Visibility of Luna and Lunar Crescent

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IE it ir ma dly lh koglh of.ilsc.d 6d nodo! htr lh. vilibL with of {tt*.alb! lo diminjrl rlso. Wh@\tr lhc cr.rcdt it ilviliblc 'nvi.w of (5.19) 4r'bs toc*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 Dlrtdilh!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'llcogth oflh. ctelcai k Sivcn bY:t;rr*"CY'*)(t.l.lr)Dmt
'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 $c Fis 5. l l the *8nent [D orAC is the ninimm width lil- at dv ARCV inlisibl€ according to Yallop's cliterionThe scgnenl AB is rhe thorcdcal widlh ltl" at fie cenrE of fie cresccr! Al sngularspaBrion vr from tbc centre olc€sent ED equh4(nrl/" 'lheefore the ponnt onrhe ouler linb oi rlc cresceni tbal las dguhr separaion fon cerrc geal$ ihans. = ZDOA should noi be visibl€ TIE lisiblc cls€ then crtnds fom D o D' @dhas letrBlh 2!rn. One should nole lhal Nheneve! ttl" (nininum vhible wid$ accordnr8 bYallop s nitrion) is Srearer tan ttlq ($coetical widtb) {5 1 13) can nor bc sed ind thecresceDi isnotlisible, ie iihas m lengdr'The tr1odel developed nl this Nork lo cotrlpute tlB lenglhoflhe crcsccnl hrs beenapplied 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 oflighl orARCL,ae ptscnled in lable 51 1and in Fig t'l2 Tlre loBlhs mcalculaFdby 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 ofrhe lcatioD of obseryer (Ldlilude and longitud€ Fspeclilclv) tbe rclatilc umull)PAZ). rlre dladve .hnude (ARCV) lhe clon8alion (ARCL) of $e Moon at lhc be'('r:drinc ofobstvalion. lbllowcd bv setr1i_didetr and lhc cental widh ol cr'scnl in arcninules. rlt 4_valu., lhe niDimum cF$enl sidlh viiihle at lbe rclatile alritudec.lculated lom (5.1 8) and finallt the cE$e'r lensth cdlculared usiie (5 1 11) Thetablcis aFmged in chmnotogi@t or<lr of ob$mtio's dd co't'ains onlv Paiof th€ conPleledata s€l lhat hs b€en used for conpaine mod'ls for carli esl crescenl siehting in pe!'ous180
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ON I'HE COMPARATIYE STADY OF MATHEM
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CERTIFICATEc. incd thn th. ..ndidlt
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Dedicated to my late motherAnwer Su
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AbstractThe pmbl.m of delemining ft
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allow visibilil, ofthe cltsm wilnou
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ilf'LLf' c)'i ",( ),1-t z-r -t z,li
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/'t' f'L )) L 72' A ety { d-- w L,t
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Phyaic.l Modala & their Evolution4.
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moden (Reingold & Dschowttz, 2OO1).
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SuDpoe ('-.r",/.)!d (.,,r",t) E thc
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5.6,1.E.10.B€dTimeofvhibilily TrA
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Thi! figue clorly 3howr th.! for hi
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and a.rc$cnr snh ldgc clone.lion $a
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Flarively r€c.nr rimes, ho$v€r,
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Solsr Cal.nd6 m b4d on the ulrl mot
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Arnhn.tic calcndar ther. are cilh.r
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8@rly vdied s6r lo s@n, 'fte t€en
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visul sighring epo.t must b. suppon
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visibility curve. So fd th. mod€l
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Chapter No, 2ASTRONOMICAL ALGORITHM
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O@ thc rim. of thc g.cdric biil of
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ine argunent md the explicii tin€
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Onc. lhe lincs of fting edor seltin
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L2.LPl&erary otbiB d. clliptic with
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BdicaUy a nhcory of pldelary ed lun
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$.t%'sr'(sfl + dI'.,)(r25)Tb vdB 6f
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a - sdimjor uis of th. dbill, = m@
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,is = I +l8O! Fs= -e 12.2.2t)ond th
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F " M@'!.4ruqtof hind.- ! 6'0.? ! a
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elled th. Julid Dare abb@ialed B JD
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How.r s noE @nhtlon l !'pNch ir ro
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Now orc n6ds ro c@t 6. nub.r of diy
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LMU-UMMstcFr2: alMM>2 { UW-C-1716 }
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DE to lh. nodotr of thc ob6*d. th.
