×א א א ، א " ! Ĝ # א)' א&%א$ א ,+*"א ,+*(، 678+#9 *5 4א 23א *01א/..*-א ، )0*:*- א&>!*;א K0 א א ? א #$ א ،ī ú א:A$ @ א $ " א .Ù ? א 3 0*-א 0 א، ĦEJG*KLאM9? ،DE*0"F*,GHא 3 0*- 4: 60א/.*NO אP*,Qğא #)J، א/#א)J0א 0א/A ،:#א(א/S@0G*א @1H*8 ،0* ħVא/T ، א9Hא("א ×א ، W4 )*$א Ħ0 א אY*0(!84א @X#$ /VאK ،*SE*0Z #א'א +7\א +א #אK]، 9#1*"%אO، !@#א &%S*א&^*[א K0 `E_ 9אא *ħVa%*1bK Pא/ א ،08 9*,0 * 8# c%d5"60(?9א א ، %f[G*%*S@ 6Q 6K O*@E ، O#Q0G*Ì" D;?%#אG]א א K _א 6Qא&/*@1EO S#$א aא ,+*، g8א/ *09 א/3Q *-א 0א/E 3 S8* א E L× ? א&:*:hG S " -*0*$ א ,+*(، K *@1E *+K G&#א אHא0Z*- א ,+* א Ĝ QE L; #א1' א& %א$ א ,+* " א ,+*(، + ħV *G אG*:H 8* :#*-א 0 1# @%0 i*G*īV Ed56K'[@%ħVi*@*8`0+9א :#*-"S א *-QE#>9* 4! א ,+*(K lE א 6Q א .*k ħV _G 6+ אj*:H א _ a א ,+*، 0 W " *@< QE S"0:6 m#>7*9א ,+*(، )GØoV*אj*:Hא cא _אj*:Hא&_K *א 6Qא .* V'+ĞsQoאpq*ÌTZ-*0Z ?א @X#$א KT+*%*(-" א # א _، א SE9*7?īL*?@3@*אtĞאM9)*ÚĦ0E"*@!( ،0 א @X#$ :#א( Ú`8*(9* א/ ? OTo א ,0+*- אğ. א/,A " א * ، )
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4 O#Q'0J+5V*+Kא *EP i* 3E4 #f?<*ĩ-*0 E,* א *>(" S א:E-*#fP*0א KO#Q "א*8$EFNV{,N$*Ġ V" 9*:?6KħV7 א;9אא **8so ،P K אW*:H א _ :*Í + א D( */ 0Ğ g8 " d*mV ;*5
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6 א 6Qא&O %tא 0* א aא ,+*
א aא ,+* Celestial Sphere F`8lØא aא&>E01 00ĝ aK:' W+A1א-)cK#9*9cK_q*SGN3 א aא&>0ęl l
א&)P*3א ,+* Celestial Poles
*V'kא;f#>;>אFא aא&>01' :3א aא ,+*"W*+9Ħ3G • א 3]א , +*א *+7 P_ • א 3]א ,+*אP' _8#@Ğ X0G >אFא aא&>fO#01#>9*? א ħVPtא Fb$#6Ka27א a
א ,+* E D@+mE*Ĩ <E *SG`K?%א$ Ú* ?א ħ V27א 9O#PtאאÒ#> א ,+* ، 3 M94אVKğ: אKğ א h* 9 א 0#0 %א$א ,+* K
9 oאH:#א(א ,+* Celestial Equator
*>a ?;אaq 4+h 3:4א a א ,+*QGħV*S+,E W*+9Ħ*,Ħ • QG א aא ,+*א +7* _ • QG א aא ,+*אĞ@8#_ o'@QאH:#א(א ,+* 'Q Q ^א )*f'+q #>א >אo× ، PP'F אH:#א(א ,+*Ġj*:VאH:#א( אtĞא" 4א aא ,+*K
;אqא cאOא ,+* Celestial Meridians ú*QGúEא אqא 4+h 3:4א a א ,+*א Ħ86QEL)3א aא ,+* 'SG`8 PP*;אqא cאOא א qא ,* 0 _9 HA ;#+ o4אH:#א( א ,+*'E، QQ×;אqא cאOא ,+* j#3Ġj*:Vא O#3אtĞא0 4א a א ,+*K
10 #א^*-א/60 Parallels of Declinations
*>a ?;אt!q 3:4א aא ,+* #א^ĠאN:#א(א ,+*'*8 QQ * S__ QE@'^א)*f'+q#>א >אK PP'F+* ĩ.6 א/,*>א-א 0 0#א h*9 %א$א ,+* ، E×#א^*-א/j#3Ġj*:V60א l אtĞא0 4א aא ,+*K א ,+Jא @Ùh Zenith & Nadir *V'kא;QG )3א aא&>01א/*> 8 * א!O ' א aא ,+*"W *+9Ħ3G • 3Gא ,+ ZJ 2#3G4א א! • 3Gא @: Z'Ùh M*ě*8D3G6א O#(*7 L3G'1#Ùtא ,+Jא @Ùt8Ùh#)' א א! 3:4א aא&>K01
11 ;אaqאN Horizon Circle
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*>a ú*QG?;אq 4+h 3:4 א aא ,+*L3GĦ86QEא ,+Jא @Ùh 'QE ZZ@'^א)*q+';אaqאKN
12 #א^*-אE *>a ?;אt!q 3:4א a א ,+* #א^ אaqא*8N * QE_S_@' ^א)*q+'אĠא #א!L3GĦ86א ,+J א @K ZZ'Ùh ;אaq^אOא א! Observer's Meridian *>a ?;אaq 4+h 3:4א aא ,+* Ħ86QE)3א aא ,+*'L3G PP א ,+Jא @WĦ+,(ħV , @E_9 ZZ'Ùh • o^אOא א!א #'PZP • o^אOא א!א , _'PZ'P 13 א אaqא :0א 0,0q Principle Vertical Circle úEא אaqא 4+h 3:4א a א ,+*א Ħ86QEL)3א aא ,+* 'L3G PPא ,+Jא @SG*8 ZZ'Ùh* א אaqא :0א E_90,0q, א a א ,+*QGħV W*+9Ħ E _(5 QG • W_8 QG • G_9 S,*;אaq^אOא א!K j ***GGG*GאěH*9*-א&!0 Cardinal Points k*E'א אaqא :0א 0,0q ;אaq^אO א א! ';אaqאW*+9Ħ3G"N • 3Gא NO*+7 9_ א @3אP(N ħVא 3]א ,+*א *+7 K P_ • 3GאSP#@Ğ 9_א @3אP(N ħVא 3]א ,+*אK P'_8#@Ğ L3G'Eא E27 א WPt 4;אaq אęN,]א 0EØ]א/0ęú 3GF#E א E27 Ħī4 א א! א/#א%D @3 א NO*+7 ، א WPt K M<*,4 14 א אaqא :0אħN Prime Vertical Circle *>a ?;אaq 4+h 3:4א a א ,+*، L3GĦ86QEא ,+Jא @Ùh '3E ،ZZ';אaqא& @3G Ħ3G א E27 א WPt، 9_ +#; 4 6K?;אaqאNא אaqא :0א K0,0q א cאא ,+ 000 Azimuth O#kא #Y 4;אaqאN، א cא @א ,+ZJ *:?א אaqא :0 א 40,0qא אaqא :0א/*>Ğ*8a$ א ,+* c ، X cאא ,*8 0+ c W_9+hGZT.8Y*E_9 Az • א 8';א8V 90˚- 0˚?qא( ? 3Gא NO*+7 אM*ě*8 SP#@Ğ א 27 א KPt • א @Q ;א8V 180˚- 0˚?qא( ?3Gא NO*+7 אSP#@Ğ a<*5 V[,ę lא א!M*ě*8 א 27 א KPt • א א8V 360˚- 0˚?qא( ? 3Gא M*ě*8 NO*+7א K27 15 א/60 Declination úא/60 O#kDG4א #Yא/* Y 4 ;אaqא cאOא/*>Ğ*8a$א ,+*، 8Vא( ?;אaqאH:#א(א ,+*'QQ #4)' אi*8#@% iN*Û 90˚- 0˚?Y*$Ğ K Dec c *860+ c ?א : אĞ$א ,+*%60W X@8#_ 08@+*אĞ$א ,+**Û60W Y K_ א א 3 Polar Distance O#k#9א #Yא/*Y 4;אaqא cאO א/*>Ğ*8a$א ,+* ، 8Vא( ?א 3] א/E '#4)'אĞ$ א ,+* *Y? ˚c 180˚- 0 א *83 KPD c ?א : ī.6א #PX Y א א 3 ī*+@08 X$X.6א #PYY א א 3 KY$X א Ħ8 (Tא/60א א 3 PD = 90 ± Dec H א/60א úTĚlאa<*5H J א/60א 8l@ \אa<*5H 16 E Altitude E א א ,+L X$א ,+* Zenith Distance O#k#9א #Yא/*Y 4א אaqא :0א/*>a Ğ*8$א ,+* 8Vא( ?3Gא ,+ZJ 4 #)'אY*E( ، 90˚- 0˚?Y*$Ğ ?˚c 180˚- 0 א ,+*8L ZD c ، @hğ>אĞ$א ,+* 4;אaq ^אOא א!Fbא א ,+0L@ ,4+א א ,+Lא cא _c *8D Kmer.ZD c א E 17 א cאא ,* 0א0Ò Local Hour Angle O#kא #Yא/*Y o4אH:#א( א ,+*'QQ א cא @א P[3 8Vא( ?oא cאOא # א!'PZP o4א cאOא/*>Ğ*8$א ,+* M*ě*8 360˚- 0˚?Y*Eא KPt+* ī?א Ù S@*#8א-^@0?0– 24 K LHA c *8*xc *: א cאא ,* 0 t@ Greenwich Hour Angle O#kא #Yא/*Y o4אH:#א( א ,+*'QQ א cא @א P [3 8Vא( ?oא cאOא # G@t o4א cאOא/*>Ğ*8$א ,+* M*ě*8 360˚- 0˚?Y*Eא KPt+* ī?