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I am d.cply graleful to Prolcssor Dr. Nasituddin Kndn, my SrDervisol aor his patience. inkluble sriNlla(on and counlloss sugg6tions dsht from the bcSinning rill rhG poirrt *hen I .n ablc ro complerc lhis $ork. I sould ole lile lo expess Dy CFlilude for tne valuble suSgestions polided by Prcfessor Dr. Roshid Kadal Ansli of IcdeEl Urdu UniveBily. Karachi_ in rhe bcginnnrs ol tlis prcjed My spccial $hks for Prcfcssor Dr. Mtrhamn)ad Ayub Khar you$rlzai ol Urne6nj ofKonchi$no Emincd a nofiaror tor mc nbuglour rhis \ork I mus,tso suhnrit nry hunblc tanks lo Prolcser Dr. Muhannad ltoys of rjnilcGny of Kuata l-!mpur. Maliysia, Dr Abdul Haq Suhan ol Univeriry of Sanaa,yenren tor reir kind cnconmAcment during $is sort. lhanls !E ats due aor Mr MulNflrnrad shotrl Odch n nleins rhc wcbsllc NN\.icoon)ior! dnd Mr (hitid shorkor nriNgilg \\\rr!r!]N4lt!!!!.9r1!rr. uorh lhc* "ohsitc rcnraincd ! eurcc ot infomllliotr. rcscd'lh prpeu aDd.laln lbr rhn \orl lo hrve b..o posibt€. l_asr b nor rhc leasr; I subnjn m, stccral rhdnlis llr Dr Shlbbir Ahs.n oi Lahorc Universny of M.meeNnr Scienccs $hoe {aluablc nrge$iions helped nre in cdnins rhn dissedation. I sish b cxtcnd my sirrccrc thanks to lhc University of Knrachi. i! pirticutar ns vicc chrnc€ll . Prolcs$lpr Pecuda Qasinr Rm. lor rhc consislcnl DoRI suppon tor rho My sife. cbildo. and in-laws enained under lols of prcsure durine lhis proloneed periodofny\ort lor shich no gralirude nay bc enough. MSQ
Abstract The pmbl.m of delemining ftc day when Uc nev tunar crcs.nl can be 3en ti6t ar an, site of observarion hs Efrained an opch pobtem since andquirr, The phenon.non ImniB imFnel for beeioing ! luw mon$ in a puEly ob*rvariomt lunar calcnd.i. In li. n6! chapler the asrrcnomicat pdamercn relare.i lolheprobtcnr are !.!ieRtd alohe si$ a briefdcsriplion oasme rules oafitrnb arribut.d ro rhc ancicnr and lhe nr!ie!.1 nodets lhc afecrs ot geognphical loc.rion on rhc problcr orc aho dcscribed. A brief Evierv ofc.tendaB lnd.ssociared celestiat cycles h atso pescnled $nh splri.l chphasis on |hc rulcs enurcjarot for Islamic ob*rarionat lu.arcalcnd,r a .{rlr as lo'r cemu, AD. ln lhe end of the ch.prf Eviov or rhe conlrib[ion of thc .strcnoncrs of 2orr' cenrurr is pesentcd $al b.8im rvirh thc etoFical toodct or Solvins fte pnblm ol lhe ti6l visibilny oa lbe n.$. lumr crcsccnr inlolvcs lenedy colcrlations and thc trsc ofatt ctcFenrary !slrononjic0t rechniqucs. A tovi.w ot n e tcchniq,es and algorilhms is pEsc .d in rhc *cond chlpr. Sp$i.l emphNis is Ailrn lo r|r dekminarion oa linr of oriunclion of Moon sirh rhe SuD. i c binh of nc* Moon. rh. risinsand seu'hgol thr Smnnd rhe M@n_ posnionsofrhc sun,nd thc Moor ar 2n! tnrc on rhc dll or rc day aftc. conjL .rion .t.tc ch.prr cnds rith a brict dsscrption of the .ompurer prosranr Hitotot dsvebp.d r'.r compftrioN done ir rhis \ort A n$v posam is deEloped in ordq lo prcdnce the dala Fquied aor rhis \ol[ $ar is Cencrally.or avlitabte troh orher sotlwarc lhat aheadycxrsr ShniDg $ilh simtl€ Ulbytonian crncrion. fic lhnd chaprr eiptores rhe ancienr dnd the Drdielal hlrbeoaricat hodets follo\€d b, rhe dcscriprion ol. narh.natical trploEion of oedieval Mutim Aslomn6. Condricat considehions asiaGd wilh the prcblen are.xplorcd in nrore dclaitin oder ro evalu0le the Lunlr Ripencss Las o.0 sMcess, suggc$ed in lhc medieval e6. 