Visibility of Luna and Lunar Crescent

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t0.0 < .1R,. < 1.6 p8tbiti,tr o! ,hltw o! Ji6t M@nt btrh ond withouloptt ol h staq !o, tigt.r tdlituds. Lo.a!|rA N6t tuith opticd! a ! a".!th.a try nelnE lt Nlth haL.d e!. h6 a eood .ranc. o! opticdlr u"tidedne,> 1.6 th. pNtlbnrr oJ' tbi!i!, oifust cnse wtuhout optcat t st onaJor bo& Iow.r and highu tatttud.t,,Another way oI lootjng inio ih€ delaih of Lue Ripene$ hodel is lo look inrothe plots ofaverage ripehess fmcrion md rhe acod ,ipenes tuncion for borh vhibh &dinvisiblc crcsei$ for single talirude, U.forluarcly, rhe dru avaitable dd considercd inlhis work h Esrficlcd in rhc F6e lhat scieltifically re@rded ob*dalions fo, a sinetchnud€ a€ nor found lery fr€qucnrly €xcept tor Athens (ladrude 38 dc8,as .orrh) edCape Tou (laritude 13.9 degr4s so!rh). !n panicula, for sn,I€r tatitudes. plac6 cto*IoequarorobseruatiouarelolvcryfFquenuyav.ilable.Anunb€rofplaccsecsetecredherc od tbeir d.h pto(cd for Alerage Ripenes Fundion &,, and the Acllal Ripen*Fuiclion R6y for borh rhe Eponedty inlisibte dd the vilibtc oe*mr! Thesc jnctudcplees with laritudes L8N, 33 95, 6.5N dd 38N (FiguB 3.3.6 1o 1.1.9).Figure 3.j.6 for tadtude 3 L8N snows tbe b€sl slcsieh,incs ou, of 6 (83.37") in asrcen€ wnh $" ,_J:'iff:ln:"11,'#:J:obscdat'ons (6 our of6) e in agrccm€nl wilh the ta* toi this larilud€. Nexr is Cap.'rown-(hnndell.9 S) wirh succcss percenhgc 65% (ll posrlire siehings in sgenenrod, ol 20, the needrvc obseryauons fo, Cap€ Toq are In agrehenr sirh la\ tor9lJ% c66. This 6 ao owed by ,40r.6 (ladrlde 39N) w,rh 2 oul of3 {66.7910) posirivceghlingsad II o of l8 (61.l%) neSariv€ sighdnes a8rce snh fic lav. Ior laritude 6.5deg!.es, I our of2 (50%) posilive sightings od 4 oul of6 (66 ?y.) asE. wirh rhe tan.I05
I415't00 loo zlo3b400^ actual RF br in\isibte . e.lrrr nr Or ri"tOreFia No. 3 3.6: Rjp.@r Fundion for r-ditute 3 L8 d€g.c Nonrr---r;-+:;b.,RF6.'"".b,..acrld RFig. No I 1.7: Rip€lB Fudid for C.p. Tow4 Sqth Anic!, Lgnbde r3.9 it€lr*t06
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ON I'HE COMPARATIYE STADY OF MATHEM
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CERTIFICATEc. incd thn th. ..ndidlt
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Dedicated to my late motherAnwer Su
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AbstractThe pmbl.m of delemining ft
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allow visibilil, ofthe cltsm wilnou
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ilf'LLf' c)'i ",( ),1-t z-r -t z,li
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/'t' f'L )) L 72' A ety { d-- w L,t
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Phyaic.l Modala & their Evolution4.
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moden (Reingold & Dschowttz, 2OO1).
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SuDpoe ('-.r",/.)!d (.,,r",t) E thc
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5.6,1.E.10.B€dTimeofvhibilily TrA
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Thi! figue clorly 3howr th.! for hi
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and a.rc$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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$.t%'sr'(sfl + dI'.,)(r25)Tb vdB 6f
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a - sdimjor uis of th. dbill, = m@
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,is = I +l8O! Fs= -e 12.2.2t)ond th
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F " M@'!.4ruqtof hind.- ! 6'0.? ! a
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elled th. Julid Dare abb@ialed B JD
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How.r s noE @nhtlon l !'pNch ir ro
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Now orc n6ds ro c@t 6. nub.r of diy
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LMU-UMMstcFr2: alMM>2 { UW-C-1716 }
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DE to lh. nodotr of thc ob6*d. th.
Page 69 and 70: I. =6r4t-50'.54841+E tot84,.s12s66I
Page 71 and 72: t,-'i^,-"(t"*", \2tL,-ZA,s\8,+c,. I
Page 73 and 74: The coftcctions for Abe@don md Nura
Page 75 and 76: FimUy the coordides ofthc Ss @ Edcd
Page 77 and 78: Si"At = Sinpstnq +C6e,Cot6,CotH,(21
Page 79 and 80: An |pDDxiE.r. valu. of "'*" wirh e
Page 81 and 82: ranlAt =c6(Ir)s,,{t) rz,(d)co{l)(2.