א Ù S@*#8א-^@0? KGHA c *8*xc *: 24 –0 א Ħ8(Tא cאא ,* 0אLHA 0Ò א cאא ,* 0 GHA @t LHA = GHA ± Long _(5 Long O#ko H _8 Long O#ko J 18 א אaqא ,+* Celestial Circle / Ecliptic úא/,*>א ,@#א h*9א DÚEא +7\אSK)*@Z00ğ*א O#9*hא&>8l* אaq א ,+* 'K4+,E ، EE א אaqא ,0#א ×0% ، 9_;אaq QE4+h@'^אא>9* ˚o' 23.439אH:#א(א ,+*'Ĩ QQ*,84+ */60א _( k*E L3GV úE ، (ε' א אaqא ,+*'oאH:#א(א ,+*8 @3אH אOא Mxc ، _08א @*83 K γc א O#3א ,+* Celestial Longitude *>a ? א/,* א cא א/*: i*(5 4 ,# א אaq א ,+*، 8Vא( ? 3G אH אO א γ _08 4 א אaq א 4+h א #א! 08? א 3 KK' ?0 א/*>Ğ*8 a$ א ,+*، E 360˚- 0˚ ? Y*E ,4+ *8i*G*0 O#3א ×%_א ,#"K א lא ,+* Celestial Latitude *>a ? א/,*א cאא/*: M*ě*8א O*+7 אP#@Ğ V4א;א אaqא 4+hא #א!08? א 3 KK'?0 א/*>8V ، $Ğ*8aא( ? ,# א אaqא ,+* ، Y*E ? ˚0 -˚90 ، 0 #+0(F lא 3]א +7* _ אaq א ,+**8i*G* 04+, H، 90˚#9 K l א ×%_א ,#"K 19 א cאא ,* 0א @0+X Sidereal Hour Angle O#kא #Y o4אN:#א(א ,+* 'QQ ^א @א o ?:* P[3א cאOא/*> 8 @3אH אOא o4 γ_08א cאOא/*> Ğ*8$א ,+*i*8Y*E?˚0 -˚360 ī?א Ù S@*#8א-^@0?0 :* K SHA c *8*xc *: 24 4 א/3'א/,0 Right Ascension O#kא #Y o4אN:#א(א ,+*'QQ ^א @א o ?:* P[3א cאOא/*> 8 @3 אH אOא o4 γ_08א cאOא/*> Ğ*8$א ,+*i*(5Y*E?˚0 -˚360 ī?א Ù S@*#8א-^@0?0 :* K RA c *8*xc *: 24 4 א Ħ8(Tא cאא c@0א @SHA 0+X א/3'א/,RA 0 h SHA + RA = 360 or 24 20 hG*$א Hא0Z*-א ,+* Systems of Coordinates E*+K ;א/#א)' 3:4א aא&>#801א:3אHא0Z*-אtĞא0א/Ěא l oא E ،O#3 K; #א)'א&%א$א ,+*א/A 3:4א aא ,+*#8א:3 אHא0Z*-א ,+*، א 0EL @*! # א1'א&%א$א ,+*"! א ,+*(א Ù @M9úE،01*<t0Q8*SאHא-*0Z hG*SG4+ א/#א)' 3:4א a א ,+*V:@*;אħVi;אĦ*ÚĦEq ĦE*Ħ +0h Sm84+*א Ì ،g hGa+ א0Z*-א ,+*ę *S@08*+0 ĝ,] *;(אH:@*;א/0% א @*!א/,A" א A:V (# ،Y*0א$W ú4א !א ، P*,ğ g8_ א/#א '1 6m A: Vא$V$*hGאFĦ"،Ħ_Z #אA: V[3Eo '1א$ V$*hGאF; o_Z M9S5&01#E _*+0 ،MÙא&W hG+ hG*$אHאh@ -*0Z#א אqא 4+h @*!אHא0Z*- אE ;אaqאH:#א(א ,+*، ;אaq^אO א/Dec 60 א @h*$אH:#אq_ א א! א cאא ,* 0אLHA 0Ò ;אaqאH:#א(א ,+*، ;אaqא cאO א/Dec 60 א @h*$אH :#אq_א .*G_ א/*>8a@3אH אOא 08_ א/3'א/,RA 0 א אaqא ,+* ، א אaqא #א!Ħ8 א O#3א ,+* λ א @h*$א ,+* )3 S0* א/*>8a@3אH אOא 08_ א lא ,+* β 21 אHא0Z *-א& 0 Horizon System אHא0Z *-א& 0 X$א ,+*#81#E Xא:3 @*!א WY*0 • אE 22 אHא0Z*-א ,+* Ecliptic System אHא0Z*-א ,+*K4+,E א ,0# א ×0% X$א ,+*#81#E Xא:3 @*!א WY*0 • א O#3א ,+*λ • א lא ,+*β א hGĦ86# אHא0Z*-א ,+* iNW א V$*hGħV_ $*hG?6#:#אq_ Sin (Dec ) = Sin (h)Sin (Lat ) + Cos (h)Cos (Lat )Cos (Az ) Sin (h) − Sin (Lat )Sin (Dec ) Cos (LHA ) = Cos (Lat )Cos (Dec ) i*0G*Z א W V$*hG?6#:#אhGħV_q*$ _ Sin (h) = Sin (Lat )Sin (Dec ) + Cos (Lat )Cos (Dec )Cos (LHA ) Sin (Dec ) − Sin (Lat )Sin (h) Sin (LHA )Cos (Dec ) Cos (Az ) = or Sin (Az ) = Cos (Lat )Cos (h) Cos (h) 23 *Z W i*. א V$*hG?6#:#אÚ$*hGħV_q* Sin (β ) = Sin (Dec )Cos (ε ) − Cos (Dec )Sin (ε )Sin (RA ) Sin (RA )Cos (ε ) +Tan (Dec )Sin (ε ) Tan (λ) = Cos (RA ) >אW i*8 א V$*hGħV*Ú$*hG?6#:#אq_ Sin (Dec ) = Sin (β )Cos (ε ) + Cos (β )Sin (ε )Sin (λ) Sin (λ)Cos (ε ) − Tan (β )Sin (ε ) Tan (RA ) = Cos (λ) 24 א #א-א c@0 א #א #א # א- א א א cא A,E$א # א-א 0@c a;*"א Ù g8?^א*א Y*0א _، .6א cאא ,* 0 K א/3'א/,0 %א$א ,+*، 0 l*, ?א #א-א #:F 0 א cא E א/+.8* >%*-א )*qא .#אG_א #:80* #א-א c@0א/+.8* ,* *-א )*q א .#אG_ א K 0@c ī@@*א 3E *+K6#] א& ĦE*9Ħ8 א #WVĦEא +@ *F`8א aא&>Ka<; E 01* h h #fO#>9*˚360 ;>%"^?א>*: 24 6*K$# a 6K%<; 15˚4@Ĩ ، 1 :* 360 ° *8 ، 24h * ī_@@*א Ħ86#א #OTo?ĦE), +א #א-א cאא/*: *8 -*%< 15˚4 O#Q 4א-^@*8:*0 *, P1 ،-*א #א-א c@0 "˚ 15 O#Q 4א-^א،1#אM*G;OĞא #א-א cא**S8*? א-^@0א \K א-)#:0 א-^@0 *: 24 %<; 360 *: 1 %<; 15 0@^0(; 1 0:#(0(; 15 0@^0G*Z 1 0:#(0G*Z 15 h /*JG*Kא א*8O;*Eaq *8 360˚-*%< *, O*"[NDGb ،24 -*?א&#אFO E^*XEא 8+0א ،i W# ú?8Tא>;אKaq*˚360 ?)+0 h א cא "*JG*KOא #aא/,A"א 9Y*0_א >%*-، *: 24 ú O*" aJG*Kא *8Y*0 *, K-* 25 6#Ĝ א cאא ,0+ ?א @h*$א ħV_8א @h*$א אq א 8'א&N E O א 8'א אN W '8 Az = 360˚ - Z Az = Z א 8'א .*S E _G א 8'א .* S W Az = 180˚ + Z Az = 180˚ - Z 26 .*WV W E1FOא +F J)+0א/ Dec 60 gא @W _9$#X Canopus 52° 42 ′ 15 ″ S Deneb 45° 19 ′ 58 ″ N Betelgeuse 07° 24 ′ 31 ″ N Fomalhaut 29° 32 ′ 42 ″ S %א א P.D3 X@#$א/ a<#K MT 8* @, א!oW *Ûl K_ PD = 90° ± Dec Canopus 90° + 52° 42 ′ 15 ″ S P.D = 142° 42 ′ 15 ″ Deneb 90° - 45° 19 ′ 58 ″ N P.D = 44° 40 ′ 02 ″ Betelgeuse 90° - 07° 24 ′ 31 ″ N P.D = 82° 35 ′ 29 ″ Fomalhaut 90° + 29° 32 ′ 42 ″ S P.D = 119° 32 ′ 42 ″ .*WV W E2FOאF*K א א D.P 3 Vega X@ ,*″ 52 ′ 47 ° 128 8* @, א!W l %@8#_ +*)+0 א/ Dec 60 X@ ؟ PD = 90° + Dec Dec = 90° - PD Dec = 90° - 128° 47 ′ 52 ″ Dec = 38° 47 ′ 52 ″ N .*WV W E3FOא +F J)+0א/ Dec 60 Û 89 ° 19 ′ 33 ″*, Polaris X@* _ M8א *8 P.D3 ,@ ħV>א!W Ûl* _؟ PD = 90° - Dec PD = 90° - 89° 19 ′ 33 ″ PD = 00° 40 ′ 27 ″ 27 .*WV W E4FOא +F J)+0 אE Sirius 90° - 36° 43 ′ 35 ″ ZD = 53° 16 ′ 25 ″ Rigel 90° - 28° 40 ′ 35 ″ ZD = 61° 19 ′ 25 ″ Pollux 90° - 78° 44 ′ 46 ″ ZD = 11° 15 ′ 14 ″ Hadar 90° + 21° 22 ′ 51 ″ ZD = 111° 22 ′ 51 ″ .*WV W E5FOאJG*K )+0 אE .*W E6FO %א>א cאא ,* 0א LHA 0Ò X$א ,+*X "אN*ğ-א * W0 oM<hğ J^אOא א!א #א , _ K hğ LHA +0(F#E>אĞ$א ,+*o X^אOא א!א #˚hğ*+@08 360 >oM^אOא א!א , _K 180˚F#E 28 WV J PאJG*Kא cא @א E P[3,*˚10 ) 6>אo$Ğ^אOא א!א # K M<8 ) 6>אo$Ğ^אOא א!א #F#E)+0א cאא ,* 0א0Ò˚350 ،* 8 >0 10˚F#EM M* ě*8Y*E*SGא 8V Ptא( ?oא cאOא # א!K [ WV JאJG*Kא cאא ,* 0 O#ko 240˚*,E GHA @tא א!