Visibility of Luna and Lunar Crescent

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. Th. d.pend.nc. ofth€ dlendsB on th. cyclic moiion ofth. Moon sld $e Suh.. txB c.l.ndar of $. Mulih! .spei.lly a lh.i. b.li.rts lticrty dphais. utltliarsidtingorrhetwloNcr$.a fois.niosaldcldilglun&ndrha. A! rccou ofrh€ eilons ofrhe rsrorcmd oflhe oodc6 rim.s |o rd.lr.ss theprcbhm ofderemining$e fiisl day ofsishdnsofnew Iund c'.eenrItr lh. b&ksound of tlE$ cfon! w tFrc qplor€d all lh. old ald thc modmmrhodi Mthcm.dol dDdel or crirdion dEr r.quiG ro be $tisfi.d for 0E lirsr vGibilityot ihc !w lu{ cEsdr, Duing lhi! qploGtion rn E$ltr of lh.$ nod.ls NcomFcd lnd nodifietios baw b..n 3uSgcrt d $,lEE fler posibl.. Funhd ft. mo$authentic of the hodeh hav€ b€en uscd to .xolod fie ob€crvationil lunar cal.hdarfouowEd in Pakhhn. A.sed o. the rcsulF ofthese exDloHions a luturc obervrtiomllus calcndd for Patislm is anDut d,23
Chapter No, 2ASTRONOMICAL ALGORITHMS &TECHNIQUESFor lhe determlnatlon ol th€ prsiso locallon ol the obJsts in th6 SolarSFtem, panbulany the Sun .nd rh6 Moon, ih6 Fr€nch planetary theory VSOPaT,(sretagnon & Francou, 1994) and th. lunrr rh€ory ELP-2000 (Chapront-Tou# .ndChapron!1943, €91) rr. well sulted. A number of sotlwaE hav6 ben develop€dtor lho shulatlon of cel€stlal phenomona based on the$ th€o.16 and similar otnerworks.In the cunanl studylhe same lh€ori.s havs b6.n u*d lo lollowthe pGitlonsotthesun and rhe Moon.Moreoler, to conven the theorles Into computatlonal iechnlques,malhematlcal lechnlques, tools and dlgo thms nave been dtloted. Moch ot thecomputailon.l work is ba*d on the algorithms devoloped by Me€us (Me€us,199a)but a subslantlal ahount or work on computatlonal aEonthms has been doneInd€pendsnlly. For a ihorolgh und.Franding ol lhE compul.tlon.l toob theproblem of llme ls explor6d rnd discused in d6tatl. ln this 6Ebrd the @nblbutionof a numbd of authors has beon sludled in as much detail as ls required (Aokl et.al., 19aa. Sorkoskl, 1944, Clomen@ 194a, 1957, de ,ag6€, and ,lappel (Eds.),197l- Dl.k, 2ooo, E$€. and Parry, 1995, E3*n et, al., 195a, Gurnot dndS6ldelmann, 1944, Markowiu er. Er. 1954, Mullor 6nd rappel, 1977, t9unk andlrlacoonald, 1975, Nel$n et, al., 2001, Newcomb, 1495, Sadler (Ed.), 1960,seldehann rnd Fukqshlmai 1992, Spencer, 1954, Stephenson and Moi$n, 1944,1995, Sleph6n$n, 1997, W€lls, 1963, otc.).
Page 1 and 2: ON I'HE COMPARATIYE STADY OF MATHEM
Page 3 and 4: CERTIFICATEc. incd thn th. ..ndidlt
Page 5 and 6: Dedicated to my late motherAnwer Su
Page 7 and 8: AbstractThe pmbl.m of delemining ft
Page 9 and 10: allow visibilil, ofthe cltsm wilnou
Page 11 and 12: ilf'LLf' c)'i ",( ),1-t z-r -t z,li
Page 13 and 14: /'t' f'L )) L 72' A ety { d-- w L,t
Page 15 and 16: Phyaic.l Modala & their Evolution4.