'ls Son nodincado.s to rh€ la$ aru ate suggesled Thc shoncominss of the ripenc$ lav a,c then di*ussd and lieht is shcd oD rhe Easns rhat lead ro lhe dcvelopnent of ARCV-DAZ ,.trrion b4d nodels b, the
Page 1 and 2: ON I'HE COMPARATIYE STADY OF MATHEM
Page 3 and 4: CERTIFICATE c. incd thn th. ..ndidl
Page 5: Dedicated to my late mother Anwer S
Page 9 and 10: allow visibilil, ofthe cltsm wilnou
Page 11 and 12: ilf'LLf' c)'i ", ( ),1 -t z-r -t z,
Page 13 and 14: 't' f'L )) L 72' A ety { d-- w L,t
Page 15 and 16: Phyaic.l Modala & their Evolution 4
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€dTimeofvhibilil
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 and 38: visibility curve. So fd th. mod€l
Page 39 and 40: Chapter No, 2 ASTRONOMICAL ALGORITH
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: L 2. L Pl&erary otbiB d. clliptic w
Page 49 and 50: BdicaUy a nhcory of pldelary ed lun
Page 51 and 52: $.t%'sr'(sfl + dI'.,) (r25) Tb vdB
Page 53 and 54: a - sdimjor uis of th. dbil l, = m@
Page 55 and 56: ,is = I +l8O! Fs= -e 12.2.2t) ond t
Page 57 and 58:
F " M@'!.4ruqtof hind. - ! 6'0.? !
Page 59 and 60:
elled th. Julid Dare abb@ialed B JD
Page 61 and 62:
How.r s noE @nhtlon l !'pNch ir ro
Page 63 and 64:
Now orc n6ds ro c@t 6. nub.r of diy
Page 65 and 66:
LMU-UMM stcFr2: alMM>2 { UW-C-1716
Page 67 and 68:
DE to lh. nodotr of thc ob6*d. th.
Page 69 and 70:
I. =6r4t-50'.54841+E tot84,.s12s66I
Page 71 and 72:
t,-'i^,-"(t"*", \ 2t L,-ZA,s\8,+c,.
Page 73 and 74:
The coftcctions for Abe@don md Nura
Page 75 and 76:
FimUy the coordides ofthc Ss @ Edcd
Page 77 and 78:
Si"At = Sinpstnq +C6e,Cot6,CotH, (2
Page 79 and 80:
An |pDDxiE.r. valu. of "'*" wirh e
Page 81 and 82:
anlAt = c6(Ir)s,,{t) rz,(d)co{l) (2
Page 83 and 84:
"='"[ (289) Sinc. ihc acienl dd thc
Page 85 and 86:
9. JD of Conjunct, rh€ Julie Dat
Page 87 and 88:
h*.@rdin l€s @ c.bdat.d th. etr
Page 89 and 90:
TL dl irpde dgsitor tu d. ddroni4 m
Page 91 and 92:
In rhb ch.pter we stan wtth a b,t.f
Page 93 and 94:
wA diislaled by S. Oddz 6 Crlr of M
Page 95 and 96:
80 (r. I r)
Page 97 and 98:
for visibilny thftud rel.$ope. IlE
Page 99 and 100:
(3.2.2) (3.2.1) FDm ridcle sh, st n
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) erhl
Page 109 and 110:
As mc ioned abov. dE Mulin sao&Ders
Page 111 and 112:
vi€w of $udying ihe behaliour of
Page 113 and 114:
. yomg.r ct!.c. (f8; 3J.1). Tb nioi
Page 115 and 116:
'Ihe table in App€n.tix'U shos S.
Page 117 and 118:
All lhe* conditions falolr rhe lisi
Page 119 and 120:
''if h. nns tizt b.nv.r -3,t otd 0.