˚K 25 45 LHA = GHA + Long (East) LHA = 240˚ + 45˚ LHA = 285˚ h m s .*WV W E7FOאF*Kא/3'א/, RA 0 Hamal X@ ,* 00 08 02 +*) +0 א cאא ,* 0א @ SHA 0+X X@ ؟ SHA = 24 h - RA SHA = 24 h - 02 h 08 m 00 s SHA = 21 h 52 m 00 s .*0;f*Ú$%M*ěV!<Ë@0hğ" W E8FO JG*K^אDא ,h@80+*$ א Y*0א F#E N 25 W*,E Z_8 )+0^אא ,*8 Az 0+ h@*$א אq؟ Az = 360˚ - Z Az = 360˚ - 25˚ Az = 335˚ 29 .*V W E9FO,]אHא0Z*-א ,+* @WV Sirius Xא +FJ א/60א _ ε א/Dec 60 א/3'א/,RA 0 h m s 06 45 47 16° 44 ′ 13 ″ S 23° 26 ′ 15 ″ 101° 26 ′ 45 ″ Sin (β ) = Sin (Dec )Cos (ε ) − Cos (Dec )Sin (ε )Sin (RA ) Sin (β ) = Sin (−16 ° 44' 13" )Cos 23( ° 26' 15" ) − Cos (−16 ° 44' 13" )Sin 23( ° 26' 15" )Sin (101 ° 26' 45" ) Sin (β ) = (− .0 264218 ) − .0( 373324 ) Sin (β ) = − .0 637542 β = −39° 36' 32" Sin (RA )Cos (ε ) +Tan (Dec )Sin (ε ) Tan (λ) = Cos (RA ) Sin (101 ° 26' 45" )Cos 23( ° 26' 15" ) + Tan (−16 ° 44' 13" )Sin 23( ° 26' 15" ) Tan (λ) = Cos (101 ° 26' 45" ) .0( 899248 ) + (− .0 119610 ) Tan (λ) = (− .0 198441 ) .0 779638 Tan (λ) = − 0.198441 Tan (λ) = − .3 928807 λ = −75 .719727 (+180 °) λ =104 ° 16' 49" 30 א 6Q א .*G_ אk*:H*-א 0 j*:V)*7GV aא ,+* E+?0+9>: א aא ,+*7GVa;*%V*(אk*:H*-א 0א/ ,QE S" ، 3#> %tא0א aא ,+* א ğ*8 *@(3EL S@* "3'9אא *P ، 0 %*(- 654 Q <*E 0 1#E :88# G ،_#;"9א א 6Q V23@ 3E678*S0 _0 #G× Ħ ~ Ħ?אk*:H*-א W*+90 • אj*:H 4;אaqא cאO • אj*:H 4;אaqא& #) A:Vא+9$* ?א¢o 4 a #אS+9 ،6* @*!א Y*0א/a*3"א/,` א 0، א/@h#>א/D£<P#3?א aא ,+*، א t*? 6+אj*:Hא ĜL;9* k 0א/,` א 0، "0'א&#אDGbO א 4 @>: אk*:H*-א 6780 *$ W*S+9?0:*: j*G a • א/@h#>א/D£<P#3?א aא ,+* ، ;W Vk? @*!א Y*0 9_ א cאא ,Wb ، AZ 0+אJG*K א cאא ,Ħ8a<#Qf 0+א Ħ+0˚0 -˚180 #Fא/@h#>א/D£<P#3?א aא ,+*#9א/@h#>א WV* ، E_(7אJG*K א cאא ,Ħ8a<#Qf 0+א F# 360˚- 180˚Ħ+0א/@h#>א/D£<P#3? א aא ,+*#9א/@h#>א K W_8t • 3Gא F#E E27;אi*+q 3GĦī4א GF#E*+@08 NO*+7 3א WPt ;אi*+q 3G<*,4א E ،NO*+7 3G4אSP#@Ğ " אM*ěHא/*K\ @3א K NO*+7 • "j#3oא lא +7* 0;אF#*i*+qא 3]א ,+*א/E F' א/E _q 2#א#9N א 3]א ,+*א *+7 F#*+@08 ،Pn _א 3]א ,+*אPs _8#@Ğ #9א 3] א/@ A Fg א E _qÙt : 6 אN "אM*ěHא/*\K MÙh@א +7* _، 8@ \)+0 E 33 3G4א NO*+7 אD9*ěV[,ę6KSP#@Ğ o@ !l F o@ אH:#א(אtĞא" KE • E 34 j*:V 4;אaq א cאO ī.6א 67א * _j*:V 4;אaqא cא_8 <#h@/O aא ,+*، א!W l WF 0_ *Û • ĩ Pn Z Ps.6;אaq^אOא א!א # "ĩ Pn Z' Ps Ħ.6א , 0 . . • ī NWS.6;אaqאh@?N#>9*א W_8t. • 'īZWZ.6א אaqא :0א9ħN_ +#; 4;אaqאN . . • f6.ī PnPs#>;>אFא aא ,+*. • 'o6.ī Q W QאN:#א(א ,+* q*(#9 f4#>א >אF. • 6.ī Z Q lא א!. • E 35 @h#>5)_ א! *Û h@ _#>8_ א!Û* _ @h#> 5)_ א!%@h@ _8##>8_ א!%@8#_ 36 #3oא->: j*:V 4;אaq^אOא א!iN*Û 10˚60W X*Ú$Ğ،א>E * ˚20 ،^א SW 08 0 8#@% 0Ú oF`8i*+ lא א!˚KiN*Û 35 A:*8א$א %*>G: ;אQGaq )93* 45 *Y*0Ĩ 90˚O;*Eא : א/,0$A ĩ.6;אaq^אOא א!، 3G Z'א אĚaq ,o_ 0>:_ >א9cKĨi*، +0 .6 אĠאN_ ;אaqאF *Ĩ ،N א cאא ,0+ X$א ,+*%@F#0 ، SW 08 0 8# א/@h#>א _8t aא ,+*#9א/P#3 ، *8 * 3G;¦_א/8cK@3א WPt ¦; L3Gא NO*+7 אę SP#@Ğ,]א 0EØ] א/ú، 4אĠא/,0 א :_א ī.6 א אaqא :0א;¦ ،ħN L3G*S0 א ,+Jא @K ZZ'Ùh oF*Ĩ lא א!*Û F#0 ،_א 3] א ,+*א/E F' א/E _q #9א 3]א *+7 Pn _ F#*+@08א 3]אA@ Ps _8#@Ğ g ، ;>%E 37 o 0G +#; 4אĠא #א!Ħ86א 3 Ħ א ,+*Ps ،Pn Ħ *>א8i@3א/ī ، WcK.6 oאH:#א(א ,+*'0ę QQ E Y*0אE Y*0א/mG Dec 60'א/@ V4א;o אN:#א(א ,+*'0G Z QQ\;>%א/60 N˚10 ?א;¦ĦSĞ S@086QG Z، T+* @Ě 6Q #4א^א/60א/*>K X$Ğ*8 38 6K'k*E 3G?#א^אE cKG:?א %*> V4א;;אaqאNWS N @: א אaqא :ZXZ'0 א/*>Ğ*8a$א ,+*X ، 8@ \ א E Ĝ;@*8א : . b8úK: א/. א _ 0 PXZ WF • א #$*ĩ6.ī PnZ Y lא א! co-Lat • א #ī ZX Y.6א א ,+ZD L • א #ī PnX Y.6א א PD 3 • א cא ĩ Pn.6א cאא ,* 0אLHA 0Ò • א cא ĩ Z.6 א cאא ,+ Az 0 39 j*:V o4^אOא א! X$א ,+*X 8`1*~ 40 j*:V 4;אaqאN ī.6א 67א * _j*:V 4;אaqאN aא ,+*، א!W *Ûl 0_ WF • ī NZS.6;אaq^אOא א! . . • ī WZE.6א אaqא :0אKħN • ī NESW.6;אaqאN. • o6.ī WQEאH:#א(א ,+*. • E 41 j*:V 4;אaqאN א!W Ûl* _ j*:V 4;אaqאN א!W l%@8#_ 42 #3o_*+0א->: j*:V 4;אaq אE 43 8@ \א 3א ,*E 44 O#Q 4א cאא ,* 0א LHA Ò X$ mG':?א %*> V4 א;א6Òאx@:_ j#3Ġא cאO*¦O>: א #PnX Y א o6.īא cאOא/*>3GĦG Z? ،$Ğ*8 j*:VאĞ$א ,+* X o4אH:#א( א ,+* WQE 9_א @W ، X'3 F& )Y*0א cאא ,* 0אF# LHA Ò 4 oאH:#א(א ,+* 8V WQEא(?o ^ אOא א!o4א cאOא/*>Y*E$Ğ*8 M*ě*8א KPt O#Q E+0(6m4 0 cאא ,* 0 אA,G LHA Ò$א %*>"qcěא #Y א/*>*8 c%8<ħV WQ #9 X'3@א( ,*S@)c%6K*,*˚22.5 0 אF K*6א #P*,ğ*8 90˚*, WQ Y א cאא ,* 0א6Q¦ LHA Ò 4 א K 55˚+0 Ĝ;@*8 * : א/. א _ 0 PXZ WF • א #ĩ6.ī PnZ Y*$א co-Lat l • א #ī ZX Y.6א א ,+ZD L • א #ī PnX Y.6א א PD 3 • א cא ĩ Pn.6א ,* 0אLHA 0Ò • א cאĩ Z.6 א cא א ,+ Az 0 45 k*:V*- 4אN X$א ,+*X 8`1*~ Lat(30N) – h(22.5) – Dec(11S) – AZ(242) Lat(30N) – h(49) – Dec(30.7N) – AZ(80) Lat(30S) – h(38) – Dec(42S) – AZ(240) Lat(30S) – h(31.5) – Dec(7S) – AZ(80) 46 .*W E1FO 38 אj*: H 4;אaqא& %א cאא , Az 0+ WV X X@א +WFJ א א ,+ZD L א cאא ,* 0א LHA 0Ò lא א! Lat 30˚ N 290˚ 60˚ Y*0א : א/,1$A 6˚2 G: ;אĩ 45 *93( QGaq.6;אaq א&¤i*0:<i*3o*>אE cKĨiא אaq o6.ī^אOא א! 0G Z oi*3oD0 +#;*>אKi cKĨא אīaq.6א אaq א :0א&E 47 290˚\0G o4 אH:#א(א ,+* א ĩL.6)+0 א cאא ,* 0אLHA 0Ò @8V X Xא(?o^אOא א!א # M*ě*8א Pt S@0_ @א @A, G Z X'3$ א %*> ?ĜOToא/1#'א/@*:] 4 Vא;oא6Òאj#3Ġ_:@xא cאG O: oא cאO #9א #Yא #א!3GĦ86 א Pn [3 ,א @ X' X o4 אH:#א(א ,+* 30' #א^אE 48 א 6Qא .