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CONTENTS Urdu R.ndenng of Abslracl 2. Introduction Ll P@nd.6 for visibiliry olNry Lumr Cr$chr L2 sienillcmce o| ceogdphical t calion t.l Tbe Rut.s oaThunb: The Ani.m & fi. Medievrl 1.4 Crl.ndas and CelesdalCycles L5 condbution oflh€ zod cotury Aslro.on6 Astronomicsl Algorithms & Techniqucs 2 l0 tl 20 24 2.1 2.2 2,t 2,5 2.6 2.1 2.8 2,9 Dyne cs ofMmn ed |he Eanh Coordindtes of rhe M@n Nes Lu@ Caenl visibihy Pard.ic'! Thc Softve Hiblol.qpp 25 l0 4i 5l 55 58 63 3. Ancicnt, Mcdicv{l & Etrly 20$ Ccntury Modcls l. | 'ftc ltabylonian Crilcri! 3.2 Some Sph€ncd Trigonomebc Consi.lcations l.l Thc Lud Ripehess I,3w md ils Modiicdlion 1.4 Ehpidcal Models of Edly 2d CenNry 1.5 ConposonahdDiscussion 15 76 82 t03 122
Phyaic.l Modala & their Evolution 4.1 Bruid s Physical Model 4.2 Y.llopl sinslc Pamel.r Mo.lel 4,1 Srch.f.ls Umitiog Magritudc Mo&l 4 4 A Nry Crirrion For vilibility of Nry Luc cEsdt 125 t27 l3 ta6 tt9 t67 5. Applicrtion 5.1 L€n$h of Cd!c. 5-2 Ob6.ri{tional L|lM C.lctrdrn of Pakkur t'|2 l7l l9l 6. Dircusion t9E Th. sonwm Hihlol.cpp 205 fte Anci.nl Med'.valrnd E dy 2of 'enluo Models 2ll Th. PhysiolModcls 24! Lwcd.nd.r2000'20{t 255 Futurccalendar2ooE-2ol0 264 21t
Page 1 and 2: ON I'HE COMPARATIYE STADY OF MATHEM
Page 3 and 4: CERTIFICATE c. incd thn th. ..ndidl
Page 5 and 6: Dedicated to my late mother Anwer S
Page 7 and 8: Abstract The pmbl.m of delemining f
Page 9 and 10: allow visibilil, ofthe cltsm wilnou
Page 11 and 12: ilf'LLf' c)'i ", ( ),1 -t z-r -t z,
Page 13: 't' f'L )) L 72' A ety { d-- w L,t
Page 17 and 18: moden (Reingold & Dschowttz, 2OO1).
Page 19 and 20: SuDpoe ('-.r",/.)!d (.,,r",t) E thc
Page 21 and 22: 5. 6, 1. E. 10. B€dTimeofvhibilil
Page 23 and 24: Thi! figue clorly 3howr th.! for hi
Page 25 and 26: and a.rc$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: $.t%'sr'(sfl + dI'.,) (r25) Tb vdB
Page 53 and 54: a - sdimjor uis of th. dbil l, = m@
Page 55 and 56: ,is = I +l8O! Fs= -e 12.2.2t) ond t
Page 57 and 58: F " M@'!.4ruqtof hind. - ! 6'0. ! a
Page 59 and 60: elled th. Julid Dare abb@ialed B JD
Page 61 and 62: How.r s noE @nhtlon l !'pNch ir ro
Page 63 and 64: Now orc n6ds ro c@t 6. nub.r of diy
Page 65 and 66:
LMU-UMM stcFr2: alMM>2 { UW-C-1716
Page 67 and 68:
DE to lh. nodotr of thc ob6*d. th.
Page 69 and 70:
I. =6r4t-50'.54841+E tot84,.s12s66I
Page 71 and 72:
t,-'i^,-"(t"*", \ 2t L,-ZA,s\8,+c,.
