Visibility of Luna and Lunar Crescent

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25F-d;:Fi8 No 144A last sque qu.d6dc poltDnnl 6ncd b $jt d.L iGld! [E fi)llowing cl.rion:at-v DAz'1 PAzl + tt (r.4 s,lm 20Usiig lbls polynoni.t ed $e @nditid $d the (,B@tt would be visiblc if:ARC1'> !4: V1+r(34e)a.d lppli.d i to dd. us€d by rdtsirghd $e @h3 obrlid 4c prc&tn d in t$lc m3 4.4 !dfig.no 3 44 In lh. tabb t t lh. 'visibility p.m€rcl dcfin.d asl,,fl!0o20)), =f no", -l DAzl -P4.,\\(3 4 r0)II?
35302520151050-10. hisible Cre€cents . Visibt€ Cr€scontsfig. No 1.4.5Th. rrbl. 1.45 3how U[r !E @ft! br.d on Medd,s oaM &. suchinprevcd Md rhs. b dly * obqvdid j.. m 4j d le?l t4, tS7l, thd dqin6eon rhc @rdidoa (3.4 9) IE irbt. j 4.4 and dr fg!rc ooln sr|N rh|r ood.t du€ roM.udq is nu.h inpotld s ohprld lo rh. Dodet (!l. b ho Ein*hrn.rin.lly in rhis vort bolh the @ddq .trl. Forhdi|ghe .tr rh.r due |o M&i<t, &€appljed ro thc Ft..i.d 463 obs.rio$ nm '!brnr6d),e (Od.b 2OO4) nE @lbe p'lsrd i! ffBod m. I 4 6 (Fo.tEngn n,r mdct) &d 1.4 ? (Mr!id6t mod.t)arld oc rpFndix-tr (Colu@ C .d D, r6p€djidy).Th. fiCW m. 3.4.6 Dd dE r.bte i, r'p.ndir-n (@bm C) lhow Lt l rhq. !E alarae tumbd (90 our of t96 po.nirc 3igtni.g) of obb ,on! wh.n rh. dcaar Breloned vbibte fi.r dwin. AM FortEi.eho,s trFdet rd Lc betow rt. linir mvij.rtby th€ tul€ (3 4.4) d@ to Fdtdi,Bh.r Thi. a|€g.q! tb.r rrh. ll@s of the dte ishighly relr.icted to ih€ d!r. m which Fothdingnm wdr.d on and .equind sioull8
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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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$.t%'sr'(sfl + dI'.,)(r25)Tb vdB 6f
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a - sdimjor uis of th. dbill, = m@
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,is = I +l8O! Fs= -e 12.2.2t)ond th
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F " M@'!.4ruqtof hind.- ! 6'0.? ! a
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elled th. Julid Dare abb@ialed B JD
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How.r s noE @nhtlon l !'pNch ir ro
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Now orc n6ds ro c@t 6. nub.r of diy
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LMU-UMMstcFr2: alMM>2 { UW-C-1716 }
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DE to lh. nodotr of thc ob6*d. th.
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I. =6r4t-50'.54841+E tot84,.s12s66I
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t,-'i^,-"(t"*", \2tL,-ZA,s\8,+c,. I
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The coftcctions for Abe@don md Nura
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FimUy the coordides ofthc Ss @ Edcd
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Si"At = Sinpstnq +C6e,Cot6,CotH,(21
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An |pDDxiE.r. valu. of "'*" wirh e
Page 81 and 82: ranlAt =c6(Ir)s,,{t) rz,(d)co{l)(2.
Page 83 and 84: "='"[(289)Sinc. ihc acienl dd thc n
Page 85 and 86: 9. JD of Conjunct, rh€ Julie Dat
Page 87 and 88: rh*.@rdin l€s @ c.bdat.d th. etr
Page 89 and 90: TL dl irpde dgsitor tu d. ddroni4 m
Page 91 and 92: In rhb ch.pter we stan wtth a b,t.f
Page 93 and 94: wA diislaled by S. Oddz 6 Crlr of M
Page 95 and 96: 80(r. I r)
Page 97 and 98: for visibilny thftud rel.$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 $udying ihe behaliour of
Page 113 and 114: . yomg.r ct!.c. (f8; 3J.1). Tb nioi
Page 115 and 116: 'Ihe table in App€n.tix'U shos S.
Page 117 and 118: All lhe* conditions falolr rhe lisi
Page 119 and 120: ''if h. nns tizt b.nv.r -3,t otd 0.
Page 121 and 122: I415't00 loo zlo3b400^ actual RF br
Page 123 and 124: All thes. figu6 show ! lend for lhe
Page 125 and 126: In cae ofMoon nonh ofediflh:DAZ ! E
Page 127 and 128: 69{0. Fo(brilgb.(l (t910) hs &!.rd,
Page 129 and 130: w. d.firc a pa@et . !r ,.,visibihy
Page 131: fhis nbdi6c.tio! i! rn oL by Fo$dnB
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
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
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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){
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
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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
Page 251:
236
Page 254 and 255:
2t9
Page 256 and 257:
24rI
Page 258 and 259:
APPENDIX.IIIPHYSICAL MODELS211
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245
Page 262 and 263:
241
Page 264 and 265:
249
Page 266 and 267:
9!!!!!.39!44!C94-9!_q4!!,-!!:,-9!l9
Page 268 and 269:
253
Page 270 and 271:
APPENDIX-IVOBSERVATIONAL LIJNAR CAL
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ll:lf-Lt-ltlItlt6tTlITlt,ItrL tsllt
Page 274 and 275:
6 2P 3e g 9E:-Fa659 i it z p 5tI I
Page 276 and 277:
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
Page 280 and 281:
Hti 3 t I :3 ?tI I i6t5t93 t f3sa;2
Page 282 and 283:
\"9n30 An-"gR--=aii"R6,:6.;,{d3.- :
Page 284 and 285:
s:;;;g" :;iiR;;--6,itl=sl;!i9;p".-s
Page 286 and 287:
\9ia9g;:;5555;6,.liisi.-eFae:E-;(sF
Page 288 and 289:
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
Page 296 and 297:
?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
Page 302:
,a:Ill5. Sutt n, A. H,, 2005, Th. L
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Visibility of Luna and Lunar Crescent

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