* #א)'א @X #$ 0Sĩ dØ(V Í*א א&/*" ( 1625 – 1572 ) *8F*9#%_G a%k $ 1603 $*" E,0+א @*Sm8*9 c00ĩ $#X W ، g8? A :*8א$ ú א&Ę א 0G*G#0 א F#EL ? c0E" i* 24א @K#K6K"*SG* / a5 [,ę$#X 0+p M 4، א EL 88 K#K 0ę c X@ א&/'"K#K *8* c Z ( α ) * א ( β ) *08c D0" א +*G?F \א #K Z א ; Z ( γ ) **%c δ ) * ) ،9א 9FNV، Ö KKKאא ,,6 א `a5[,ę_Eא +*F i*k5\0 D@א *t E K [ M9'א #^V8*8: א #K א @0+Xא L S*א @X 8* 67א/K# ، QA אQoV[E Aries 6+ğ*>אK#K ، Ari i א , QoV[E Cancer F*k*>אěO*" ، Cnc i*^- א;א @X#$"א #K א #אa ; אúğא 0G*G#0 אúğ*8G*:Hא *0Gא S0E Z ? ، a , b , c aÙtQ* אúğ א aÙ ، '9אא&:#c0E"Pא @V$#X p'/Jh#$א ,+*(Sq*Ú`8* אĠ*! א/א/א Ħ8א @*Y، 4: 60א/.*pO *אĞ α Ori <* #9@]אĞ#^א( p ، Betelgeuse *א ]א&α CMa ×K #9 א 7א K Sirius 0G*+0 "9אא V *@%<;6QאK pq*ÌTZ -*0Z+*%*( -"א # א _ ,@ 2014 א Q*;> ? ! א א&Ø5H*8 0א ' ] א/, א0x>א" 8*/+ א/ M9 ، a א @X#$א/9a<*A_ ?א >א Ei*G*/.K` 3.5 9*h *QE *3[,ęi* S*א/,+0 O*Û 90˚4P#@% 70˚?60"a<#Qf،9א* DE9*7lØ ?א @X#$ "@3@*אt ĞאK0 אúğ א ª אúğ א ª אúğ א ª < ρ *E#V ι * α *+t0: σ *8*K κ *08 β N λ ** γא E τ* F#,8 υ #0 μ * ; δ * φ #0G ν F#,8V ε ξ *^ ζ ^א 7E χ_ *,8 ψ F0 ο *V η *t0 ω *8 π *0Z θ %O אúğא 0G*G#0 Sh* 51 )*q+א #K *- א @0+X >) א #K F E_8 א #K QoV Ec0pV F*> >) א #K F E_8 א #K QoV Ec0pV F*> Ori Orion 23 And Andromeda 1 א/aא/,, אĞ *> Ser Serpens 24 Boo Bootes 2 א #א( א0ğ Psc Pisces 25 Del Delphinus 3 א Ħ אğ#- CMi Canis Minor 26 Dra Draco 4 א @Ħ א ]א&!t Leo Leo 27 Tri Triangulum 5 א/. א&: Tau Taurus 28 Aur Auriga 6 w,א& @ א .#> Ara Ara 29 Equ Equuleus 7 )3א Y אa+Ó Crt Crater 30 UMa Ursa Major 8 א Pא&K× א *0k CMa Canis Major 31 Her Hercules 9 אZ*Ğ_ א ]א&K× Lep Lepus 32 Cas Cassiopeia 10 Wא-א :_ א&>G] Crv Corvus 33 Cep Cepheus 11 א/S] א tאP Sgr Sagittarius 34 UMi Ursa Minor 12 א Pא&!t א א_ Sco Scorpius 35 Cnc Cancer 13 א ,F*k א P Cap Capricornus 36 Lyr Lyra 14 א a<*.0 אĞ Corona Corona CrA 37 CrB 15 א60KHא *+7 Borealis _ א60KHאAustralis _8#@Ğ Piscis PsA 38 Peg Pegasus 16 א Yא& h אğ#-אAustrinus _8#@Ğ Lib Libra 39 Per Perseus 17 *Y<6א O#t א/c0אF Lup Lupus 40 Sge Sagitta 18 א ,S א , ' Cen Centaurus 41 Cyg Cygnus 19 א %*% א @3 #> Vir Virgo 42 Ari Aries 20 א6+ğ א >א( Oph Ophiuchus 43 Gem Gemini 21 א #*F אğ#א( Eri Eridanus 44 Aql Aquila 22 א *P א @S 52 q*( '8*E+א #K *- א @0+X >) א #K F E_8 א #K QoV Ec0pV F*> >) א #K F E_8 א #K QoV Ec0pV F*> Cet Cetus \30( 45 67 א #Pup Puppis 6Z 46 א # Aqr Aquarius 68 6+א @ *- Scl Sculptor 47 א Hya Hydra *X7 69 א #> For Fornax 48 אCha Chamaeleon )*8ğ 70 א @*» Cae Caelum 49 א Mus Musca 8*8 71 א * Car Carina a 50 א ,+א Vol Volans aq*3 72 אx#א( Ant Antlia 51 אInd Indus @x 73 א :*$ Pic Pictor 52 0א/*( Hyi Hydrus 74 אMic Microscopium SÓ 53 א Gru Grus _K 75 א 7 Ret Reticulum q*k 54א ;Aps Apus Y 76 א .+? Oct Octans 55 א Pav Pavo Y*3 77 א ,* Hor Horologium 56 א @*( J08 78 Phe PhoenixאPyx Pyxis a8H Dor Dorado 0: 8_ 57 79 א 7א Vel Vela Triangulum Men Mensa 80 TrA 58 א/. אAustrale _8#@Ğ אĞ 6 59 א Tuc Tucana F*(#3 81 א/)] Tel Telescopium 60 א Lac Lacerta a)*h 82 8'א @Nor Norma <*X 61 א .] Vul Vulpecula 83 א Cir Circinus <*0 Canes Cam Camelopardalis 84 CVn 62 א ,#)Venatici F*0 א c>א 63 א&:א&!LMi Leo Minor t 85 !0]אCru Crux P#@Ğ 64 א Lyn Lynx 5# 86 אCol Columba *+ğ 65 א Sct Scutum YØ 87 0א Mon Monoceros F Coma Com 88 Sex Sextans 66 א ,Y אx Berenices 53 #א)'א @X#$ V: א @X א > V: א @X א/3'א/,0 א/60 HR K#K c0pV _8 2.06 + 29° 10 ′ 14 ″ 00 h 09 m 08 s α Alpheratz a: 15א Y א/aא/,, 2.27 + 59° 13 ′ 47 ″ 00 h 09 m 58 s β Caph 21 א אW [0mĠא-א :_ 2.83 + 15° 15 ′ 51 ″ 00 h 13 m 59 s γ Algenib 39 אĞ@] א Yא& h Deneb Al 3.56 - 08° 44 ′ 37 ″ 00 h 20 m 10 s ι GW 74])30\א *+7 Shemali _ )30\ 2.39 - 42° 13 ′ 38 ″ 00 h 27 m 00 s α Ankaa 99 א @*( א @*( 3.27 + 30° 56 ′ 25 ″ 00 h 40 m 06 s δ Delta And 165 :א/@ Ħ א/aא/,, 2.23 + 56° 37 ′ 00 ″ 00 h 41 m 20 s α Schedar W<! 168א-א :_ Wא-א :_ Deneb 2.04 - 17° 54 ′ 26 ″ 00 h 44 m 19 s β GW 188])30\אKaitos _8#@Ğ )30\ 3.44 + 57° 53 ′ 30 ″ 00 h 50 m 00 s η Achird S 219א @*) Wא-א :_ 2.47 + 60° 47 ′ 42 ″ 00 h 57 m 36 s γ Gamma Cas W** 264א-א :_ Wא-א :_ 3.31 - 46° 38 ′ 27 ″ 01 h 06 m 44 s β Beta Phe 322 08*א @*( א @*( 3.45 - 10° 06 ′ 21 ″ 01 h 09 m 19 s η Eta Ceti 334 ?א @**- )30\ 2.06 + 35° 41 ′ 49 ″ 01 h 10 m 33 s β Mirach 337 38?אğ#- א/aא/,, 2.68 + 60° 18 ′ 37 ″ 01 h 26 m 47 s δ Ruchbah 403 א K Wא-א :_ 3.41 - 43° 14 ′ 40 ″ 01 h 29 m 00 s γ Gamma Phe 429 **א @*( א @*( 0.46 - 57° 09 ′ 48 ″ 01 h 38 m 15 s α Achernar o 472א @S א @S 3.50 - 15° 51 ′ 42 ″ 01 h 44 m 45 s τ Tau Ceti 509 ?א @**- )30\ 3.41 + 29° 38 ′ 56 ″ 01 h 53m 55 s α Mothallah Y< 544א/. א/. 2.64 + 20° 52 ′ 42 ″ 01 h 55 m 27 s β Sharatan 553 א F*k7 א6+ğ 3.38 + 63° 44 ′ 27 ″ 01 h 55 m 27 s ε Segin WF#,8V 542א-W _:Kא-א :_ HR : The Bright Star Catalogue, also known as the Yale Catalogue of Bright Stars. 54 V: א @X א > V: א @X א/3'א/,0 א/60 HR K#K c0pV _8 Head of 2.86 - 61° 29 ′ 59 ″ 01 h 59 m 14 s α Y< 591אHydrus 0ğ 0א/*( 2.26 + 42° 23 ′ 55 ″ 02 h 04 m 48 s γ Almach 603 @*2א&>l א/aא/,, 2.00 + 23° 31 ′ 49 ″ 02 h 08 m 00 s α Hamal 617 א @*k אğ+ 6 3.00 + 35° 03 ′ 19 ″ 02 h 10 m 25 s β Beta Tri 622 08*א/. א/. 