ncc .! cl'in d abos (ii) 0F dttdgbdic n!td4' cloe ro lqizd trN|l tfrecr li'

cr$ent losrh., cl.imcd bv McN.[v ald Silrd MoEov{ v'rv wi'lc cle'ot!

ftal

c invilibte dn lo $.it d4 vicitritv qftb $t hori4o mull mt v|tilh $ddolv for s

invisiblc crcsc.nr the elongaiion mv ba ttiSc $d nult not h'r'' as lcngh (i3 msl'

dt b. i isiblc) !.dding to cLi$ of scn*&t Ttt invisibilitv of t eidt'!l*al

!t

de to ii! clo..n6 io lFdzon (sd[ ARCV) Ho*E'sftn dft$L diiod' (ARCV)

$e rnc G..nt 3lEI bc d!ibl.. Ot <ftosnlid lnd cltir b tbai for r sw' of

rrn (sfrcidt) $idlh tlt stving tud' (ARCV) mud clN lo dtc4" dt ldgft of

.le.nl fron nt mdinwn (al DAZ = 0) 10 iB minimun (terc lcnr$ vh'n itt {-valu' is

h.low limils of !tuio!) sooulv dd iot sdltolt' b nE $din'd 69 5 12 odlv dto*

obsflllloB .rc coNidctld tri.n lh' d!€c'!t M cltimcd b h!rc b'@ i"n or [E

cr.!c.d Loglt i! c!a!.bla

lEr



182



T.bl. 5.1.1 {Continued

r8l



Tabl€ 5.'1.1 (Conllnued)

Durins rhis {ork $e ?O obw.tions of Dfljon (ne ionc{ bv Scha'lTs

and Fabohi €1. al.) @uld nol he acc6sd, howvc. the pictotjal data of cdccnt ltngth ir

beins eeneraied at fte Asaolonical Obsdllory al Univdilv of Kdachi. Th! obseNed

cBcell lengh fon phologEphic Ecoids i5 given in Tabl€ 5 1 2. This inclldes sone

obsryadons made by olhe^ durirg past fe{ ycas and tbeir pictutes ate availoble liom

M.icproi.on maiDtaindby oteh,

184



Tne nodel dcvcloped in lhis e for borh Ih€ brigh$6s ad th. lenglt of

cmce.i is nainly geomerric, suppl€n .led by rhc single pmercr crilcrjon for $e

earlien visibility of ncq lunar cFsc€n1, Thc model prcvid6 a simpte method of

cdculaling lenglh of lunar ce$eot and tak€s inlo accounl lhe atnospheric afects

indiicclly through singlc pdaneler crit ria for th. vnibility of new llnar cressenr only.whenerer t/. < n/- fi€ €r€$ent l6grh is nor cakulaled dd rh€

according lo eordcd obsedation (lable 5.1,1), TL nodel hd been Gn.d in nw $ays

I:i6r. ior so6e of $e rcccnt obeflarions whose phologlaphic Ecoids arc available $e

cilculated dd obscrvcd cescenr le.erhs tre compared and shown in jablc 5.1 2 and nr

lig 5.1 7. The cFscent l.nerhs calculared ushg ou! lornula (5.1.13) arc SEaler thm lhc

obseoed values dd rhose due ro Sultan srechnique arc genedllt closer to the obefled

!alu6. In calcul{ions using th. fomnla of McNrlly A-t = ,r- dd X = seni'diafreter ol

The colu$ns nr rable 5.12 show rhe dalc ofobseruation lhc coor\iiMlcs ol rhc

locatior ofthe obseNer (lalirode md longitudes ii degr€e resp*li!ely),lhe elongation o1'

rhe Moon fod rhe sun in d€8rees, the seni-diamcrer oflhe Moon. thc c.nlral rvidt[ ol

lh cEsce.l. ninioum visible width of cre*.nl (all in dc minul6). lollosed bv lhe

crescenl length crlculated by our nodel ,id $e obsded crc*chl l€nglh. lhc .a'nc ordrc

obseNer Th€ l.( No colunns contain cGsce|n lcngtlrs as calculaled usirr8 rlE nrodek

rlu" ro sutron onj Uctlutty .,p.ctvely. Thc du(a in rhh ubl€ has bccnlnlnucd iD ordcr

oiincre.sine elongalion ot ARCL.

