thesis on the visibility of crescent

8/22/2019 thesis on the visibility of crescent

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Chapaer No. 6

Dtsct ssroN'ftis rvork $is inrsd.d to qplorc fld.ompae fic mathcmaical nodels for the

crneds under which rhe new lund cresenl could be lnible at silen locdion on thEanh, Mormk!, it was intendcd that acomparhoD offiese nlodcl is conducled and themodels are nodified if posible, The lask of compdien od nodiEcadon of the nodelhs ben succcsstuuy achielcd dd a neN model the r.vahe criterion has heendcveloped. A sumdary ofthis wo is presnted below sith r dkcusion on the najorachicvedenG ofllrc Nhole eihll.

Fi6t ofalla bener undcFt.nding ol$c issues. conpubrional, aslrononrical ddobrerarional, associated wilh rhe prcblem;f l|t firet sishri,lg of$e new lLmtr ssenris devcloptd. Wc have xplodd the comPulalional tchniqucs and tlrc asrcnomicalalSornhm dd rhcir applicadon (o $e extcnt that is .ecsary aor rhe calculationsirrvolved in solving lie problem desribed in nr pEviors paraeraph lrritially lhcrcchtriques wcre nnptmenled on Miciosoft Drcd work slcels bui duc lo leDglh,calculalions and lhe use oflong fomuld Ne \cre for.ed to dcrclop a cortputfr prcgnDtlilalol. T]le prognm has been used lo do allcrlculations lbt detemining c@ldinalcs of$c sun sd $c Moon.s well as the padmelcs inlolved in oor pobhm lhe rc$'lts ol'nr. applicalion of $ne of tne modcls @ obunEd $ithin ln. pro8nn and lltosc for othermodcls arc done on fic basn of $e dala generaled by pngEm thal is salcd as ao ouqulfllc. This file is $e. kanslom.d into an MS-Dxcel rork shet md lhe resuhs of orhcrmodeh re oblained therc. Tbc hbls comp sing thse ts!l$ tifiin dre m.in txl andthar apF{ in |hc apFndiG rc all dvelopd fon rhes *otk shets

The modcl due to Babylonies as d*dibed by Fatoohi et$at wa modilied by the MuslintAFbs is bricfly desribcd ir

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1..2) dd is ns applicarion is srudicd jn companson with other nodh in cbapls ] (anicleLl) and chaptq .t This tule is based on lhe sun of$c elonca(ion ahd the dc oflision-the Lunar Ripcness rule dednced by Muslins of rh. mdieval eh in exploEd moreerrensirely. h is loun'i rhal though, $e Lutur Rip.!6s function is fo Dorc sophisl,caleda compaEd ro the Brbylonian rulc, the luo mclhods prcducc almost equivalent Esuhswhen applied to rhe re{nl obseRational ccords.

'lhe $ct|rds h3sed oD relalions bclwe$ arc ofvision (ARCV) and $e tclJrivcazimurhs (DAZ) rhar \ere extcnsivcly develop.d durinerharlypanoflhe 20- ccDrutvae loud noE sucesful dlrins lhis study in compdison lo U ancienr and DcdielalDerhods The suoce$ in masuEd in ho* nany obseNalions are in agrcened wnh lhemodels. I lorv mdny rines lh. cFsccnt is seen wlEn fi. modls suggcsls ils visibihy.ndhoN nan! tiDcs lbe c:.sceol is nol seen shen lhe nodcl aho suCgesls inrisibilny.

lhc rcnen rhl fie oodels blrd I'n ARCV-DAZ tlalions are norc $cccsslul isirar wilh ihcrcasins rrlative azinu$ thc biCllNs corrdsl oflhc crcsccnt aalnrn rhoskybrilhhess impro\.s and the crcscentsofloseirclariveallitude ure visible. Sm.llerisrlc DAZ lhis b e]trr$ com6l dclerionlcs lnd lhc crcscn( is only \isible al hiel'cr,^RCv. h comprnotr to lhcse models lhc Lunlt Ripcncss tutrclior is slronglv buscd onrc of scpdlion. lh. toblcm $nh arc ol sparaiion is th $nh l ge DAz n tan ti-nruch snaller rhdn su-lgesrcd by lnc Lunft Rip$es law (10 to t2 d$recs) loi a lisibldcr.sceit. ln rl$e cas.s \vilh large DAZ tlrc Ripene$ luncliorr ,4,r can bc llrgc so lhrlrhe larger valLEs of R,,, arc eq Ed. Conseqlendy. aor lrse. lrtirudcs ldgc .rc ofscparalion is EqutcJ But lescr DAZ for larger laliodes auoNs snaller ARCV rtrdcon*qucnrlt smrll( rc of scpration. fhercfore, cspeci.lly for localioDs Nit largcrhdudes Lunar Ripcn.ss law beomcs more inconsnrc s comparcd b the obscNtrionsand thc ARCV-DAZ nodels.

