Visibility of Luna and Lunar Crescent

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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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cxnibircd in n8 9 ir is mr.d lhnl a
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For thimer c6c.nr rh€ ,r + s aSai
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t32
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tJ4
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1lzOur ofth. 196 positiv€ sighrin
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rr' = ls<t - c.{A RCv).os(D,4z))(4.
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i{Fig No 4'2 2lD addirion 10 @Ndtin
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In all crloldjoE in rhis rcrk rhe c
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@l@) of lhb wolk lb@ e 33 .M our of
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4JSCHAEFFER'S LIMITING MAGNITUDE MO
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i = l,.cor ,+ 1i - lL I+441(4 t.2)r
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,.tdchltl = K, r ^ s + K,' x, + Ko'
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Thdhold conExl vr| f.e.ltld. conbtt
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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$h cd be dalualed
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182
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Tabl€ 5.'1.1 (Conllnued)Durins rh
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Fig. No. 5. L7: Mesuemcnr of Length
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180160'1101m1008060zlo15ELOIGAN()|{
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*.Fi8. 5.l.9i D.fici@y Arc rg.ind E
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ours-value crirerion-baed crireria.
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Freque.dy. claims of lery dy sighii
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Tlrc'€ seE 6 c66 when thc ag. of
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Chapaer No. 6Dtsct ssroN'ftis rvork
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dau ofnininum aE ofvision for difcr
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'fte najor achjevem€nt of this m*
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old! b !|dc! in ruirD frr lh. Ft! 2
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{ cl6c{): maime.u0; cltsqo; Daiuour
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rvhile(nex|sl=V');Eolory(50,29):@ur
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,t){i(ho!P-24.0)iqhoul<0.0)ni.{hou'
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){gmr4c6-0r{41.0+50.5484V60.0y60,0+
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iisha<o.0)sdelb-sinGlarrPvl80-0f co
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]fo(i=o;i<l l4ii+){ fs.d(fpL2,'%li
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li((dnon8<90.0)&&(slon8>100.0))ddon
Page 235 and 236: )I(24299161.0) e=z; el${ 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
Page 249 and 250: 234
Page 251: 236
Page 254 and 255: 2t9
Page 256 and 257: 24rI
Page 258 and 259: APPENDIX.IIIPHYSICAL MODELS211
Page 260 and 261: 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
Page 272 and 273: 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 288 and 289: RETtrRENCtrSLAlned, M., 1991. Oigin
Page 290 and 291: 17.Bouwcr,D&Ctcmence,c.Ac.d€nic P
Page 292 and 293: 36. Dulka J,, 1988- "oi th. Grcgond
Page 294 and 295: 57, ffys, M., 1985, "vi5ibilily ofd
Page 296 and 297: ?6. McNarl, D., 1983, The trnsth of
Page 298 and 299: 96. Plulmq, H. C,, 1966, An Intlduc
Page 300 and 301: 116. Schefcr. B, E., 1990, "T.l@pic
Page 302: ,a:Ill5. Sutt n, A. H,, 2005, Th. L
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