To d€Gmine rh. l€ngh ol! crcsenl fom picroial record the dieital phoroemph

is opened in any sraphic $nw l@l- SeleclinS coordinales of lhe oa the poin6 (*o

ofr&n do*roeachoftu cusp md on€ closc ro supposed cenftof$ccrc*enoon the

vhible oute! liob ot lhe oe$eol an equation of circlo h developed $at leads to dre

coordinales of lhe centre of the luft disc, toining lhe cenlre of the lund disc with lh€

two yisible cusps of thc crsce.l tbe dsle made al fie centre bv thc tso cnspc is

mc6u€d. Tn€ picue of one of tlE cre$ent m.$u.d in this Mv is shoM inFi8 5

l?

185



Fig. No. 5. L7: Mesuemcnr of Length for Cterent of Mav 28. 2006 aspholoeraphed

rrXffiltr UtoveElty obsefrd@ry.

'the dlta aor the obsiedcEscehl lenglhshoM in |able 5 12 and the cbart i. fig

5. L? shows inlqesrine paficn. Clain d by Schacfer (Sch@fer, l99l ) fie crc$ent lcngh

is a sn@$ fiDction of elonSatio.. but lhis drE er sho*s a tMd that cl*lv exhibns

delialion tion oy such sn@$ rel.tion. I]lc dala sdple is snall bnl lheE de lwo

subsets eech having neally sE@th relations, separatelv. b€twcc. lhc crescent length tnd

the €longation. Hovever, rhen consideed s a conbiNd dala sel lh€ obsflatios uith

elongarion ll93 de8lees (by AnFa} l44l de8@s (bv Oner) 1667 degEes (bt

Ralini) md 20.12 degrees (by Qwshi) deviarc Mk€dlv lbm $e apPaEnl snoofi

rclarion exhibiled by the rcsl oflhe dala set Cecchl l€nsths in rhcse four cNs are huch

snallcr thm lhe uend shown by the rcsl ofob$wationsas wellss thcresultsofe&h rhc

mod.ls co.sid€red abovc fot calculaline lhs le.gtb of $e ciesccnl

186



AII the* fout deviati.S cdes ae photogdphically Ecoded dd have the ledi

posibiliry o| obseNational ercs. Out of |he t€s1 of th. €ight ca*s anothcr six @

plDlosnphic. Thc rccords due lo Sch&fq de lhc only cag 0tar "ob$nation.l lcngrh

of .ew lunr cE$ent is @nMed ils Eladon wift elo.Salion mul nol bc sneln 6shoq in flsuE 5. L2 as w€u 6 table 5. l2 (or nsurc 5. L7).

It is tunher nored $ar rhe rool mear square erot calculated foi lhe lhree

conputational frdhods (Ouls, Sultmt and McNally t it n found $at Suhan s melhod

h6 rhe led( cror (4.76 degr€et follosd by McNally's thal ha m .mr of 6 16 decrs

dd ourmodel

hdan

erorof ? 22

degR'The najo. difer€nce h€lwen our model dd

rhN Sulbn's dd McNaUy s is that olr nodel 8iv* coosislmtlv hisher valucs ol the

lenefi oi crc$ent, wliets $e orner lNo nodcls havc bolh posidve lnd n.8flive emn

Th€functionalrel.tionbet*eenelongationardlhecrcscenll€nglhissinlilorinolrtuodcl

aDd $ar due to Srll.n s. bul lhe oneerhibi(ed by McNally's model is m.rkedly difitrcnl