ll is sftn du ng $c di*usion ar rhe .nd of lh. 4ri cbaplr lhal lhd ARCV_DAZba*d nodeb, the ForherihShmr's modcl. th Maundeas mojel and lhe lndian nrodel aEsuccessivly belrr. These imprct.menls ae due to deducrion of b.ner and b.trer basic

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dau ofnininum aE ofvision for difcrc el.tiv. uinurhs- tlowrcr. all th.* modclsisDrc the ridrh of fi. n.w lba cas4.d ftar vdie SMrly with thc Eanh-M@ndiskrcc for rhc saec elongllion. Thk c.!s!s vdiatioB in thc elully bdshh.s or th.Eeent of emc donsdion. Cons.qEntly, ft. s. pln of ARCV ad DAZ $ct'i8hh.s of casnt v&i6 for dif.rcnt Eanh-M@n disranc.s. Th lsk of thisconsiddrion is rh. Fain caus. of l.ss.r succ.ss pec a8. of $.* n.thods NconDlEd to the later ftod.ls foi posnilc ob*nations.

Th. Glliaion of vdyiiS bid nas of crc$crl si$ fic widrh or cE*.nt ro!se lonSa on (and $m. pih ofARCV-DAZ luct thc phriical d.$nPlion otth.poblcm by Bruin lead Yallop ro dcduce bdic dala lating widtu ol cErent to $c arcol visioi. Yallop d.dwed this dll! fod $c minima of lhe linning visibihy .ur$ ofInuin. Cons.qu.ndy. Ydlop @s su.cc$ful in dcducins hh3inel. p.6nttc' r.sr. rhc 4_ulue ciledon. This crir.ion Produed bdler Gsuhs i. compari$n to atl th. ptcviousmdhod!. Th. dcdudion ofvadous visibiliry condirionson lh. bsis otdircBnt dngcs o!.r.valu.s $d rh2t ol rhc besr rimc of visibility' of .een frem rh. limitins risibilirvcunes of ENin !'e thc motr markable of Yallop\ contibution l-hc \isibili'!condirions pro\ idc ruidclinca lbour uds *h.t condnioos rlt co*cnr \ould hL casilvrisibl. $hcn n $ill b. visiblc undo P.rfcd st.rhct condnions whc. Ue opricrl \o(ldb< Eqlircd .d when fte cB$ent $ould bc sinPlv nor visible $ith ot Nnhout atrvopti.al aid. rfu* condilio* har. poKd ro b. noN and morc Eli.blc $i$ incBtsnB

Thc najor co bution ol or e is rhc comp.ri$tr ol .ll fi. htljcls@rclically, frathcm.ricElly, phytictlly.nd in vi.w of$eir success p.rcentagcs 'or as.r of ob*wations colled.d tom d. l.t. l9ri c.ntorv till dcntlv. Anorhcr 3isnillcstcontribudon ol lhh wott is lo convcn aU th. mo


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", =(^* - l- # -e4,:!.,'l)f "v, =ltncv .lo.no - o.orn1o.tz1-

tt =(^RCV - lrt.8311.- 6.3226tv + O]llgr2 -O.tOl8V3rttO\t, -t5 + py rxtr+,pfl

vr=ARCL r !rc olscpaBlion - 21"