Page 17 and 18: moden (Reingold & Dschowttz, 2OO1).
Page 19 and 20: SuDpoe ('-.r",/.)!d (.,,r",t) E thc
Page 21 and 22: 5.6,1.E.10.B€dTimeofvhibilily TrA
Page 23 and 24: Thi! figue clorly 3howr th.! for hi
Page 25 and 26: and a.rc$cnr snh ldgc clone.lion $a
Page 27 and 28: Flarively r€c.nr rimes, ho$v€r,
Page 29 and 30: Solsr Cal.nd6 m b4d on the ulrl mot
Page 31 and 32: Arnhn.tic calcndar ther. are cilh.r
Page 33 and 34: 8@rly vdied s6r lo s@n, 'fte t€en
Page 35 and 36: visul sighring epo.t must b. suppon
Page 37: visibility curve. So fd th. mod€l
Page 41 and 42: O@ thc rim. of thc g.cdric biil of
Page 43 and 44: ine argunent md the explicii tin€
Page 45 and 46: Onc. lhe lincs of fting edor seltin
Page 47 and 48: 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 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 $udying ihe behaliour of
Page 113 and 114:
. yomg.r ct!.c. (f8; 3J.1). Tb nioi
Page 115 and 116:
'Ihe table in App€n.tix'U shos S.
Page 117 and 118:
All lhe* conditions falolr rhe lisi
Page 119 and 120:
''if h. nns tizt b.nv.r -3,t otd 0.
Page 121 and 122:
I415't00 loo zlo3b400^ actual RF br
Page 123 and 124:
All thes. figu6 show ! lend for lhe
Page 125 and 126:
In cae ofMoon nonh ofediflh:DAZ ! E
Page 127 and 128:
69{0. Fo(brilgb.(l (t910) hs &!.rd,
Page 129 and 130:
w. d.firc a pa@et . !r ,.,visibihy
Page 131 and 132:
fhis nbdi6c.tio! i! rn oL by Fo$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
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$h cd be dalualed
Page 197 and 198:
182
Page 199 and 200:
Tabl€ 5.'1.1 (Conllnued)Durins rh
Page 201 and 202:
Fig. No. 5. L7: Mesuemcnr of Length
Page 203 and 204:
180160'1101m1008060zlo15ELOIGAN()|{
Page 205 and 206:
*.Fi8. 5.l.9i D.fici@y Arc rg.ind E
Page 207 and 208:
ours-value crirerion-baed crireria.
Page 209 and 210:
Freque.dy. claims of lery dy sighii
Page 211 and 212:
Tlrc'€ seE 6 c66 when thc ag. of
Page 213 and 214:
Chapaer No. 6Dtsct ssroN'ftis rvork
Page 215 and 216:
dau ofnininum aE ofvision for difcr
Page 217 and 218:
'fte najor achjevem€nt of this m*
Page 219 and 220:
old! b !|dc! in ruirD frr lh. Ft! 2
Page 221 and 222:
{ cl6c{): maime.u0; cltsqo; Daiuour
Page 223 and 224:
rvhile(nex|sl=V');Eolory(50,29):@ur
Page 225 and 226:
,t){i(ho!P-24.0)iqhoul<0.0)ni.{hou'
Page 227 and 228:
){gmr4c6-0r{41.0+50.5484V60.0y60,0+
Page 229 and 230:
iisha<o.0)sdelb-sinGlarrPvl80-0f co
Page 231 and 232:
]fo(i=o;i<l l4ii+){ fs.d(fpL2,'%li
Page 233 and 234:
li((dnon8<90.0)&&(slon8>100.0))ddon
Page 235 and 236:
)I(24299161.0) e=z; el${ 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
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 286 and 287:
\9ia9g;:;5555;6,.liisi.-eFae:E-;(sF
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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Visibility of Luna and Lunar Crescent

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