McNally s mod.l is Sivins betre esuhs for larser elo.gaion but a3 $. clo.Sation

becond snaller the emr given by McNally s nod€l beconcs leser and ltrger

Tdhl. No t.1-2tth:.^r"la r'!h,lak.t L?ngths o[CrctehB

t87



180

160

'110

1m

100

80

60

zlo

15ELOIGAN()|{

+OBSERVED FOURESHTS r SULTAMS o MCMI.LYS

Fia. No 51.7

200

i60

160

E.ro

:100

380360

20

0

15 20 25 3)

ELq{GAIOI{

Fig 5 | 8r C'lsat tdgo5 $rinc Eloqiion withdn wi.rioa dc ro aRCv

188



Tlre modcl for rhe calculation of cc*ot lenglh may be u$d d rh. .dli6tvisibiliry ctuerion 6uch in the smc say 6 Yallop\ cilcdon cm b. usd, Hos.ver, our

€nphasis *6 nor b dcv€lop d allcm e cdr€.ion for $c s€. This *ork ws i .nded

for a b€rter und.htdding ofthe grcme$y of the lunar cEscent md lo delelop a ne$od

for cllcuhting iis l€nsrh.

The scond md indi@t tesi of the 6odel is its conparison qitb the rcsuhs of

Ddjon ncnliored in Fal@hi el- al. Ifthe niiimlm visiblc eidlh ,/, for vdious ARCV

according lo Yallop's critcrioh is r.placed by rhe nininum ever visible cenralwid$ of

0.18 aa ninuks tlEt is equivalor b igoring $e atmospheric allst for lower ARCV

|hen the Eladon b.tsen cEscdr lcngrh and .lon9rioo bccon€s snoolh as pE*nrcd by

Schaefer (Schaeftr. l99l). The smc is shoM ii Fis. 5.1.8. The chart in figwc 5.1.8 aho

sho\s lhat limiling value ofelo.gation lor po$ible lisibilily oflh€ cEscsr is areund 8

d.grees. As our compurlrions do considerthe an'cctofparallaxrhis limil is equivatenr lo

te ? degrce linil very popultrly rlown $ DanjoD\ linit.

On thc b6is of $e calcuhred lenghs of {escenr and ns elonearior using ou

hodel the Ddjon deficicncy arcs aE calculrted igno.ing the af&ch ol ARCV by

aomula giv€n by Danjon and thal given by McNally (shown in Fig. 5.1.9 and s.t.lo

Bpedi!€ly) These resuhs ae in clos agreencnr wilh fte Fig I in Flroohi el al (lbar is a

^rrcduoionof Danjon\ lis 2)-

189



*.

Fi8. 5.l.9i D.fici@y Arc rg.ind Elongtiod f.dding to D6jon

Pig.5.1.l0: D.tr idct A!!.gd!d Eld$tLa...qdiosb LlcNdly

;r3.

190



6.2 LUNAR CALENDAR FOR PAKISTAN

Mosl of the hlami. counri* follow d ob*wadonal lu.d cal€nde, ar leasl fot

ftn rcligious purposes, Although subslantial work is done to cvolle a pediction

ciiie on ro dcvclop a univerel calenda! by llys (1984b, 1988, 1991, 1994a, 199,1b,

1997) ed otheB, r truly lnilersd calendd could nor be d€velop.d. As according Io

coDmon Islmic b€liefactual sighline of$c n6! L6d crceenl is n*essaty to b€gin a

Lund monlh, such a univesl calend& $cns lo be inpo$ible. This b |fue €speci.lly

b€cau* just aner conjuncion $e new luna! crcscenr is nol visibl€ on rhe sme day

lhroughoullh€ worl,l, eveD ift*o places ofobseNatio.areoD sm€ loDgirude. According

1o recent delelopnenb (Scabefer. 1991. Yallop, I998, Qurcshi &Khao.2007)ob*ryational l@r calendaB for each Isl.mic counlry m be d.veloped bur dc ooi

s.ncally acceptcd b)'' rarious Isl.nic conmunities.

