Visibility of Luna and Lunar Crescent

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impossibtc io 3a thc cr.!ent, TLse circmshnc.s aF shom in the 68ure 3.2.2 on theiDiii)Cl, lh. cclsli.l .q@lor, 1 i! th. vdal eqlinor.TS is the diuFal path of th. Sm thar is just *riirg al s.DE b thc diumal palh of the Moon th.l s€t before thc sUNl 3t E.Ds = 6M - 6s, letpendi.ula.to the c€lesial equlo. is lh€ dif.rence of lhedecliMtion 6M of ihe M@n &d the deli.ation 6s of rhc sun. Declinalion ofthe Moon t south of lh€ sun md rhe upper limn of Ds is 50 9'. lhe inclihalionoflund orbit to lhc trliplic.v) zcvs = 9Oo - 4 is the agle bctween $e c.l.srial equ.tor lnd $e horihnNS whee C teprenls lhe lotitude oflh€ Pl&. TheztSD = Cvi) DM = dM - qs, lhe dilreEnce of risht a$cnsio. dM ofMoon and rhc rishreension os oflhc Sun. For higher lairudcs DE nav b. htgc allowing laigcvllues ol ncepliE LAG aftr co.junctionvii) sF = pM - 9s : 0M is p€,Fndicultr ro fi. E lifljc is $e difiercnce bctw*nlhe c.l6ial taliluds of the Men and lhc Ss As for DS Sf never €xcadsrhelinilof5'9'.viii) FE (E' .ol showo in rhc fisure 6 it almost coincides wilh E) h ptrallel lo theix) lislheVemal Equinox ed Z)6t =horizon. Dep.ndniS on laliude C andv h !h. angle of lhe Ecliptic with $elh€ se@n, 'YnaY lary ftum zeto(vhctr ecliptic is alons the botizo') lo 90 deB€6 (when €cliptic ispc+endicula! to lhe holzon) l! cas' when v is small DE thal has b bepaEllel lo the 4liplic is nuch ltrsei tha' DE (ftol is paEllcl io lh€ cqualo!)and hdc. E sd E aE mrch s.panted Tlle det€mi'arion of$is oSle mdits sienifidc. shall be di$sed in the n'xt drcLx) I'lt figurc shos rh€ SM is jN| about o sel in a pl&e oI sdall b n€diudlaftude d , $e M@n havins ddlinarion eulh of il' sun ha al@dv *l (ddwd set at poinl E) $ th.l lh€ LAG = TiG of Mdnct Tim of suNer isE'
fig. 1.2.2: G@tn r.y ofP@riv. Ag. .rtd N.gaiE L.gA@rding lo rlE luN elqdr b.!.d @ IIE binh of Nd M@ b.bc tlE ssatha nd lun|r mn$ b.gio .l dr tirc of o.!a 6 $ii vrt Ming- How6, for tll.lu@ c.lsds b.!d d rn viltbilitr of $. n4 s@4 w hN mfli &e.olb.gii on thb cming B n b 3inply ioF{bl. lo $ tlE w luu c|!g in thiscinhtee. Fd plE witt lrSc ldind.. d|r dbw for llre v.l6 of DE |,d h.@DM ln. tri&gl6 uidd 6!&l6.riB o rbt tr rtrdl .dd.!xl ..otl b. tBt.d sryhdicrt r.iugl6. tlc! d y @ll lo tr|.diun hdnd6 @ qEidqld e th|r th.tdugl. EDS i! r 3rdl dgh rlgld oilElc o *y wih dt.!gl. tt D t..Ia E .d Stu 9oo !r!d rlE a.sl. d S b.rsa D !d E i! ?. $. ldind. oftlE pL& Th@foE:SDAf(328)86
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ON I'HE COMPARATIYE STADY OF MATHEM
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CERTIFICATEc. incd thn th. ..ndidlt
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Dedicated to my late motherAnwer Su
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AbstractThe pmbl.m of delemining ft
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allow visibilil, ofthe cltsm wilnou
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ilf'LLf' c)'i ",( ),1-t z-r -t z,li
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/'t' f'L )) L 72' A ety { d-- w L,t
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Phyaic.l Modala & their Evolution4.
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moden (Reingold & Dschowttz, 2OO1).