2-10 - 02° 54 ′ 45 ″ 02 h 20 m 05 s ο Mira 681 0א )30\ Kaff 3.47 03° 17 ′ 46 ″ 02 h 44 m 03 s γ K 804 אH \30( alijidhma )*Ğ 2.02 + 89° 19 ′ 33 ″ 02 h 49 m 33 s α Polaris 424 אĞ א Pא&!t 3.24 - 40° 14 ′ 50 ″ 02 h 58 m 49 s θ Acamar 897 א 0h א @S 2.53 + 04° 08 ′ 45 ″ 03 h 03 m 02 s α Menkar 911 א/@A )30\ 2.93 + 53° 33 ′ 44 ″ 03 h 05 m 52 s γ Gamma Per 915 :* א .* *Y<6א O#t 3.39 + 38° 53 ′ 44 ″ 03 h 06 m 07 s ρ Rho Per Q ? 921 א .* *Y<6א O#t 2.12 + 41° 00 ′ 38 ″ 03 h 09 m 07 s β Algol 936 א Y<6* O#tא O#t 1.79 + 49° 54 ′ 42 ″ 03 h 25 m 22 s α Mirfak 1017 א .* *Y<6א O#t 3.54 - 09° 42 ′ 55 ″ 03 h 43 m 57 s δ Delta Eri 1136 ; * א @S א @S 3.01 + 47° 49 ′ 58 ″ 03 h 43 m 58 s δ Delta Per 1122 m א .* *Y<6א O#t 2.87 + 24° 08 ′ 56 ″ 03 h 48 m 21 s η Alcyone 1165 א G#0_ א .#> 2.85 + 31° 55 ′ 32 ″ 03 h 55 m 03 s ζ Zeta Per ? 1203 E*א . * *Y<6א O#t 2.95 - 13° 28 ′ 05 ″ 03 h 58 m 42 s γ Zaurak 1231 א c>2 א @S 2.89 + 40° 03 ′ 04 ″ 03 h 58 m 50 s ε Epsilon Per Q ? 1220 א .* *Y<6א O#t h m s Lambda 3.47 Nאא .#> λ א .#> 29 01 04 ″ 49 ′ 31 12° + Tau 1239 55 V: א @X א > V: א @X א/3'א/,0 א/60 HR K#K c0pV _8 3.35 - 62° 26 ′ 16 ″ 04 h 14 m 37 s α Alpha Ret Oct ¬ 1336 א 7 3.53 + 19° 12 ′ 41 ″ 04 h 29 m 28 s ε Epsilon Tau 1409 א 0? א .#> 3.40 + 15° 54 ′ 07 ″ 04 h 29 m 30 s θ Theta Tau 1412 ? א sqT א .#> 3.27 - 55° 00 ′ 55 ″ 04 h 34 m 19 s α Alpha Dor 0:_8 0:_8* 1465 0.85 + 16° 32 ′ 14 ″ 04 h 36 m 45 s α Aldebaran 1457 א 8אF א .#> h m s 3.19 + 06° 59 ′ 08″ 04 50 38 π Tabit 1543 א .*J8 אĞ *> 2.69 + 33° 11 ′ 16 ″ 04 h 57 m 56 s ι Hassaleh W[K 1577 א @*w F,א& @ 2.99 + 43° 50 ′ 36 ″ 05 h 03 m 01 s ε Almaaz 1605 א/w c,א& @ 3.19 - 22° 21 ′ 09 ″ 05 h 06 m 05 s ε Epsilon Lep W 1654)?א&>G] א&>G] 3.17 + 41° 15 ′ 10 ″ 05 h 07 m 32 s η Hoedus II 1641 אĞא .*w _G,א& @ 2.79 - 05° 04 ′ 07 ″ 05 h 08 m 34 s β Cursa 1666 א :_ א @S 3.31 - 16° 11 ′ 21 ″ 05 h 13 m 35 s μ Mu Lep FWV 1702א&>G] א&>G] 0.12 - 08° 11 ′ 09 ″ 05 h 15 m 14 s β Rigel 1713 >6%אĞ *> אĞ *> 0.08 + 46° 00 ′ 40 ″ 05 h 17 m 46 s α Capella 1708 א w 2#0,א& @ 3.36 - 02° 23 ′ 05 ″ 05 h 25 m 12 s η Algiebba V 1788*אĞ *> אĞ *> 1.64 + 06° 21 ′ 42 ″ 05 h 25 m 55 s γ Bellatrix 1790 א @*% אĞ *> 1.65 + 28° 37 ′ 06 ″ 05 h 27 m 13 s β Elnath 1791 א @3 א .#> 2.84 - 20° 44 ′ 56 ″ 05 h 28 m 52 s β Nihal SGO* 1829 א&>G] 2.23 - 00° 17 ′ 22 ″ 05 h 32 m 45 s δ Mintaka 1852 א/@3 אĞ *> 2.58 - 17° 48 ′ 46 ″ 05 h 33 m 22 s α Arneb 1865 א&>G] א&>G] 56 V: א @X א > V: א @X א/3'א/,0 א/60 HR K#K c0pV _8 3.54 + 09° 56 ′ 34 ″ 05 h 35 m 56 s λ Meissa F*,0 1879 אĞ *> 2.77 - 05° 54 ′ 05 ″ 05 h 36 m 09 s ι Nair al Saif ÙG 1899א ,0 אĞ *> 1.70 - 01° 11 ′ 37 ″ 05 h 36 m 57 s ε Alnilam 1903 א @ h*$ אĞ *> 3.00 + 21° 09 ′ 01 ″ 05 h 38 m 31 s ζ Alheka 1910 ^*א .#> א .#> 2.64 - 34° 04 ′ 02 ″ 05 h 40 m 11 s α Phact o* 1956 אğ+* 2.03 - 01° 56 ′ 09 ″ 05 h 41 m 30 s ζ Alnitak 1948 א @3*2 אĞ *> 3.55 - 14° 49 ′ 03 ″ 05 h 47 37 s ζ Zeta Lep 1998 ^* א&>G] א&>G] 2.06 - 09° 39 ′ 56 ″ 05 h 48 m 27 s κ Saiph 2004 :0 אĞ *> 3.12 - 35° 45 ′ 49 ″ 05 h 51 m 28 s β Wezn F^ 2040 אğ+* 0.50 07° 24 ′ 31 ″ 05 h 55 m 57 s α Betelgeuse 2061 @]אĞ#^א( אĞ H <* 1.90 + 44° 56 ′ 51 ″ 06 h 00 m 36 s β Menkalinan W[@ 2088 א @*w F,א& @ 2.62 + 37° 12 ′ 44 ″ 06 h 00 m 43 s θ Theta Aur w *0Z 2095,א& @ w,א& @ 3.28 + 22° 30 ′ 05 ″ 06 h 15 m 45 s η Tejat Prior 2216 א a*0א/$ א #*F 3.02 - 30° 04 ′ 14 ″ 06 h 20 m 52 s ζ Furud 2282 ? א ; א ]א&K× 1.98 - 17° 57 ′ 50 ″ 06 h 23 m 20 s β Mirzam 2294 א/^$ א ]א&K× h m s Tejat 2.88 א a*0א/μ o א #*F 50 23 06 ″ 18 ′ 30 22° + Posterior 2286 -0.72 - 52° 42 ′ 15 ″ 06 h 24 m 16 s α Canopus 60S: 2326 א * a 3.17 - 43° 12 ′ 33 ″ 06 h 38 m 12 s ν Nu Pup #0G 2451 א #6Z א #6Z 1.93 + 16° 23 ′ 08 ″ 06 h 38 m 33 s γ Alhena 2421 אx@ א #*F 2.98 + 25° 06 ′ 56 ″ 06 h 44 m 49 s ε Mebsuta W 2473>אאN:א/ ,#k א #*F 57 V: א @X א > V: א @X א/3'א/,0 א/60 HR K#K c0pV _8 -1.46 - 16° 44 ′ 13 ″ 06 h 45 m 47 s α Sirius 2491 א 7א 0G*+0 א ]א&K× 3.36 12° 52 ′ 44 ″ 06 h 46 m 06 s ξ Alzirr 2484 א c> א #*H F 3.27 - 61° 57 ′ 26 ″ 06 h 48 m 20 s α Alpha Pic 2550 א :*$ א :*$ 2.93 - 50° 37 ′ 56 ″ 06 h 50 m 18 s τ Tau Pup Ħ860S: 2553 א #6Z 1.50 - 28° 59 ′ 33 ″ 06 h 59 m 12 s ε Adhara 2618 א> א ]א&K× 3.47 - 27° 57 ′ 23 ″ 07 h 02 m 18 s σ Sigma CMa 2646 ?א א> א ]א&K× Omicron 2 3.02 - 23° 51 ′ 19 ″ 07 h 03 m 38 s ο 2653 ?