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I. =6r4t-50'.54841+E tot84,.s12s66I
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t,-'i^,-"(t"*", \2tL,-ZA,s\8,+c,. I
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The coftcctions for Abe@don md Nura
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FimUy the coordides ofthc Ss @ Edcd
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Si"At = Sinpstnq +C6e,Cot6,CotH,(21
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An |pDDxiE.r. valu. of "'*" wirh e
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ranlAt =c6(Ir)s,,{t) rz,(d)co{l)(2.
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"='"[(289)Sinc. ihc acienl dd thc n
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9. JD of Conjunct, rh€ Julie Dat
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rh*.@rdin l€s @ c.bdat.d th. etr
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TL dl irpde dgsitor tu d. ddroni4 m
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In rhb ch.pter we stan wtth a b,t.f
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wA diislaled by S. Oddz 6 Crlr of M
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80(r. I r)
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for visibilny thftud rel.$ope. IlE
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(3.2.2)(3.2.1)FDm ridcle sh, st nir
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fig. 1.2.2: G@tn r.y ofP@riv. Ag. .
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usirg (3.2.l0) il tlr4 lat s into:(
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Sm p.r.[d lo lqldo. (difrcqE of ddr
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sin rr'r _ rh&sn(e+a) @s(e+a)erhlr
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As mc ioned abov. dE Mulin sao&Ders
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vi€w of $udying ihe behaliour of
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. yomg.r ct!.c. (f8; 3J.1). Tb nioi
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'Ihe table in App€n.tix'U shos S.
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All lhe* conditions falolr rhe lisi
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''if h. nns tizt b.nv.r -3,t otd 0.
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I415't00 loo zlo3b400^ actual RF br
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All thes. figu6 show ! lend for lhe
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In cae ofMoon nonh ofediflh:DAZ ! E
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69{0. Fo(brilgb.(l (t910) hs &!.rd,
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w. d.firc a pa@et . !r ,.,visibihy
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fhis nbdi6c.tio! i! rn oL by Fo$dnB
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35302520151050-10. hisible Cre€ce
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:i::alF{s_?{";+E:'-.-l {-:'lFia. No
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of Fsnivo 3igidier dwidirB froo rbd
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(54.lYo). Howv.r, in t m of th. su.
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e{inctton .nd sky briShtn* ds€ to
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Page 145 and 146: For thimer c6c.nr rh€ ,r + s aSai
Page 147 and 148: t32
Page 149 and 150: tJ4
Page 151 and 152: 1lzOur ofth. 196 positiv€ sighrin
Page 153 and 154: rr' = ls<t - c.{A RCv).os(D,4z))(4.
Page 155 and 156: i{Fig No 4'2 2lD addirion 10 @Ndtin
Page 157 and 158: In all crloldjoE in rhis rcrk rhe c
Page 159 and 160: @l@) of lhb wolk lb@ e 33 .M our of
Page 161 and 162: 4JSCHAEFFER'S LIMITING MAGNITUDE MO
Page 163 and 164: i = l,.cor ,+ 1i - lL I+441(4 t.2)r
Page 165 and 166: ,.tdchltl = K, r ^ s + K,' x, + Ko'
Page 167 and 168: Thdhold conExl vr| f.e.ltld. conbtt
Page 169 and 170: TheE is only onc noc clain ofnajcd
Page 171 and 172: t56
Page 173 and 174: t58
Page 175 and 176: T$LNa43.ltf t li rl!.a.l a, -r.81l1
Page 177 and 178: On lhe bais ofthh dlatioo wc tlcnre
Page 179 and 180: In gendl l@kingd Lhe @npt.rcdsl! $
Page 181 and 182: Wlen a ctirerion allows oprielty ua
Page 183 and 184: visibihy cws inii.lly corceived by
Page 185 and 186: nay be considced for an adv&k pGdic
Page 187 and 188: Chapter No.5APPLICATIONSDurin8 rhls
Page 189 and 190: l.nglh of new lum ccscenl (Qucshi a
Page 191 and 192: l2t +w \{5.1.5)wirh w is the dim€
Page 193: siglling of such a youg ed rhin ces
Page 197 and 198: 182
Page 199 and 200: Tabl€ 5.'1.1 (Conllnued)Durins rh
Page 201 and 202: Fig. No. 5. L7: Mesuemcnr of Length
Page 203 and 204: 180160'1101m1008060zlo15ELOIGAN()|{
Page 205 and 206: *.Fi8. 5.l.9i D.fici@y Arc rg.ind E
Page 207 and 208: ours-value crirerion-baed crireria.