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SuDpoe ('-.r",/.)!d (.,,r",t) E thc
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5.6,1.E.10.B€dTimeofvhibilily TrA
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Thi! figue clorly 3howr th.! for hi
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and a.rc$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
Page 49 and 50: BdicaUy a nhcory of pldelary ed lun
Page 51 and 52: $.t%'sr'(sfl + dI'.,)(r25)Tb vdB 6f
Page 53 and 54: a - sdimjor uis of th. dbill, = m@
Page 55 and 56: ,is = I +l8O! Fs= -e 12.2.2t)ond th
Page 57 and 58: F " M@'!.4ruqtof hind.- ! 6'0.? ! a
Page 59 and 60: elled th. Julid Dare abb@ialed B JD
Page 61 and 62: How.r s noE @nhtlon l !'pNch ir ro
Page 63 and 64: Now orc n6ds ro c@t 6. nub.r of diy
Page 65 and 66: LMU-UMMstcFr2: alMM>2 { UW-C-1716 }
Page 67 and 68: DE to lh. nodotr of thc ob6*d. th.
Page 69 and 70: I. =6r4t-50'.54841+E tot84,.s12s66I
Page 71 and 72: t,-'i^,-"(t"*", \2tL,-ZA,s\8,+c,. I
Page 73 and 74: The coftcctions for Abe@don md Nura
Page 75 and 76: FimUy the coordides ofthc Ss @ Edcd
Page 77 and 78: Si"At = Sinpstnq +C6e,Cot6,CotH,(21
Page 79 and 80: An |pDDxiE.r. valu. of "'*" wirh e
Page 81 and 82: ranlAt =c6(Ir)s,,{t) rz,(d)co{l)(2.
Page 83 and 84: "='"[(289)Sinc. ihc acienl dd thc n
Page 85 and 86: 9. JD of Conjunct, rh€ Julie Dat
Page 87 and 88: rh*.@rdin l€s @ c.bdat.d th. etr
Page 89 and 90: TL dl irpde dgsitor tu d. ddroni4 m
Page 91 and 92: In rhb ch.pter we stan wtth a b,t.f
Page 93 and 94: wA diislaled by S. Oddz 6 Crlr of M
Page 95 and 96: 80(r. I r)
Page 97 and 98: for visibilny thftud rel.$ope. IlE
Page 99: (3.2.2)(3.2.1)FDm ridcle sh, st nir
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 $udying ihe behaliour of
Page 113 and 114: . yomg.r ct!.c. (f8; 3J.1). Tb nioi
Page 115 and 116: 'Ihe table in App€n.tix'U shos S.
Page 117 and 118: All lhe* conditions falolr rhe lisi
Page 119 and 120: ''if h. nns tizt b.nv.r -3,t otd 0.
Page 121 and 122: I415't00 loo zlo3b400^ actual RF br
Page 123 and 124: All thes. figu6 show ! lend for lhe
Page 125 and 126: In cae ofMoon nonh ofediflh:DAZ ! E
Page 127 and 128: 69{0. Fo(brilgb.(l (t910) hs &!.rd,
Page 129 and 130: w. d.firc a pa@et . !r ,.,visibihy
Page 131 and 132: fhis nbdi6c.tio! i! rn oL by Fo$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
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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$h cd be dalualed
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182
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Tabl€ 5.'1.1 (Conllnued)Durins rh
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Fig. No. 5. L7: Mesuemcnr of Length
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180160'1101m1008060zlo15ELOIGAN()|{
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*.Fi8. 5.l.9i D.fici@y Arc rg.ind E
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ours-value crirerion-baed crireria.
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Freque.dy. claims of lery dy sighii
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Tlrc'€ seE 6 c66 when thc ag. of
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Chapaer No. 6Dtsct ssroN'ftis rvork
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dau ofnininum aE ofvision for difcr
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'fte najor achjevem€nt of this m*
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old! b !|dc! in ruirD frr lh. Ft! 2
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{ cl6c{): maime.u0; cltsqo; Daiuour
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rvhile(nex|sl=V');Eolory(50,29):@ur
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,t){i(ho!P-24.0)iqhoul<0.0)ni.{hou'
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){gmr4c6-0r{41.0+50.5484V60.0y60,0+
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iisha<o.0)sdelb-sinGlarrPvl80-0f co
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]fo(i=o;i<l l4ii+){ fs.d(fpL2,'%li
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li((dnon8<90.0)&&(slon8>100.0))ddon
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)I(24299161.0) e=z; el${ 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
Page 251:
236
Page 254 and 255:
2t9
Page 256 and 257:
24rI
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APPENDIX.IIIPHYSICAL MODELS211
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245
Page 262 and 263:
241
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249
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9!!!!!.39!44!C94-9!_q4!!,-!!:,-9!l9
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253
Page 270 and 271:
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
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
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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
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\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
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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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