ln Pakisian an Offrcial Commiirle (Ruer-e-Hilal Comnft(ec) decidcs about when

1o beg$ a Lunar nFdrh on tbc bdis ofpublic cvidence and obseNatioos. This connilre

sa$e6infodaioi 3bour thc claim ofsishriig rhe

csceThc clrims arejudged oi

rhc basis oflhe diFdncsof$e Islmic Laws. Som€ FpEsenlalivesofvdousscienrific

organiatiom de cle consnhed. Oncc $c clain/s is jNritled relisiously andor

soientilicauy, $e Ennoucemenl is nDde rboul begiming ofthe nexr Lun,r m.nrh In x

way,lhe beginning ofE\v lunemond is bascd on public obscBations ' verined ii licw

ofde pnncipals laid dosn br lslamic shariaat laws (lisled inanicle 1.3).

'lle advmrae. is rhal a larse numb$ of ob*Ne6" trle pan in $e exeai$ and

wilh it the pmbability of sighlins .ew cBscenl is incesed. Morcover, hon oa thcsc

observeis de iionr rural arcas sherc thde is leasl ihduriallraffic 6nd liSht pollution,

aid n k higlJy prob.blc thal lhe obseNing condilions d€ n€ar perfect. TheEfore in this

sluljy lhe* public obs.rvations e considcrcd |o bave a hki degE. of autnendciry. ln

lhis \ork all lhcsc public ob$dation-b.*d d.res ofsiart of€ach Lunu nonth frcn ye.r

2000 b 2007 ae reproduced and 4 srudi.d in conparison wirh thc Yallop\ q value and

l9l



ours-value crirerion-baed crireria. A similar wolk for the period2000-2005 has akeady

bcr reFned (Qu€shi snd Kh0, 2005)

TIE resuhs of E 95 lnDation during the Jmualy 2000 lo Scprenbd 2OO7

(Shawl, 1420 AH lo RaM, 1427 AH) .tong *nh obsRalional data 4 presenred

in yeady lables in appcndixlv All rhe conpuklio.s fo! the* tables de basd for the

city of KaEchi (Larirud. 24o 56, Longitude 6?0 l.). The fisl cotom indicales 16r

conjDct'on wjrh nonrh, day, hour, ninde and seco.d for rhe l@al rim€ of conjuictioi

in the sub-columhs. Thc calcularions are done for rhe day oftast codlncioi, fo! $e nexr

day and vherc Equird two days tater, indicaled undc. colunn hcaded .Ldt Coij

followed by rhe Dale in Oregorian catendar. Nexl

$ocotlmns givc lhe r€larive ahnude

(ARCV) and reladve azimuth (DAZ) in degrecs foltowed by nooDset-sunscr tag irm,nules. ftc age ofM@n (in houc), rhe arc or tignt or €tonsalion {ARCL in degrtand fie cBscenhvidrl (irr arc minlret apper $e iexr rhre. cotunns, iolhsed by

colhns indicaling the r-value, visibilily condition otr q-value. lhc .elahc and the

visibihy conditio.s on s,value. Thc visibitiry condirions are lho* de$nbed in hblc

4.2.4 (for Yallop\ oiterion) dd labt€ 4.4.4 (tor euEshi & Khan qirerioD). Under rhe

hcrding of 'Momh $c colmn givs rhe nrhc of Isl.nic mondr $at begi$ anq a

sighring reponed on $€ previous evening foltowed by $c CreBorion d.te ot slan ofrbh

lDnlh.In lhis 16l coluDn und$ Cregori& dare ofsiafling lunnnDnrh, numbsofdar-s

in dE nonrh, iE also 8nd Ttu la{ colunnr conr.ins a comnenl. If rc dccision oa

sl.nrng new lunar noDlh is in agrccment vi$ the prediotion critsioD Gratur q.ilqioi)

thc column conrains I,ROPER. tle ..ob*ryalionaldecision .nd tbc Nodet arc

consideed lo b. i..gEeme.t only $ne. thc s-value clirerion show Ev, i.e. crcscenr is

clsily visiblc. Tbe conrhenr in ttE tasl cotuDn cobrains ,LATE, if thc dcchion of

startng new lund nonrh is one day lare 6 indicaled by rhe dat of csy visibitiry on r_

lalue and EARLY iI the lunar nonlh has been naned ooe day edlier rhan lhar

indisted by the prediclion crn€ on. A5 staled eelier all de* calculariohs @ doDe for

KaEchi and for rhe b.sr local lime for €E$.nr lisibitily. Hower, ir should b. nored

lhal observarion claios are couected from alloverlhe counry.