Page 209 and 210: Freque.dy. claims of lery dy sighii
Page 211 and 212: Tlrc'€ seE 6 c66 when thc ag. of
Page 213 and 214: Chapaer No. 6Dtsct ssroN'ftis rvork
Page 215 and 216: dau ofnininum aE ofvision for difcr
Page 217 and 218: 'fte najor achjevem€nt of this m*
Page 219 and 220: old! b !|dc! in ruirD frr lh. Ft! 2
Page 221 and 222: { cl6c{): maime.u0; cltsqo; Daiuour
Page 223 and 224: rvhile(nex|sl=V');Eolory(50,29):@ur
Page 225 and 226: ,t){i(ho!P-24.0)iqhoul<0.0)ni.{hou'
Page 227 and 228: ){gmr4c6-0r{41.0+50.5484V60.0y60,0+
Page 229 and 230: iisha<o.0)sdelb-sinGlarrPvl80-0f co
Page 231 and 232: ]fo(i=o;i<l l4ii+){ fs.d(fpL2,'%li
Page 233 and 234: li((dnon8<90.0)&&(slon8>100.0))ddon
Page 235 and 236: )I(24299161.0) e=z; el${ alph<doubl
Page 237 and 238: li(|enrd)s.t6i8_n0ilt{(3€c<1.0){
Page 239 and 240: nmFsin({50_c/60.0).Pv180.0)-sin(pla
Page 241 and 242: mooi coord(i),llii'i--.Ji. i:s'pv r
Page 243 and 244: gobxy(l 6,1 9);conven-dns(fabs(sdel
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fem-Doq(IO0,(o I5'telomorv400)|'62'
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2!2
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234
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236
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2t9
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24rI
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APPENDIX.IIIPHYSICAL MODELS211
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245
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241
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249
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9!!!!!.39!44!C94-9!_q4!!,-!!:,-9!l9
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253
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APPENDIX-IVOBSERVATIONAL LIJNAR CAL
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ll:lf-Lt-ltlItlt6tTlITlt,ItrL tsllt
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6 2P 3e g 9E:-Fa659 i it z p 5tI I
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Ellel];Il;ln-tlslft flflt"6rT<Fl!tg
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3p 5t E Et c T & Is$i$:lt I I:Ea!aI
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Hti 3 t I :3 ?tI I i6t5t93 t f3sa;2
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\"9n30 An-"gR--=aii"R6,:6.;,{d3.- :
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s:;;;g" :;iiR;;--6,itl=sl;!i9;p".-s
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\9ia9g;:;5555;6,.liisi.-eFae:E-;(sF
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RETtrRENCtrSLAlned, M., 1991. Oigin
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17.Bouwcr,D&Ctcmence,c.Ac.d€nic P
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36. Dulka J,, 1988- "oi th. Grcgond
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57, ffys, M., 1985, "vi5ibilily ofd
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?6. McNarl, D., 1983, The trnsth of
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96. Plulmq, H. C,, 1966, An Intlduc
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116. Schefcr. B, E., 1990, "T.l@pic
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,a:Ill5. Sutt n, A. H,, 2005, Th. L
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Visibility of Luna and Lunar Crescent

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