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kplM\ ficory of luM hotior, Publish.d in 1802. cnploy.d rrmfo@ing th. eqution ofmolions $ tlt.t the lruc longltudc wa an independ.nt ldiable Hh wotk also povid.d e dpl.n tion of lh. sdo a@1.61io. of the M@! ripl@'s mdhods w.E cdied io a high degrce of accu!@y by sevetal malhedaicies One of then was Dmoi*e. who publthcd his th@ry dd r.bl6 in 182? that Gmaircd in *id' Ne until Ha.Fn! sork dppeaed. P. A. Hasen's wolk ext nded for over fonv veds fon 1829 dd his r.bl4 w.re publkM in lE5?. ThGe labl6 rcmain.d in s for w.ll ov'r finv yds. Delaunay publishcd his work ih 1860lhal M basd on disturbiry tunctions $ai in€ludcd 120 t€ms. By sn.ltti.al m.4 h. Gmov€d 0E teru of disorbins turulion on' by one ahd gEdually builds up th. $lution. Autho6 cl.im thar Delaunav s vorl( n thc mo$ Frf{t elulion of th.l@r problm v.t found {D&bv 1992) Thc posilion of $e M@n dodd th€ ElnI is desdbed bv spndical pold coordinatcs (r,,190 p) wnn r bci.s th. heli@.ntric disr:nce or rhe tltncr' ? $e eliflic lonsitudc and I lhe ecliFic laliode The most commonlt Gd edv lo handl€ lunai $bles dlrinB the nosr Pan of 20't c.n$ry \rcG dDc lo BrcM (Bmm 1 960) This ll]M $.ory w3 inpo!.d bv Eckefi &d ws tnown 6 ILE, sho^ tot Inprored Lrnr Epr,rdr,r. Tnc lh.ory coGtruct d bv ChcPont and ChaPon(_Toul is knosn 6 ELP (Chapo er. al,. 1983. 1988) shon tot Ephtina des I air's Pukienhes ln ELP simplifi.d tables have ben cxlEclqi from lhe lheorv lo rcplcsnt lh' luDa nolion in $e fom of explicit line sries fomule. Th6e tabl's @ b€ lsed to direcllv compute $e luntr coord'nabs. ELP h Dol onlt morc Peci* md complele in conpdien ro ILE it ale povides noe nodern valEs oi l(M pdmelels md olh€r Phvsical coislsts' For 6000 y.4 on eacb side of J2ooo o ELP povid€s lund c@rdiMt€s that l4lv have eno$ .xc.eding few arc secoo.ls Toeelher with th' d€v€lopment of VSOP (Vdialrons Sacnl.ifs des Olbires Ple€titt bv Bctagllon ed Fdncou (t9E8) lhe t!bl6 due ro Chapront er. al destib€ the motion ofall major bodies (€xcept Pluio) ih tbe solar sysrem. Both rh€ $€ori6, ELP &d rhc vsoP w dcv'lopcd d rhe Buean d's ll
BdicaUy a nhcory of pldelary ed lund motion involvd inies ionolasysrcm of di0eGnial eqladoi dat constin&s th. major pad of th. sfudy of elcstial n46mic' Therc & i. gddt t$o.ppoachcs for slving such dyndical systctu, ealytol ud nusical, Anallri€l nerhods m b6ed on solutio. by Iouder sen€s ed thc Poiso.\ S€lies. Thc ELP-2000-85 (Chdprcnl€r,al, 1988) is semidalttic sd has be€n obla'ncd frod a fil o f ELP-2000-82 (Cn!po!i cr. al. I 983) to th. nlncrical inrcer.tion of lhe .lei Propulsion Labomrory DE200/LE200 (Slstrdish l98l). P@$ion in this o@ry ha b€en $keh iion Lasrar Gsklr, 1986). For te an lylic par! ELP-2000 Fpet€s th€ nain lEblm fbm th. penurbarions. Th. 6ain problem tak s into accout thc &tio. of thc E nn's ce E of m6s aid lhe acion ofrhe Sun's orbir aound lhe Eorlh-Moon baycentr. such lhat Ihe Sun\ odit is asuned to be Kepl€rid cllipse. This rcrulls inlo Fouri.r series w'lh numdical c@fiicie s snd ar$mdb th.t m suns ol mulripls of fou fundade.tal paBmeted D (diffeence of ihe ned longitudcs of the Sun ed $e M@n). / (mean monaly of rh€ Moon), l(hem anohaly of $e Sun) lnd a (M@n s argumen( ol h ude). Tlis main problem 6uhs inlo dne *.ies fomnld for Mmn\ longitudc. ladtude and gocenrric disrscc @daining 2645 rcos in all. Apan flofr lh* *rics acrons of all rh€ other significant objects in solar sysren dt consideed N 'Fnurbadons lo ihc mdin pbblen lhol include: L tndiKr pl&c(ary perturbarions rbar re induced by lne diff.tsoc.s b€lwecn the lrue orbit of the Sun aound lhe Eanh-Moo. bdycenue and tssuned Kepbnm Elliplhal orbil oflhc Sun *uned in the min Pmblem. 2. Dir€ct planerary penub.tioN due lo etions of othr plan$ on ibe M@n lor borh the direct ad rhc indt€ct planetlry penubalions lhe ELP-2000 co6id6 th€ orbib ofthe pldct giv€n by BGlagnon\ VSOP82 rh@.y. L P.rurbations du. ln€ figues of $e Edh md thc Mon (Moons, 1982). 34
Page 1 and 2: ON I'HE COMPARATIYE STADY OF MATHEM
Page 3 and 4: CERTIFICATE c. incd thn th. ..ndidl
Page 5 and 6: Dedicated to my late mother Anwer S
Page 7 and 8: Abstract The pmbl.m of delemining f
Page 9 and 10: allow visibilil, ofthe cltsm wilnou
Page 11 and 12: ilf'LLf' c)'i ", ( ),1 -t z-r -t z,
Page 13 and 14: 't' f'L )) L 72' A ety { d-- w L,t
Page 15 and 16: Phyaic.l Modala & their Evolution 4
Page 17 and 18: moden (Reingold & Dschowttz, 2OO1).
Page 19 and 20: SuDpoe ('-.r",/.)!d (.,,r",t) E thc
Page 21 and 22: 5. 6, 1. E. 10. B€dTimeofvhibilil
Page 23 and 24: Thi! figue clorly 3howr th.! for hi
Page 25 and 26: and a.rc$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: L 2. L Pl&erary otbiB d. clliptic w
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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