o.ooot uaz2\lto

v | = tARcv - \t2.4023- 9.4818W + 3.9512W | - 05612Wt D t rc

ln rhis {ork schactels modcl of dldritc bdshrn$ is ale erPlond in t.ms ofnasnitud contrrst tnd thc dsllE aF in lsRD.nr $i$ his wo* (Schelet 1988.) -n'hhas ben ehieved by iniplcmenrine lh. rshliqus d.r.loPed bv Schel.r and o$ets |oev.luarc sky brighhes (in tems of linninB mgnitud.) and r brishtocss ol lhecE$nL Biglrness ofsky and that otcE$cnt dcp.nd heavilv on various ihosphencarsrs Amongsr ths lenpeBluE and clolivc humidnv arc lcpl \2riabl. in theposram Hilalol in ord.r to exPlor posiblc condilions undd which claims of nlted ctcv'sibihy m.y b. Br.d for dillEnt condilions fhis lc.ds lo wh.t Ne h!v. rmcd 4Magdlude Conl6r (Amag _ maenilud. of Moon - skr's linritnl8 a!!iNdr) lfmognnrd .onl6{ is n.galit n is lalour of cN*tnr visibililv o'tunvie Dol [orcxftnEly crilical n.kcd cyc obserylrion ckn$ of Nw lunlr ce*cN lhe magnitudeco 6l lE ber dallaled nrinut lv h i5 tolnd $d $he of ftcs cdcs appear doublful6 fie oasniude conrEst @ n.v.r in Lvout or cc*ent tisibililv cv'tr with hidlvex.8g.ra&d wathr coDdnioB (v.ry tow clttivc humidnv and lcmPtdur) lor thevhole dudtion of th. ooonsd-suet hg |inc. Using th. pogim Hilatol the tin$ haveben evaluat d of(i) \$en $c nasnitud contGi is ndinn (ii) whcn rh' nasniludeconlldr jnrl bccodc ialouEble for crcsa risibililv and (iii) {hen rhc masnirudcconm was last in falolr or ccsenr vkibilirv Th.s. esulN .r. sinild $ whar isde*ribed by. veniccl line ovr. liditing lisibili(y cur. ofBruin

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'fte najor achjevemnt of this m* is th. romulation of t neq sincle pstuerercireion on lhe b6is of rhe Fchniqus deleloped bv Bruin and Yallop using lhebngnrrc$ modcls develoFd bv Sch&fer dd othe6 rhc visibilirv cuFes and thcliniting visibilily cwes aE developed for crceenls ol diffeEnl widrhs ll'!l wcrcactually obened tnd hav. bcen rcpodcd in lile6tue Bruin dcvelopcd lhe$ cllvcs on|he bdis or{i) lhe ale6se bdshlnss ofthc tult M@n md thc wv i dalt,s *nh rhedecrsing alftude abole hoi@h and (ii) tbe avedge brighiness ot the skv dudrgt*ilid &d fic way n depends on lhc dolld d'prc$ion b'lov horizo' On lhc olherhand tc bave usd rhe adual brightncss for Ihe obscb-ed cEscnB ola fixed wid r llEnlor tn sne ofobselvation we hare calculared th' al ude of skv poins bavins rtrc smsbridft$ d $ar ol lh dcsenr for difrercht solar depcsions such compuratios mEpai.d for a nunber ofobseryed cE$e 5 of the sahe wjd$ al dilIelenl localions anddmes. The aliudes or thc skv poitrts lhu obt'ined re ten 'vc6Bcd our Thc wnoleprccess h rhe. rcpeaFd for cnsce.t ofdilTereni widlhs

These conpulations tesulled inlo our lisibililv curycs ed $c linnins visibihvcuryes. The linitihB lisibilitv cses we have obEined ae slishtlt diferenl 'iod $oseof Bruii with nini@ slightlv displ&cd The ntlighl linc joining thc ninina oi dEscudes has a slope of9 3/5 as compaftd to 9/5 for Bruin s cutves Tnis lcads lo slighd,differe b.sl dme of visibililv" which is 4 l/9 1 rine th noo'elsuosl lag aller thcsuet (6 cohPdcd lo Yallop s be$ tine which 4/g rincs $e noonst-sunscl lae afietrhe suset). Th bdic dala ob$inod fion the ninim olor liniringlisibilnv cu8e l-rttdb a fiird desee Polvnodial tsuls inlo the fouowine

visibihv pdamslcr:

s =(.4RCV - (4351 31 /3 + 2222075057t4! - 5 422641ritf + l04l4l?tt)/l0we have als dedeed visibilitt condi$ons in a tumt simild io lbar of Yallop'

Our vhibihy condilions tre sliCh v difiere lron those of Yallop Howevet' ltplj_'n8our model on the obseNatioml dal! the succcss

pcrcenrage is iound lo b' thc besldongn all the dot nodels tll erist and lhar dc ncd dd conpaed in lhis \orr'Thc e6on is tbat our model is baed on $e acrual skv brighhre$ and lhe btislrhss oi

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(escenr $idr varying wea$cr condilions whercas Bruin s nodel h based on aleragdbrishlncssofsky dd rhe FullMooo.