א א> CMa א ]א&K× 1.84 - 26° 25 ′ 01 ″ 07 h 08 m 59 s δ Wezen 2693 א #^F א ]א&K× 2.70 - 37° 07 ′ 27 ″ 07 h 17 m 39 s π Pi Pup 2773 8* א #6Z א #6Z 3.53 + 21° 57 ′ 16 ″ 07 h 20 m 59 s δ Wasat 2777 : א #*F 2.45 - 29° 19 ′ 56 ″ 07 h 24 m 40 s η Aludra 2827 a<אĞ#^א( א ]א&K× 2.90 + 08° 15 ′ 33 ″ 07 h 27 m 56 s β Gomeisa 2845 א Q0+t*( א ]א&!t 3.25 - 43° 19 ′ 53 ″ 07 h 29 m 41 s σ Sigma Pup t0: 2878+* א #6Z א #6Z 1.98 + 31° 51 ′ 19 ″ 07 h 35 m 31 s α Castor Y< 2891א #$א/$ א #*F 0.38 + 05° 11 ′ 13 ″ 07 h 40 m 04 s α Procyon 2943 א 7א 7*0 א ]א&!t 3.57 + 24° 21 ′ 44 ″ 07 h 45 m 19 s κ Kappa Gem K 2985*8* א #*F א #*F 1.14 + 27° 59 ′ 24 ″ 07 h 46 m 12 s β Pollux Y< 2990א #$א/o א #*F 3.34 - 24° 53 ′ 49 ″ 07 h 49 m 54 s ξ Asmidiske 3045 ^א א #6Z א #6Z 3.47 - 53° 01 ′ 18 ″ 07 h 57 m 09 s χ Chi Carinae 7E 3117_ א * a א * a 2.25 - 40° 02 ′ 41 ″ 08 h 04 m 06 s ζ Naos m 60S: 3165*> א #6Z 58 V: א @X א > V: א @X א/3'א/,0 א/60 HR K#K c0pV _8 2.81 - 24° 20 ′ 49 ″ 08 h 08 m 10 s ρ Tureis 3185 א YØ א #6Z Suhail al 1.78 - 47° 22 ′ 47 ″ 08 h 09 m 59 s γ 60S: 3207אMuhlif Ò א 7א 3.52 + 09° 08 ′ 24 ″ 08 h 17 m 18 s β Altarf úk 3249א ,F*k א ,F*k 1.86 - 59° 33 ′ 23 ″ 08 h 22 m 49 s ε Avior F#,8V 3307 א * a א * a 3.37 + 60° 40 ′ 06 ″ 08 h 31 m 28 s ο Muscida 3323 א3Ġ א Pא&K× 1.96 - 54° 45 ′ 45 ″ 08 h 45 m 06 s δ Delta Vel 3485 ; * א 7א א 7א 3.38 + 06° 21 ′ 53 ″ 08 h 47 m 33 s ε Epsilon Hya F#,8V 3482א X7* א X7* 3.11 + 05° 53 ′ 23 ″ 08 h 56 m 10 s ζ Zeta Hya 3547 ^*א X7* א X7* 3.14 + 47° 59 ′ 02 ″ 09 h 00 m 12 s ι Talitha 3569 א acא .* . א +7* 0 א Pא&K× 2.21 - 43° 29 ′ 30 ″ 09 h 08 m 32 s λ Al suhail 60S: 3634א #^F א 7א 3.44 - 59° 01 ′ 36 ″ 09 h 11 m 21 s a Car FE 3659 א * a א * a 1.68 - 69° 46 ′ 37 ″ 09 h 13 m 21 s β Miaplacidus 3685 08* א * a א * a 2.25 - 59° 20 ′ 11 ″ 09 h 17 m 29 s ι Aspidiske E#V 3699* א * a א * a 3.13 + 34° 19 ′ 50 ″ 09 h 21 m 56 s α Alpha Lyn 3705 * א 5# א 5# 2.50 - 55° 04 ′ 23 ″ 09 h 22 m 34 s κ Kappa Vel K 3734*8* א 7א א 7א 1.98 - 08° 43 ′ 19 ″ 09 h 28 m 18 s α Alphard 3748 ;א א X7* 3.13 - 57° 05 ′ 55 ″ 09 h 31 m 40 s N Vel FFE 3803 א 7א א 7א 3.17 + 51° 36 ′ 37 ″ 09 h 33 m 49 s θ Theta UMa 0Z 3775* א Pא&K× א Pא&K× Omicron 3.52 + 09° 49 ′ 33 ″ 09 h 41 m 55 s ο 3852 ~]א&: Leo א&: Ras Elased 2.98 + 23° 42 ′ 25 ″ 09 h 46 m 40 s ε 3873 אAustralis _8#@Ğ א&: 59 V: א @X א > V: א @X א/3'א/, 0 0 0 א/60 HR K#K c0pV _8 3.01 - 65° 08 ′ 22 ″ 09 h 47 m 28 s υ Upsilon Car F#,8 3890 א * a א * a 3.52 + 16° 41 ′ 29 ″ 10 h 08 m 07 s η Eta Leo 3975 ?אĞ S א&: 1.35 + 11° 53 ′ 45 ″ 10 h 09 m 09 s α Regulus 3982 א/0 א&: 3.44 + 23° 20 ′ 40 ″ 10 h 17 m 30 s ζ Adhafera 4031 א m a 0 א&: 3.40 - 61° 24 ′ 18 ″ 10 h 17 m 34 s Q Car E #0K F 4050 א * a א * a Tania 3.45 + 42° 50 ′ 29 ″ 10 h 17 m 58 s λ 4033 א acא .*0Gא *+7 Borealis 0 א Pא&K× 2.61 + 19° 46 ′ 04 ″ 10 h 20 m 46 s γ Algieba 4057 א Ğ S א&: Tania 3.05 + 41° 25 ′ 34 ″ 10 h 23 m 11 s μ 4069 א acא .*0G אAustralis 08#@Ğ א Pא&K× 3.32 - 61° 45 ′ 37 ″ 10 h 32 m 33 s P Car PE F 4140 א * a א * a 2.76 - 64° 28 ′ 14 ″ 10 h 43 m 29 s θ Theta Car 0Z 4199* א * a א * a 2.69 - 49° 29 ′ 50 ″ 10 h 47 m 24 s μ Mu Vel 4216 #0 א 7א א 7א 3.11 - 16° 16 ′ 11 ″ 10 h 50 m 21 s ν Nu Hya #0G 4232א X7* א X7* 2.37 + 56° 18 ′ 16 ″ 11 h 02 m 43 s β Merak 4295 א/ א2 א Pא&K× 1.80 + 61° 40 ′ 21 ″ 11 h 04 m 37 s α Dubhe 4301 א 8 א Pא&K× 3.01 + 44° 25 ′ 10 ″ 11 h 10 m 28 s ψ Psi UMa 4335 8,* א Pא&K× א Pא&K× 2.56 + 20° 26 ′ 39 ″ 11 h 14 m 53 s δ Zosma S 4357א&: א&: 3.34 + 15° 21 ′ 00 ″ 11 h 15 m 00 s θ Chort 4359 אĠ - א&: h m s Alula 3.48 א ac א&ħא *+7 ν 0 א Pא&K× 16 19 11 ″ 54 ′ 00 33° + Borealis 4377 3.54 - 31° 56 ′ 17 ″ 11 h 33 m 43 s ξ Xi Hya 4450 ^אא X7* א X7* h m s Lambda 3.13 Nא א @λ <#3 א @#3> 27 36 11 ″ 01 ′ 06 63° - Cen 4467 60 V: א @X א > V: א @X א/3'א/,0 א/60 HR K#K c0pV _8 2.14 + 14° 29 ′ 27 ″ 11 h 49 m 48 s β Denebola 4534 א Q א&: 2.44 + 53° 36 ′ 51 ″ 11 h 54 m 35 s γ Phecda 4554 א A א Pא&K× 2.60 - 50° 48 ′ 11 ″ 12 h 09 m 07 s δ Delta Cen 4621 ; * א @#3> א @#3> 3.00 - 22° 42 ′ 01 ″ 12 h 10 m 52 s ε Minkar 4630 @*>א tאP א tאP 2.80 - 58° 49 ′ 46 ″ 12 h 15 m 55 s δ Delta Cru 4656 ; * !0]אP#@Ğ !0]אP#@Ğ 3.31 + 56° 57 ′ 08 ″ 12 h 16 m 08 s δ Megrez 4660 ^א/t א Pא&K× h m s Gienah 2.59 %@*dא tאγ P א tאP 33 16 12 ″ 20 ′ 37 17° - Ghurab 4662 1.33 - 63° 10 ′ 46 ″ 12 h 27 m 25 s α Acrux 4730 * !0]אP#@Ğ !0]אP#@Ğ 2.95 - 16° 35 ′ 46 ″ 12 h 30 m 37 s δ Algorab 4757 א tאP א tאP 1.63 - 57° 11 ′ 39 ″ 12 h 31 m 59 s γ Gacrux 4763 %** !0]אP#@Ğ !0]אP#@Ğ 2.65 - 23° 28 ′ 36 ″ 12 h 35 m 09 s β Kraz K 4786א^ א tאP 2.69 - 69° 12 ′ 55 ″ 12 h 38 m 04 s α Alpha Mus F8 4798א 8*8 א 8* 8 2.17 - 49° 02 ′ 21 ″ 12 h 42 m 19 s γ Muhlifain 4819 אÒ 0? א @#3> 3.48 - 01° 31 ′ 44 ″ 12 h 42 m 24 s γ Porrima 4825 %** א >א( א >א( 3.05 - 68° 11 ′ 14 ″ 12 h 47 m 11 s β Beta Mus 4844 Ħא 8*8 א 8*8 1.25 - 59° 46 ′ 04 ″ 12 h 48 m 35 s β Mimosa 4853 08* !0]אP#@Ğ !0]אP#@Ğ 1.77 + 55° 52 ′ 53 ″ 12 h 54 m 40 s ε Alioth 4905 אF#Ğ א Pא&K× 3.38 + 03° 19 ′ 08 ″ 12 h 56 m 20 s δ Auva 4910 א #א( א >א( 2.90 + 38° 14 ′ 25 ″ 12 h 56 m 42 s α Cor Caroli K 4915 א ,+*( א ,#)F*0 2.83 + 10° 52 ′ 53 ″ 13 h 02 m 54 s ε Vindemiatrix F#,8V 4932 א >א( א >א( 61 V: א @X א > V: א @X א/3'א/,0 א/60 HR K#K c0pV _8 Gamma 3.00 - 23° 14 ′ 51 ″ 13 h 19 m 43 s γ 5020 %**א Hyd *X7 א X7* 2.75 - 36° 47 ′ 18 ″ 13 h 21 m 25 s ι Iota Cen E#V 5028* א @#3> א @#3> 2.27 + 54° 51 ′ 00 ″ 13 h 24 m 30 s ζ Mizar c 5054>א/ א Pא&K× 0.98 - 11° 14 ′ 12 ″ 13 h 25 m 58 s α Spica 5056 א ,+*א& Oc א >א( 3.37 + 00° 40 ′ 10 ″ 13 h 35 m 26 s ζ Heze 5107 ^* א >א( א >א( 2.30 - 53° 32 ′ 22 ″ 13 h 40 m 49 s ε Birdun 5132 א ×;F א @#3> 1.86 + 49° 14 ′ 29 ″ 13 h 48 m 07 s η Alkaid 5191 א *q א Pא&K× 3.41 - 41° 45 ′ 34 ″ 13 h 50 m 23 s ν Nu Cen #0G 5190 א @#3> א @#3> 3.04 - 42° 32 ′ 43 ″ 13 h 50 m 30 s μ Mu Cen 5193 #0א @#3> א @#3> 2.68 + 18° 19 ′ 32 ″ 13 h 55 m 23 s η Muphrid 5235 ;א א א #א( 2.55 - 47° 21 ′ 33 ″ 13 h 56 m 27 s ζ Zeta Cen 5231 38?