Page 83 and 84: "='"[(289)Sinc. ihc acienl dd thc n
Page 85 and 86: 9. JD of Conjunct, rh€ Julie Dat
Page 87 and 88: rh*.@rdin l€s @ c.bdat.d th. etr
Page 89 and 90: TL dl irpde dgsitor tu d. ddroni4 m
Page 91 and 92: In rhb ch.pter we stan wtth a b,t.f
Page 93 and 94: wA diislaled by S. Oddz 6 Crlr of M
Page 95 and 96: 80(r. I r)
Page 97 and 98: for visibilny thftud rel.$ope. IlE
Page 99 and 100: (3.2.2)(3.2.1)FDm ridcle sh, st nir
Page 101 and 102: fig. 1.2.2: G@tn r.y ofP@riv. Ag. .
Page 103 and 104: usirg (3.2.l0) il tlr4 lat s into:(
Page 105 and 106: Sm p.r.[d lo lqldo. (difrcqE of ddr
Page 107 and 108: sin rr'r _ rh&sn(e+a) @s(e+a)erhlr
Page 109 and 110: As mc ioned abov. dE Mulin sao&Ders
Page 111 and 112: vi€w of $udying ihe behaliour of
Page 113 and 114: . yomg.r ct!.c. (f8; 3J.1). Tb nioi
Page 115 and 116: 'Ihe table in App€n.tix'U shos S.
Page 117 and 118: All lhe* conditions falolr rhe lisi
Page 119: ''if h. nns tizt b.nv.r -3,t otd 0.
Page 123 and 124: All thes. figu6 show ! lend for lhe
Page 125 and 126: In cae ofMoon nonh ofediflh:DAZ ! E
Page 127 and 128: 69{0. Fo(brilgb.(l (t910) hs &!.rd,
Page 129 and 130: w. d.firc a pa@et . !r ,.,visibihy
Page 131 and 132: fhis nbdi6c.tio! i! rn oL by Fo$dnB
Page 133 and 134: 35302520151050-10. hisible Cre€ce
Page 135 and 136: :i::alF{s_?{";+E:'-.-l {-:'lFia. No
Page 137 and 138: of Fsnivo 3igidier dwidirB froo rbd
Page 139 and 140: (54.lYo). Howv.r, in t m of th. su.
Page 141 and 142: e{inctton .nd sky briShtn* ds€ to
Page 143 and 144: cxnibircd in n8 9 ir is mr.d lhnl a
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
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t56
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t58
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T$LNa43.ltf t li rl!.a.l a, -r.81l1
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On lhe bais ofthh dlatioo wc tlcnre
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In gendl l@kingd Lhe @npt.rcdsl! $
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Wlen a ctirerion allows oprielty ua
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visibihy cws inii.lly corceived by
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nay be considced for an adv&k pGdic
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Chapter No.5APPLICATIONSDurin8 rhls
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l.nglh of new lum ccscenl (Qucshi a
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l2t +w \{5.1.5)wirh w is the dim€
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siglling of such a youg ed rhin ces
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'I}lus $e ae$c len$h cd be dalualed
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182
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Tabl€ 5.'1.1 (Conllnued)Durins rh
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Fig. No. 5. L7: Mesuemcnr of Length
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180160'1101m1008060zlo15ELOIGAN()|{
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*.Fi8. 5.l.9i D.fici@y Arc rg.ind E
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ours-value crirerion-baed crireria.
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Freque.dy. claims of lery dy sighii
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Tlrc'€ seE 6 c66 when thc ag. of
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Chapaer No. 6Dtsct ssroN'ftis rvork
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dau ofnininum aE ofvision for difcr
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'fte najor achjevem€nt of this m*
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old! b !|dc! in ruirD frr lh. Ft! 2
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{ cl6c{): maime.u0; cltsqo; Daiuour
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rvhile(nex|sl=V');Eolory(50,29):@ur
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,t){i(ho!P-24.0)iqhoul<0.0)ni.{hou'
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){gmr4c6-0r{41.0+50.5484V60.0y60,0+
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iisha<o.0)sdelb-sinGlarrPvl80-0f co
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]fo(i=o;i<l l4ii+){ fs.d(fpL2,'%li
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li((dnon8<90.0)&&(slon8>100.0))ddon
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)I(24299161.0) e=z; el${ alph<doubl
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li(|enrd)s.t6i8_n0ilt{(3€c<1.0){
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nmFsin({50_c/60.0).Pv180.0)-sin(pla
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mooi coord(i),llii'i--.Ji. i:s'pv r
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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
Page 278 and 279:
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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