As claind by Sctaefd th brightn s modcls @v b in mt by a mucb a 2elostill our Drodcl yielded be .t resul$ s comPsed 1o tho* due to Bdin ad YalloP as laras rhe posirive observatiohs arc conemed lt is lroped rhat wilh beller models of skvbrighhcss slill beiterclitrion ior fiGt !isibility ofnew lund descent can be delclopcd

sonE of$e lpplicarions of {he cnbda of.atliesr visibililv of ne\f llod 'rc$ctrthavc becn considered in $is $ork The fid ond $c mosl impoddnt applicalion lre rod(eaniDc Nhcn tbe new lunar cresceht would b visible ar soDe ldalion on lhe elobc onrhe elennrg aicr rh oonjundion Anolher ar.a ol appl'calion is lo deduce d''obscNnrioMl lunar c.lcndii- tor a 'eeion Yct anofier aBa ol apdic'tion \e hn\ce\ploreJ '.roJdrnrine lhe lcnslh ofne\ ldDrr crcs(nr

t( !1ay be recalled (hal lhe liret appcardnce of new llnn crcscctrt nrarlis rbsinning ola new monrh in obsenalional lunor calendarq rhere 'ril'ria

and models drcsiBnillcor br calendatical Purposs whefier 'n aduul o6n:ri'nol lunar calendai likcrlc hliNic Lunar calendar' ulilizrs tb6e cril.da for a!6nging its cltndar ot Dol lhcsccLirdia ptuvidcs a guidancc Ibr bolb tesing an tvidcnce oi oescenl sightirrg bv connnonpeotlcdnd tacingdowndtdtrlesofac.lndar inhhrorv{herc approprirle dates arc rol\ll Ncordcd. rhus $c frtin ' ililt of the pcdicrio! crileria 'or $e carliesr visibiln)' olnrv crc$.m is lo egntalc tnc obsefl.lional lunar calendtr dd tcsrifv lh clainrs olrisibility of ne\' lunar crcsccm

Although fiIsl ordc! iPporirutions like Arnh'neLic Lunar Calendtr tlrat di'based on lle concpr of Le.p Yea$ md rne a!.rage oorion o' rnc Moon havt be'n nr lseMuslims h.vc been follosin8 acoal sighing of crescDLs 'r l@l lor lhe monlhs oli6rii8 (R.maan) $d pilsinage (zil hajjah) Thc calendars if bled o' a PEdicrionoir*ion like tbat of Yallop or dre ohe dcveloped in this work arc $e cLosest lo rncobervarional calendd Conpan$n of rhese criteiia wiih lhc actual obFNsdonll

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old! b !|dc! in ruirD frr lh. Ft! 2000 io 2005 blc Da dc (q!!thi sdKlte, 2005). h lbir q'!rt 6. mrdy it cid.!d.d lo tb y{ 20(I|. It i! biDd lb. dlvdsc 9J% obtlnltiol! lrc m.oding to th! Y.llop'! r-uh. dt rion d our GEluc(d Q&K) dilrio D. diltgt@t is lb. !!3rlt of lithd th. t d wtt|t r dM !o *hi'h&e rw |E|r c{&. codd nol t tigln d dd tb Lud E olh b.t!! oE &v l.|c qrbo AdrDirtic cLiu6 of otsElion tld {t L|e dot:t t g.! oE &t dlicr U|n

Tbit tt|ldttbL !|gs for th. vi.ibnft, (ritsi. for ol@t'.ridl pltrPo" hBoorivcd |' to d.dE e "bt 6v.liodl lE[ c.lct b." for P'lii..r 0|al ts tctr

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thesis on the visibility of crescent

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