Page 73 and 74:
The coftcctions for Abe@don md Nura
Page 75 and 76:
FimUy the coordides ofthc Ss @ Edcd
Page 77 and 78:
Si"At = Sinpstnq +C6e,Cot6,CotH, (2
Page 79 and 80:
An |pDDxiE.r. valu. of "'*" wirh e
Page 81 and 82:
anlAt = c6(Ir)s,,{t) rz,(d)co{l) (2
Page 83 and 84:
"='"[ (289) Sinc. ihc acienl dd thc
Page 85 and 86:
9. JD of Conjunct, rh€ Julie Dat
Page 87 and 88:
h*.@rdin l€s @ c.bdat.d th. etr
Page 89 and 90:
TL dl irpde dgsitor tu d. ddroni4 m
Page 91 and 92:
In rhb ch.pter we stan wtth a b,t.f
Page 93 and 94:
wA diislaled by S. Oddz 6 Crlr of M
Page 95 and 96:
80 (r. I r)
Page 97 and 98:
for visibilny thftud rel.$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:
t56
Page 174 and 175:
4,4 A NEW CRITERION TOR NEW CRtrSCE
Page 176 and 177:
Alttudo v.6 Sohr Oottesalon 19 13
Page 178 and 179:
l6l
Page 180 and 181:
l Calculate r-vdu. (or vp @odins ro
Page 182 and 183:
Tl|rcforc, if Fothcdnghd's criGdon
Page 184 and 185:
obsMriom bul lcs sue.senn in @mpdie
Page 186 and 187:
may 6ose that nay b. lhe ay€rlse
Page 188 and 189:
criterion or our s-value (or Q&K) c
Page 190 and 191:
fomulE. by Nunins sphdicEl 6gL at Q
Page 192 and 193:
s.lld width eould nor b. visibl.. A
Page 194 and 195:
IE it ir ma dly lh koglh of.ilsc.d
Page 196 and 197:
200 F 180 fi reo 3ro Era i roo o80
Page 198 and 199:
T.bl. 5.1.1 {Continued r8l
Page 200 and 201:
Tne nodel dcvcloped in lhis e for b
Page 202 and 203:
AII the* fout deviati.S cdes ae pho
Page 204 and 205:
Tlre modcl for rhe calculation of c
Page 206 and 207:
6.2 LUNAR CALENDAR FOR PAKISTAN Mos
Page 208 and 209:
Out of rhe 95 public obsesalioDs re
Page 210 and 211:
lhe lmd ft*e.t. C€ncrally thc crn
Page 212 and 213:
oftr\i'i$ lbir tNinun rcldirio! @!H
Page 214 and 215:
1..2) dd is ns applicarion is srudi
Page 216 and 217:
", =(^* - l- # -e4,:!.,'l) f " v, =
Page 218 and 219:
(escenr $idr varying wea$cr condili
Page 220 and 221:
APPEDNIX-I COMPUTER PROGRAM HILALOl
Page 222 and 223:
gotox(52,12):p.i {"Ase = '),sororr(
Page 224 and 225:
i(ldltohonthdayslin(lnonlhl.0)l) {
Page 226 and 227:
) gobxy(2,21);cout
Page 228 and 229:
{ fs@f(fpt'%lf yolf y.lf,&sx,&bx,&c
Page 230 and 231:
+alp3'pow(!4)/100000000.0)rPI/180.0
Page 232 and 233:
mcela=sin(!lar*PI/180.0)'sin(mdclia
Page 234 and 235:
forg nodf6c(160.lo8+390.67050284rto
Page 236 and 237:
t ning-no; , void iE_tordvoio { i(n
Page 238 and 239:
t ) iqbou
Page 240 and 241:
) nmFsinc(so 0/60 ofV l 80 0)- sin(
Page 242 and 243:
d.m=@s(ptar'PvlE00)'6(md't!prPvl80
Page 244 and 245:
) { ip nt(iprr4,""/od:%d{'/o8.3lo\t
Page 246 and 247:
APPENDI'(.U ANCIENT, MEDIEVAI, AND
Page 248 and 249:
23J
Page 250 and 251:
215
Page 253 and 254:
2]E
Page 255 and 256:
240
Page 258 and 259:
APPENDIX.III PHYSICAL MODELS 211
Page 260:
245
Page 263 and 264:
244
Page 265 and 266:
250
Page 267 and 268:
2r2
Page 269 and 270:
NB 91'! 254
Page 271 and 272:
E g t 2 I a 3 I E t c s i e : f *
Page 273 and 274:
E H I : f-1 i9 i P a E E E € g El
Page 275 and 276:
El lc a P I d t : a r' 5 5 t e 3 a
Page 277 and 278:
6 6 I a I n P F 3 E I 3 I n : 3 l :
Page 279 and 280:
APPENDIX-V F'UTURECALENDAR DATA FOR
Page 281 and 282:
: I f : t I I E 8 3 P a a B 3 E 3
Page 283 and 284:
=;::eifr ;Ci{{ i; si:€ ;e;ii i --
Page 285 and 286:
;;-i= BSxdgi:' 5i3;;n* ;i B99g .S ;
Page 287 and 288:
\ ;;g;F ;;;gis :E::sF F;i;€€ g;
Page 289 and 290:
Asbbrcok, J, 1972, "Moc rbour visib
Page 291 and 292:
4o0d AtuivNry, 1582n982". Ponrifica
Page 293 and 294:
47. H.pl@, B, 1984, Bi@rionil R.fld
Page 295 and 296:
66. India M.t@olo$/ DePdlrna! 195,
Page 297 and 298:
86. Moullon, F. R., 1914,'An Inrrcd
Page 299 and 300:
106. Roenlhd, 1952. "A History of M
Page 301 and 302:
126. ShaulGr K., w-mmBirhine.6m- !2
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