192



Out of rhe 95 public obsesalioDs reponed jn rhis \o*, rher wre o.ly six

occ6ions (Jbe,2000, Juq200l, Juty 2004, ApnL 2006, Jury,2006 and Juty,2o0?)

vh.n th€ sighling war Epon€d one day latc ii compdison b rhc pcdictio, crn€ria

according ro which the New CEscent was lisible on rhe pevious day bd *s not

reponed. Tbere wasoDty one oeasion {hor rhe earty sighrnrg is rcponcd Nov. D,

2004), hus,1herc weE only 6.3% enors in rhe decisio.s oflh€ moon sightingcomineof Pakistd duing ld sven yas. llese resul$ e ba$d on verifi.d chims Tbe data

B8arding nnmberofcE*cnl siendnB d.ins $ar sre notrc ficd is nol available. The

only case of LARLY'sighring acepred by $c audonties was for rhe nonrb of

The main'e6oi

tor lare sishlinss or rtr five indicated occdsions is th€ overBrsky all o\€r lhe country in.lllbese caes.In case of$e onl)-' earty sigh ns for rh.Ianscven yea6 alt€npts for cRscenr siehring \ere n,ad€ rhe Obscdatory ofu.ireBity oa

Karuchi using 6 CodC reliacror rclescopc.'the prediction crnerion based on r-value

dllowcd cescent visibility with oprical aid and rhat based on 4-vatue did hot .llowed

visibilily eleo silh lelcsope. We failed in sighinS of the crsccnt bul rhe omcials

acccpted clains of mlied eye sighli.ss fron aR. ctoe to Kamhi. Akhough,(he d\o

$n$il cosidercd did nol allow naked ete visibitny on rhisoccasion lhc misconc+tion

lhat if rhe ph4se ol rhc cresenr is noE rh.n l% n shoutd be lisible (Asrmnonicul

AhnrnJ..:l]O7r n ayha\c leJd he,te.i. or D.Jtcr rorcer rt,e.tdtrn;.

The low percenbgc ofee6 in rhis obscryalion.l elfo,1 is much noE pbnisi.g d

compaGd b lhe 6ul$ of m@n wlch, progEms cohdEted in Unncd Slales in thc tar.1960s and rcpon€d by Dogger & Schsller ( 1994) Accordi.erorhh rcporl l5%positite

€rcs (qons clains of observing $€ cresceno and 2yo negadve eriou (cescenr was

visible bur rhe obsrveF nissd then) {qc iound monssr $c cxperienced ftoois"lche6. Thqe exF i.nccd h@n watcheu \v.rc geneElly consideFd b know wne,e lo

lind $c crcsce.r dd whar dc oiolatioo of rhe..homs" wa.

l9l



Freque.dy. claims of lery dy sighiiog e made in sonc rcgioG of paknb!

(pardculely for ianins rhe dontbs of Rd.a ad Shawat 4s ienrioned beforc) $at

ad nor accefled by rhe au|hodd€s. Oie offic Dajor @!s of rh4 dly clains ofsighting ofncw se$cnt in Pakisran is lh. kenness otlh€ clainr dd lh€ nisco.epdon

.mongst trasses ftar when lhe 'tighting" hos been eponed in the Kingdom of SaodiArabia lhe cr$€nt nrusl be sighred the ncxt day in palistan, However. tbe oilcilld<ision about slani.g n.w luiu Donth in lh. Kingdom ofsaudi Ambia is nor baed on

acrual signdng of lhe n w c6ent Thee d€cisions e based on cnrcria rhar have

chased tuee tnes ov€t $c pan two decad6 (odeh 2o0o).

