Visibility of Luna and Lunar Crescent

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T.bl. 5.1.1 {Continuedr8l
Tabl€ 5.'1.1 (Conllnued)Durins rhis {ork $e ?O obw.tions of Dfljon (ne ionc{ bv Scha'lTsand Fabohi €1. al.) @uld nol he acc6sd, howvc. the pictotjal data of cdccnt ltngth irbeins eeneraied at fte Asaolonical Obsdllory al Univdilv of Kdachi. Th! obseNedcBcell lengh fon phologEphic Ecoids i5 given in Tabl€ 5 1 2. This inclldes soneobsryadons made by olhe^ durirg past fe{ ycas and tbeir pictutes ate availoble liomM.icproi.on maiDtaind by oteh,184
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ON I'HE COMPARATIYE STADY OF MATHEM
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CERTIFICATEc. incd thn th. ..ndidlt
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Dedicated to my late motherAnwer Su
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AbstractThe pmbl.m of delemining ft
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allow visibilil, ofthe cltsm wilnou
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ilf'LLf' c)'i ",( ),1-t z-r -t z,li
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/'t' f'L )) L 72' A ety { d-- w L,t
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Phyaic.l Modala & their Evolution4.
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moden (Reingold & Dschowttz, 2OO1).
Page 19 and 20:
SuDpoe ('-.r",/.)!d (.,,r",t) E thc
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5.6,1.E.10.B€dTimeofvhibilily TrA
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Thi! figue clorly 3howr th.! for hi
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and a.rc$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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cxnibircd in n8 9 ir is mr.d lhnl a
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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 and 194: siglling of such a youg ed rhin ces
Page 195 and 196: 'I}lus $e ae$c len$h cd be dalualed
Page 197: 182
Page 201 and 202: Fig. No. 5. L7: Mesuemcnr of Length
Page 203 and 204: 180160'1101m1008060zlo15ELOIGAN()|{
Page 205 and 206: *.Fi8. 5.l.9i D.fici@y Arc rg.ind E
Page 207 and 208: ours-value crirerion-baed crireria.
Page 209 and 210: Freque.dy. claims of lery dy sighii
Page 211 and 212: Tlrc'€ seE 6 c66 when thc ag. of
Page 213 and 214: Chapaer No. 6Dtsct ssroN'ftis rvork
Page 215 and 216: dau ofnininum aE ofvision for difcr
Page 217 and 218: 'fte najor achjevem€nt of this m*
Page 219 and 220: old! b !|dc! in ruirD frr lh. Ft! 2
Page 221 and 222: { cl6c{): maime.u0; cltsqo; Daiuour
Page 223 and 224: rvhile(nex|sl=V');Eolory(50,29):@ur
Page 225 and 226: ,t){i(ho!P-24.0)iqhoul<0.0)ni.{hou'
Page 227 and 228: ){gmr4c6-0r{41.0+50.5484V60.0y60,0+
Page 229 and 230: iisha<o.0)sdelb-sinGlarrPvl80-0f co
Page 231 and 232: ]fo(i=o;i<l l4ii+){ fs.d(fpL2,'%li
Page 233 and 234: li((dnon8<90.0)&&(slon8>100.0))ddon
Page 235 and 236: )I(24299161.0) e=z; el${ 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
Page 245 and 246: fem-Doq(IO0,(o I5'telomorv400)|'62'
Page 247 and 248: 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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