א @#3> א @#3> 0.61 - 60° 26 ′ 32 ″ 14 h 04 m 52 s β Hadar m 5267*> א @#3> 3.27 - 26° 45 ′ 06 ″ 14 h 07 m 12 s π Pi Hyd 5287 8*א X7* א X7* 2.06 - 36° 26 ′ 26 ″ 14 h 07 m 32 s θ Menkent 5288 @]א @#3> א @#3> -0.04 + 19° 06 ′ 27 ″ 14 h 16 m 19 s α Arcturus 5340 א ,+*א א א #א( 3.03 + 38° 14 ′ 43 ″ 14 h 32 m 40 s γ Seginus Y<* 5435 א #א( 2.31 - 42° 13 ′ 14 ″ 14 h 36 m 26 s η Eta Cen V 5440* א @#3> א @#3> Rigil -0.01 - 60° 53 ′ 40 ″ 14 h 40 m 36 s α 5459 >6%א @Kentaurus <#3 א @#3> 2.30 - 47° 26 ′ 58 ″ 14 h 42 m 54 s α Alpha Lup 5469 *א , ' א , ' 3.19 - 65° 02 ′ 14 ″ 14 h 43 m 42 s α Alpha Cir 5463 א ×6% א 0*> 62 V: א @X א > V: א @X א/3'א/,0 א/60 HR K#K c0p VVV _8 2.70 + 27° 00 ′ 49 ″ 14 h 45 m 37 s ε Izar V 5506^א> א #א( 2.08 + 74° 05 ′ 46 ″ 14 h 50 m 41 s β kochab G 5563#>א )? א Pא&!t Zuben 2.75 - 16° 06 ′ 05 ″ 14 h 51 m 41 s α 5531 א F*8cאElgenubi _8#@Ğ א/c0אF 2.68 - 43° 11 ′ 29 ″ 14 h 59 m 29 s β Beta Lup 5571 08*א , ' א , ' 3.13 - 42° 09 ′ 41 ″ 15 h 00 m 07 s κ Kappa Cen K 5576*8* א @#3> א @#3> 3.50 + 40° 20 ′ 02 ″ 15 h 02 m 30 s β Nekkar 5602 א *> א #א( 3.29 - 25° 20 ′ 17 ″ 15 h 04 m 55 s σ Brachium t0: 5603+* א/c0אF א/c0אF 3.41 - 52° 09 ′ 12 ″ 15 h 13 m 20 s ζ Zeta Lup 5649 ^* א , ' א , ' 3.47 + 33° 15 ′ 41 ″ 15 h 16 m 05 s δ Delta Boo 5681 ; * א #א( א #א( h m s Zuben 2.61 א F*8cא *+7 β _ א/c0אF 47 17 15 ″ 08 ′ 26 09° - Eschamali 5685 2.89 - 68° 43 ′ 54 ″ 15 h 20 m 17 s γ Gamma TrA 5671 %** א/. אĞ @8#_ א/. אĞ@8#_ 3.05 + 71° 46 ′ 57 ″ 15 h 20 m 43 s γ Pherkad o 5735 4א )? א Pא&!t 3.22 - 40° 41 ′ 56 ″ 15 h 22 m 20 s δ Delta Lup 5695 ; * א , ' א , ' 3.37 - 44° 44 ′ 27 ″ 15 h 23 m 40 s ε Epsilon Lup F#,8V 5708 א , ' א , ' 3.29 + 58° 54 ′ 56 ″ 15 h 25 m 15 s ι Edasich 5744 ®א א @Ħ 2.23 + 26° 40 ′ 00 ″ 15 h 35 m 18 s α Alphecca 5793 א א60KHא +7* _ 2.78 - 41° 12 ′ 52 ″ 15 h 36 m 07 s γ Gamma Lup 5776 %** א , ' א , ' 2.65 + 06° 22 ′ 51 ″ 15 h 44 m 59 s α Unukalhai 5854 @ א0ğ א0ğ 3.53 - 03° 28 ′ 25 ″ 15 h 50 m 23 s μ Mu Ser 5881 #0 א0ğ א0ğ 2.85 - 63° 28 ′ 26 ″ 15 h 56 m 26 s β Beta TrA 5897 08* א/. אĞ@8#_ א/. אĞ@8#_ 63 V: א @X א > V: א @X א/3'א/,0 א/60 HR K#K c0pV _8 2.89 - 26° 09 ′ 17 ″ 15 h 59 m 44 s π Pi Sco 5944 אĞ@8#_ ?א60KH א P 3.41 - 38° 26 ′ 13 ″ 16 h 01 m 05 s η Eta Lup V 5948* א , ' א , ' 2.32 - 22° 39 ′ 43 ″ 16 h 01 m 12 s δ Dschubba % 5953 Sא P א P 2.62 - 19° 50 ′ 39 ″ 16 h 06 m 17 s β Graffias 4G*8^ 5984א P א P 2.74 - 03° 43 ′ 50 ″ 16 h 15 m 06 s δ Yed Prior 6056 א 0א/ אğ#א( Yed 3.24 - 04° 43 ′ 37 ″ 16 h 19 m 05 s ε 6075 א 0א/`Posterior ao אğ#א( 2.89 - 25° 37 ′ 35 ″ 16 h 22 m 04 s σ Al Niyat 6084 א @j*0 א P 2.74 + 61° 28 ′ 54 ″ 16 h 24 m 11 s η Aldhibain 6132 א q]א/o א @Ħ 0.96 - 26° 27 ′ 47 ″ 16 h 30 m 18 s α Antares 6134 א ] א P 2.77 + 21° 27 ′ 32 ″ 16 h 30 m 51 s β Kornephoros 6148 *6אxאa א_Z*Ğ K<4 D 2.82 - 28° 14 ′ 42 ″ 16 h 36 m 47 s τ Tau Sco j*0G 6165א ] א P 2.56 - 10° 35 ′ 43 ″ 16 h 37 m 58 s ζ Zeta Oph 6175 א ,*8א&O אğ#א( 2.81 + 31° 34 ′ 37 ″ 16 h 41 m 50 s ζ Zeta Her 6212 ^*אZ*Ğ_ א_Z*Ğ K<4 D 3.53 + 38° 53 ′ 43 ″ 16 h 43 m 24 s η Eta Her V 6220*אZ*Ğ_ א_Z*Ğ K<4 D 1.92 - 69° 03 ′ 08 ″ 16 h 50 m 13 s α Atria E 6217* א/. אĞ@8#_ 2.29 - 34° 19 ′ 06 ″ 16 h 51 m 06 s ε Wei O 6241א a א P 3.08 - 38° 04 ′ 15 ″ 16 h 52 m 51 s μ Mu Sco G*Z 6247_א a א P 3.59 - 42° 23 ′ 05 ″ 16 h 55 m 36 s ζ Zeta Sco Z 6271* א a א P 3.20 + 09° 21 ′ 12 ″ 16 h 58 m 21 s κ Kappa Oph K 6299*8* אğ#א( אğ#א( 3.13 - 56° 00 ′ 41 ″ 16 h 59 m 50 s ζ Zeta Ara 6285 ^* אa+Ó אa+Ó 64 V: א @X א > V: א @X א/3'א/,0 א/60 HR K#K c0pV _8 3.17 + 65° 41 ′ 49 ″ 17 h 08 m 50 s ζ Zeta Dra 6396 א q]א/$ א @Ħ 2.43 - 15° 44 ′ 30 ″ 17 h 11 m 13 s η Sabik 6378 א ,*8 אğ#א( 3.33 - 43° 15 ′ 25″ 17 h 13 m 12 s η Eta Sco 6380 >א8'א a א P 3.48 + 14° 22 ′ 29 ″ 17 h 15 m 19 s α Rasalgethi Y< 6406אZ*Ğ_ א_Z*Ğ K<4 D 3.16 + 36° 47 ′ 37 ″ 17 h 15 m 33 s π Pi Her 6418 8*אZ*Ğ_ א_Z*Ğ K<4 D 3.14 + 24° 49 ′ 23 ″ 17 h 15 m 38 s δ Sarin 6410 :*>? א_Z*Ğ K<4 D 3.27 - 25° 00 ′ 46 ″ 17 h 22 m 54 s θ Theta Oph 0Z 6453* אğ#א( אğ#א( 2.85 - 55° 32 ′ 31 ″ 17 h 26 m 31 s β Beta Ara 6461 08* אa+Ó אa+Ó 3.34 - 56° 23 ′ 23 ″ 17 h 26 m 37 s γ Gamma Ara 6462 %** אa+Ó אa+Ó 2.79 + 52° 17 ′ 28 ″ 17 h 30 m 46 s β Rastaban Y< 6536א . *F א @Ħ 2.69 - 37° 18 ′ 22 ″ 17 h 31 m 45 s υ Lesath 6508 א , א P 2.95 - 49° 53 ′ 10 ″ 17 h 32 m 58 s α Alpha Ara 6510 * אa+Ó אa+Ó 1.63 - 37° 06 ′ 47 ″ 17 h 34 m 36 s λ Shaula 6527 א #7 א P 2.08 + 12° 33 ′ 02 ″ 17 h 35 m 37 s α Rasalhague Y< 6556אğ#א( אğ #א( 1.87 - 43° 00 ′ 20 ″ 