Page 121 and 122:
I 4 15 't0 0 loo zlo 3b 400 ^ actua
Page 123 and 124:
All thes. figu6 show ! lend for lhe
Page 125 and 126:
In cae ofMoon nonh ofediflh: DAZ !
Page 127 and 128:
69{0. Fo(brilgb.(l (t910) hs &!.rd,
Page 129 and 130:
w. d.firc a pa@et . !r , .,visibihy
Page 131 and 132:
fhis nbdi6c.tio! i! rn oL by Fo$dnB
Page 133 and 134:
35 30 25 20 15 10 5 0 -10 . hisible
Page 135 and 136:
:i:: alF{s_?{";+E:'-.-l {-: 'l Fia.
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:
1lz Our ofth. 196 positiv€ sighri
Page 153 and 154:
' = ls
Page 155 and 156:
i { Fig No 4'2 2 lD addirion 10 @Nd
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:
4J SCHAEFFER'S LIMITING MAGNITUDE M
Page 163 and 164:
i = l,.cor ,+ 1i - l L I+441 (4 t.2
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.l tf t li rl!. a.l a, -r.8
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.5 APPLICATIONS Durin8 rh
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$h cd be dalualed
Page 197 and 198:
182
Page 199 and 200:
Tabl€ 5.'1.1 (Conllnued) Durins r
Page 201 and 202:
Fig. No. 5. L7: Mesuemcnr of Length
Page 203 and 204:
180 160 '110 1m 100 80 60 zlo 15 EL
Page 205 and 206:
*. Fi8. 5.l.9i D.fici@y Arc rg.ind
Page 207 and 208:
ours-value crirerion-baed crireria.
Page 209 and 210:
Freque.dy. claims of lery dy sighii
Page 211 and 212:
Tlrc'€ seE 6 c66 when thc ag. of
Page 213 and 214:
Chapaer No. 6 Dtsct ssroN 'ftis rvo
Page 215 and 216:
dau ofnininum aE ofvision for difcr
Page 217 and 218:
'fte najor achjevem€nt of this m*
Page 219 and 220:
old! b !|dc! in ruirD frr lh. Ft! 2
Page 221 and 222:
{ cl6c{): maime.u0; cltsqo; Daiuour
Page 223 and 224:
vhile(nex|sl=V'); Eolory(50,29):@ur
Page 225 and 226:
, t ) { i(ho!P-24.0) iqhoul
Page 227 and 228:
) { gmr4c6-0r{41.0+50.5484V60.0y60,
Page 229 and 230:
iisha
Page 231 and 232:
] fo(i=o;i
Page 233 and 234:
l i((dnon8100.0)) ddone-nlon8+360.0
Page 235 and 236:
) I(24299161.0) e=z; el$ { alph
Page 237 and 238:
l i(|enrd) s.t6i8_n0i l t {(3€c
Page 239 and 240:
nmFsin({50_c/60.0).Pv180.0)- sin(pl
Page 241 and 242:
mooi coord(i), llii'i--.Ji. i:s'pv
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:
24r I
Page 259 and 260:
244 !.I9
Page 262 and 263:
241
Page 264 and 265:
249
Page 266 and 267:
9! !!! !.39 !4 4!C 94 -9!_ q4!! ,-!
Page 268 and 269:
253
Page 270 and 271:
APPENDIX-IV OBSERVATIONAL LIJNAR CA
Page 272 and 273:
ll: lf- Lt- ltl Itl t6t Tl IT lt, I
Page 274 and 275:
6 2 P 3 e g 9 E : - F a 6 5 9 i i t
Page 276 and 277:
El lel ];I l;l n -t lsl ft fl fl t"
Page 278 and 279:
3 p 5 t E E t c T & I s $ i $ : l t
Page 280 and 281:
H t i 3 t I : 3 ? t I I i 6 t 5 t 9
Page 282 and 283:
\ "9n30 An-"gR --=aii" R6,:6.;,{d 3
Page 284 and 285:
s :;;;g " :;ii R;;--6,it l=sl;!i9 ;
Page 286 and 287:
\ 9 ia 9g ;:;5555 ;6,.liis i.-eFae
Page 288 and 289:
RETtrRENCtrS L Alned, M., 1991. Oig
Page 290 and 291:
17. Bouwcr,D&Ctcmence,c. Ac.d€nic
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:I ll5. Sutt n, A. H,, 2005, Th.
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