- 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: ilf'LLf' c)'i ", ( ),1 -t z-r -t z,
- 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: $.t%'sr'(sfl + dI'.,) (r25) Tb vdB
- Page 53 and 54: a - sdimjor uis of th. dbil l, = m@
- Page 55 and 56: ,is = I +l8O! Fs= -e 12.2.2t) ond t
- Page 57 and 58: F " M@'!.4ruqtof hind. - ! 6'0. ! a
- Page 59 and 60: elled th. Julid Dare abb@ialed B JD
- Page 61 and 62: How.r s noE @nhtlon l !'pNch ir ro
- Page 63 and 64:
Now orc n6ds ro c@t 6. nub.r of diy
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LMU-UMM stcFr2: alMM>2 { UW-C-1716
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DE to lh. nodotr of thc ob6*d. th.
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I. =6r4t-50'.54841+E tot84,.s12s66I
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t,-'i^,-"(t"*", \ 2t L,-ZA,s\8,+c,.
- Page 73 and 74:
The coftcctions for Abe@don md Nura
- Page 75 and 76:
FimUy the coordides ofthc Ss @ Edcd
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Si"At = Sinpstnq +C6e,Cot6,CotH, (2
- Page 79 and 80:
An |pDDxiE.r. valu. of "'*" wirh e
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anlAt = c6(Ir)s,,{t) rz,(d)co{l) (2
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"='"[ (289) Sinc. ihc acienl dd thc
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9. JD of Conjunct, rh€ Julie Dat
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h*.@rdin l€s @ c.bdat.d th. etr
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TL dl irpde dgsitor tu d. ddroni4 m
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In rhb ch.pter we stan wtth a b,t.f
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wA diislaled by S. Oddz 6 Crlr of M
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80 (r. I r)
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for visibilny thftud rel.$ope. IlE
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(3.2.2) (3.2.1) FDm ridcle sh, st n
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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) erhl
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As mc ioned abov. dE Mulin sao&Ders
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vi€w of $udying ihe behaliour of
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. yomg.r ct!.c. (f8; 3J.1). Tb nioi
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'Ihe table in App€n.tix'U shos S.
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All lhe* conditions falolr rhe lisi
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''if h. nns tizt b.nv.r -3,t otd 0.
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I 4 15 't0 0 loo zlo 3b 400 ^ actua
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All thes. figu6 show ! lend for lhe
- Page 125 and 126:
In cae ofMoon nonh ofediflh: DAZ !
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69{0. Fo(brilgb.(l (t910) hs &!.rd,
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w. d.firc a pa@et . !r , .,visibihy
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fhis nbdi6c.tio! i! rn oL by Fo$dnB
- Page 133 and 134:
35 30 25 20 15 10 5 0 -10 . hisible
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:i:: alF{s_{";+E:'-.-l {-: 'l Fia.
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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
- Page 145 and 146:
For thimer c6c.nr rh€ ,r + s aSai
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t32
- Page 149 and 150:
tJ4
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1lz Our ofth. 196 positiv€ sighri
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' = ls
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i { Fig No 4'2 2 lD addirion 10 @Nd
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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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4J SCHAEFFER'S LIMITING MAGNITUDE M
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i = l,.cor ,+ 1i - l L I+441 (4 t.2
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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
- Page 174 and 175:
4,4 A NEW CRITERION TOR NEW CRtrSCE
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Alttudo v.6 Sohr Oottesalon 19 13
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l6l
- Page 180 and 181:
l Calculate r-vdu. (or vp @odins ro
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Tl|rcforc, if Fothcdnghd's criGdon
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obsMriom bul lcs sue.senn in @mpdie
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may 6ose that nay b. lhe ay€rlse
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criterion or our s-value (or Q&K) c
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fomulE. by Nunins sphdicEl 6gL at Q
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s.lld width eould nor b. visibl.. A
- Page 194 and 195:
IE it ir ma dly lh koglh of.ilsc.d
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200 F 180 fi reo 3ro Era i roo o80
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T.bl. 5.1.1 {Continued r8l
- Page 200 and 201:
Tne nodel dcvcloped in lhis e for b
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AII the* fout deviati.S cdes ae pho
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Tlre modcl for rhe calculation of c
- Page 206 and 207:
6.2 LUNAR CALENDAR FOR PAKISTAN Mos
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Out of rhe 95 public obsesalioDs re
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lhe lmd ft*e.t. C€ncrally thc crn
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oftr\i'i$ lbir tNinun rcldirio! @!H
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1..2) dd is ns applicarion is srudi
- Page 216 and 217:
", =(^* - l- # -e4,:!.,'l) f " v, =
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(escenr $idr varying wea$cr condili
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APPEDNIX-I COMPUTER PROGRAM HILALOl
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gotox(52,12):p.i {"Ase = '),sororr(
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i(ldltohonthdayslin(lnonlhl.0)l) {
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) gobxy(2,21);cout
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{ 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
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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
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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
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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,
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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