Up ro 1999 the citria vas 6 fouows lf$e Moon.s age at drsunslis t2 hou6

or horc alter fi€ New M@q ihe pevious day is the fi6t d.y of lhe Islanic

nron6. fiis actually matu lhd lhc luDr donrh begiG on tu day ofconjuncrion

oa Moon vhich occurs on€ or two dats e.rlis than $e rime shen tbe n.N

crescent becom.s vhible ro lhe naked .ye,

Fmm 1999te crilerjon {6 chareed ro the tottowing: The tunar monrh besins on

lhe eEning *hctr the sun*1is b€forc tlt moon 9l according to Mrcca. This \as

no€ di$rtuus .s ir is Fssible lhar rhc sunsel befoe moonsd sil occur even

belbre rhe conjunction. Th€Efore. rhe hmar montn may begin three days betorc

rhe ccscent b€comes vhible to nlked cye.

Ftum 2001oD\ardr rhe cirdion is:

a) Tl'e s€ocemic onjudion scurs b€foP Sb*t.b) The Moon sck aner rhe Sun.

This is nore realistic bul it is scarccly possible thal the crcscenl becones visiblc

on dE day ofconjunction.

in)

The Min p@mders signinc.nl in lh. .arti6r visibilily crnerion for lhe luoa

cEscenlaE

LAC, AOE,ARCV, DAZ, ARCL, Phas ad lh€ widrh of cE$e.t. As

n.ntioned abov€ none ofrh€s pomelets alonc decide the visibiliiy or.on vhibilitv of

t94



lhe lmd ft*e.t. C€ncrally thc crnical valuc of thc Phsc b consid€Ed lo b. t%

(Astrononicrl AlMac, 200?). Duing rhc p€riod flom Jduary,2000 b Sepr., 200? $ar

were consid€.ed in lhis 3tudy rhe'e qs nor a sinsl. incidencc when rhe sidd.s otcEscenl with phN l.$ lhan l% ws eponed and am€/.d. There weE two @c6io.s

when lhe ph6e m grcarer rhan l% bur ihrr. ws no claim of sightings a.d sighting wsnot possible accoding ro bo$ lh. oitclia considqed (Oct. 23,2006 and Dec. 2l,2006).

In lhc cae ofNov, 13,2004 th. phase ws I l9% lhal may have been lhc Eason rhat rtre

siehting.lain qas accepred (as ne.don.d earlie4.

TheyounB€slcrescentof agc t9.l hou6(!r bstdheoivisibilny)eendurinClhe

period of study was thatof

May l'7, 2OO?.Apan from b.in8 $e

youngeslcre$eht seen

duing th€ Fnod of study lhc ob$rvltion has anottrcr inleresing teatur€. Thi5 Ms $e

or y case when thc cr.eent was sccn on ft. enc cEgodm date a it N6 born

ac@rding ro Patiskn sblded line. Apari ton $is record obstualion th@ are fou.

orhd clains ofyoung Moons sighling,Nov. 11.2004(22.1hours),tan.t0.2006(21.45

ho6), June 26, 2006 (22.76 houre) dd Fcb. 17. 2007 (2 t .6 hous). ln aI $eE vee 22

(21% of Ihe studied) ascs of sishdnS daiN when $c .se of M@n @ les rhfl l0

The obsemtion of Feb. | 7, 2007 @ nadc ar fic slronomical ob*Fabry ar rh€

Instrule of Spsce & PlanetJry Astophts'cs. Unrvcrsily ol Kr',(hr *. ,pou.a U.

cre$ent nsing lhe 6' Codd Refractor T€lescoF. Both rhe prcdidion crileria alto$ed

crc*enr sighri.g wirboul oplical aid but wc could se rh. cr€scenl wi$oul tetescope. No

other claim of qesenr siShring wa ac.iv.d by $€ aulho ies on rhis day, Tte

aulho lies acceptcd ou €laim. This was $c young*r ccseft sen ar ou obseoalory

d$ng lhe period ofsludy, It is a Ko.d for ou! obs.ryarory and rhc vorld recod for rhn

part'culaf clescenfs eeli.st obervarion (sw,ftoonsiahlina,con ddsv.icoprciecr.op). Our phoroSraphic r.cord h also posred on retevanr websnes.

!95



Tlrc'€ seE 6 c66 when thc ag. of M@n @ bciwen 24 hou's dnd 30 hous

ed rhe crescenl w4 not seen. Thus, ihis srudy also suppons th. idea that age is not a

depcndablc l&to. for any pEdiction crildion.

Anodier inrporbnt pdMeler concened is rhe noonFt-sun*l LAG. There are 22occasions *hen the crescenr of lag 60 minures or less was Fen. Oul of rhese only two

*ft wnh lag less rhan 50 hinules, Nov. l], 2004 with lag ]5 mi.ur€s a.d Aprit t0,

2005 Nith lsg .l,l minut€s. In ihe *co.d of thcse c6es rhe prediclion c (ia a o$€d

naked ele lisibility. There wer€ 15 cases when the tag sas b€lveen 40 and 50 minules

and bolh dic pEdic on crileria did nor altov crcscent

visibility *ilhoui optic.l aid, Tbls lh. n@Mr-sN4lag alone is also not a dependabte

parametef for any prediclioh criterion. Out of 95 new Moons rhe predic on crileria diferfrom $e Babylonian clnerion (Faroonhi et al, 1999) only g tines when Dabylonian

crnerion (ARCL + l"Ac(in deg.ect < 22) alto$ nalcd eye visibility but ,{luc ddlhe s-laluc cnteria do tur Howld, on rhese nine ccas

I'r view of tn6c fads we conclude rhat bod q-vatue ed r-value cilcda arc N€I

suilcd predicrior cireria with r !.tue clireion delcloped in $is work has mdginalty

be cr success percenrage ibr posnive ob$ralions (chapter 4). porricutarly in viewofrh€

facl dar $cs fire.ia do not march acrual cr.senr visibitiry onty in one ou 95 cas(1.057q).nd thal @casion Ns conkoversial in liew ofrhe above discussioD. Thc nve

cases Nhcn the cEscent $as seen hler tan prcdicrd aE not conside!€d as an ero! 0s thc

probl€n occun d d!. lo ore(sr skies. TtrGfoF, tor lhe tomulaion oa turueobenarional IuMrqlendar $ese Fediction dreia de nidly dependable_

TIE € has ben only o.e occasion whd lherc mrc three co.*curivc nonrhs of29 dars elcb (during June, July and Aususl 2ooo). This is rhe ndinum fo. Fpelnion of29 days lund nondrs anticipoied s e&ly a loricentury AD by Muslims ( yas, 1994a).

The li6t (Rabi ul Awal, I42l) of$is lriphr ofnonthsbeema day talerrhan p!.dicled

196



oftr\i'i$ lbir tNinun rcldirio! @!H ml lLv. tc.n th.Ia llxr! vt&r D ac&noo of

frt! (diD|d) coorc.rlir.! tdt! of 30 d!y! 6d h 6b Fiod of'lldy.

b. sighio8' ca c.r Morlly o.cN!nn8 Ep.ririon of fou 30 d.F' @d! io

f'v! o! sil Afthow\ rh. kludc shd. Lsw (cb{i.! t) dlos for con .don a! lndet o oh..wrrion idic:!. m m., bur ftr.dvmcc ptslirg nd dcv.toFEr 6tcdfm ohsE|ioo l|E .j-n/- h.!G.t d Fcdidioo diEir b{' grarty bclp. TtAFadix-V rhosa suh r ltnr c.ldr. in qdich .oryurrioB s! bed i! Knstti dlhe +v.lu. qilai@

tvl

thesis on the visibility of crescent-5

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