17 h 38 m 22 s θ Sargas o 6553*\א a א P 3.54 - 15° 24 ′ 24 ″ 17 h 38 m 25 s ξ Xi Ser 6561 ^א א0ğ א0ğ 2.41 - 39° 02 ′ 10 ″ 17 h 43 m 30 s κ Girtab o 6580א *> א P 2.77 + 04° 33 ′ 44 ″ 17 h 44 m 11s β Cebalrai K 6603]א א _ אğ#א( 3.42 + 27° 42 ′ 47 ″ 17 h 47 m 02 s μ Mu Her 6623 #0 אZ*Ğ_ א_Z*Ğ K<4 D 3.03 - 40° 07 ′ 52 ″ 17 h 48 m 36 s ι Iota Sco Y;*: 6615א a א P 65 V: א @X א > V: א @X א/3'א/,0 א/60 HR K#K c0pV ___8 8 8 3.21 - 37° 02 ′ 48 ″ 17 h 50 m 51 s G Sco E 6630* _א #7 א P 2.23 + 51° 29 ′ 16 ″ 17 h 56 m 57 s γ Eltanin 6705 א @Ħ א @Ħ 3.34 - 09° 46 ′ 27 ″ 17 h 59 m 50 s ν Nu Oph #0G 6698 אğ#א( אğ#א( 2.99 - 30° 25 ′ 21 ″ 18 h 06 m 44 s γ Alnasl 6746 א @6Q א א_ 3.11 - 36° 45 ′ 22 ″ 18 h 18 m 37 s η Arkab 6832 א ]א/$ א א_ Kaus 2.70 - 29° 49 ′ 14 ″ 18 h 21 m 55 s δ 6859 :א #Meridianalis Y א א_ 3.26 - 02° 53 ′ 38 ″ 18 h 22 m 04 s η Eta Ser V 6869* א0ğ א0ğ Kaus 1.85 - 34° 22 ′ 35 ″ 18 h 25 m 08 s ε 6879 א #Y אAustralis _8#@Ğ א א_ 3.51 - 45° 57 ′ 32 ″ 18 h 28 m 03 s α Alpha Tel 6897 אP א/)] Kaus 2.81 - 25° 24 ′ 45 ″ 18 h 28 m 52 s λ 6913 א #Y א *+7 Borealis _ א א_ 0.03 + 38° 47 ′ 52 ″ 18 h 37 m 26 s α Vega 7001 א @,א #א)' א a<*.0 3.17 - 26° 58 ′ 29 ″ 18 h 46 m 34 s φ Phi Sgr 7039 ? א @*$א Q*;> א א_ 3.45 + 33° 22 ′ 49 ″ 18 h 50 m 37 s β Sheliak 7106 א , *2 א a<*.0 2.02 - 26° 16 ′ 39 ″ 18 h 56 m 10 s σ Nunki 7121 ? א @*$א Q*;> א א_ 3.51 - 21° 05 ′ 11 ″ 18 h 58 m 36 s ξ Xi² Sgr 7150 ^א א א_ א א_ 3.24 + 32° 42 ′ 37 ″ 18 h 59 m 29 s γ Sulafat 7178 א , *a א a<*.0 2.60 - 29° 51 ′ 29 ″ 19 h 03 m 32 s ζ Ascella 7194 ? א @*$א Q*;> א א_ Deneb el 2.99 + 13° 53 ′ 09 ″ 19 h 06 m 05 s ζ GW 7235]א *Okab P א *P 3.44 - 04° 51 ′ 35 ″ 19 h 07 m 01 s λ Althalimain N 7236א א *P א *P 3.32 - 27° 38 ′ 53 ″ 19 h 07 m 51 s τ Tau Sgr 7234 ? א @*$א Q*;> א א_ 66 V: א @X א > V: א @X א/3'א/,0 א/60 HR K#K c0pV _8 2.89 - 20° 59 ′ 58 ″ 19 h 10 m 38 s π Albaldah 7264 א a א א_ 3.07 67° 41 ′ 13 ″ 19 h 12 m 33 s δ Altais 7310 א 0\ א @H Ħ 3.36 + 03° 08 ′ 41 ″ 19 h 26 m 14 s δ Delta Aql 7377 ; *א *P א *P 3.08 + 27° 59 ′ 27 ″ 19 h 31 m 18 s β Albireo 7417 @*>א %*% א %*% 2.87 + 45° 10 ′ 00 ″ 19 h 45 m 26 s δ Delta Cyg 7528 ?א #א>Y א %*% 2.72 + 10° 38 ′ 58 ″ 19 h 46 m 57 s γ Tarazed 7525 א/c0אF א *P 0.77 + 08° 54 ′ 27 ″ 19 h 51 m 29 s α Altair 7557 א @,א q*3 א *P 3.47 + 19° 31 ′ 56 ″ 19 h 59 m 24 s γ Gamma Sge 7635 %** א ,S א ,S 3.23 + 00° 46 ′ 39 ″ 20 h 12 m 03 s θ Theta Aql 0Z 7710*א *P א *P 3.08 - 14° 44 ′ 05 ″ 20 h 21 m 50 s β Dabih 7776 : א א8 אĞ 2.20 + 40° 18 ′ 13 ″ 20 h 22 m 45 s γ Sadr 7796 א Q> א %*% 1.94 - 56° 41 ′ 14 ″ 20 h 26 m 47 s α Peacock 7790 א Y*3 א Y*3 3.11 - 47° 14 ′ 24 ″ 20 h 38 m 35 s α Alpha Ind 7869 * אx@ אx@ 1.25 + 45° 19 ′ 58 ″ 20 h 41 m 56 s α Deneb 7924 א ;ú א %*% 3.43 + 61° 53 ′ 43 ″ 20 h 45 m 35 s η Eta Cep 7957 א ¬> א/S] 3.42 - 66° 08 ′ 59 ″ 20 h 46 m 15 s β Beta Pav 7913 08*א Y*3 א Y*3 2.46 + 34° 01 ′ 31 ″ 20 h 46 m 48 s ε Gienah d*@% 7949א %*% א %*% 3.20 + 30° 17 ′ 13 ″ 21 h 13 m 33 s ζ Zeta Cyg 8115 ?א #א>Y א %*% 2.44 + 62° 38 ′ 50 ″ 21 h 18 m 56 s α Alderamin 8162 $א >א Ħ א/S] 3.23 + 70° 37 ′ 28 ″ 21 h 28 m 51 s β Alfirk 8238 א 2 א/S] 67 V: א @X א > V: א @X א/3'א/,0 א/60 HR K#K c0pV _8 2.91 - 05° 30 ′ 24 ″ 21 h 32m 19 s β Sadal suud 8232 :א ,#; א # 2.39 + 09° 56 ′ 31 ″ 21 h 44 m 54 s ε Enif G 8308 א Y א Yא& h h m s Deneb 2.87 GW] אδ Ğ אĞ 50 47 21 ″ 39 ′ 03 16° - Algiedi 8322 3.01 - 37° 17 ′ 46 ″ 21 h 54 m 48 s γ Al Dhanab GW 8353]א K_ א K_ 2.96 + 00° 14 ′ 56 ″ 22 h 06 m 32 s α Sadal melik 8414 :א/ א # 1.74 - 46° 53 ′ 25 ″ 22 h 09 m 08 s α Al Nair 8425 א @Ù א K_ 3.53 + 06° 16 ′ 11 ″ 22 h 10 m 56 s θ Baham 8450 : א S*$ א Yא& h 3.35 + 58° 16 ′ 23 ″ 22 h 11 m 22 s ζ Zeta Cep 8465 ^* א/S] א/S] 2.86 - 60° 11 ′ 12 ″ 22 h 19 m 29 s α Alpha Tuc 8502 @*>א F*(#3 א F*(#3 3.40 + 10° 54 ′ 27 ″ 22 h 42 m 11 s ζ Homam 8634 :אx+*$ א Yא& h 2.10 - 46° 48 ′ 30 ″ 22 h 43 m 32 s β Beta Gru 8636 08* א K_ א K_ 2.94 + 30° 17 ′ 51 ″ 22 h 43 m 41 s η Matar 8650 :3 א Yא& h 3.49 - 51° 14 ′ 25 ″ 22 h 49 m 25 s ε Epsilon Gru F#,8V 8675 א K_ א K_ 3.52 + 66° 16 ′ 37 ″ 22 h 50 m 12 s ι Iota Cep E#V 8694* א/S] א/S] 3.48 + 24° 40 ′ 42 ″ 22 h 50 m 42 s μ Sadal bari 8684 :א *> א Yא& h 3.27 - 15° 44 ′ 36 ″ 22 h 55m 25 s δ Skat 8709 א ,*2 א # 1.16 - 29° 32 ′ 42 ″ 22 h 58 m 27 s α Fomalhaut 8728 אğ#- אğ#-אĞ@8#_ 2.42 + 28° 09 ′ 42 ″ 23 h 04 m 29 s β Scheat 8775 @]א Y א Yא& h 2.49 + 15° 17 ′ 01 ″ 23 h 05 m 29 s α Markab ĥ 8781א Y א Yא& h 3.21 + 77° 42 ′ 47 ″ 23 h 39 m 57 s γ Er Rai 8974 א א _ א/S] 68 א 6Q א א8' א/. א א/. א Spherical Triangle úא/. א WDG4 א/. א/:#$ K3:4، א @*°E ZTZ'k*E? ;אq F# ، 4+hא/. א ?: @*!ZTZ 9 ^א* ZTZ ، A B C 0ę a b c T1 6K68* E^א* ،Ħ'1 cאE A *68א a 'm ، א cאB E *68א E*+@08 ، b 'm *68א cא C א OTo?m*+K c 'mא KM*G;67 ×#1#א/. א ?9 א/#1# *-א/E 83 א N:+0*א א א/}8 #א)'א&%א$א ,+*")fF*J;?? 3:4א aא&>01 ،) 6א6q*,-N;*"l#Ġא/. א iN8N?א ú Qq*Qo 94 אW_90:@x • ġ+#^א*א /. א K 540˚?6( 180˚?×K • T1#+ġא/. א )K 360˚?6 • K×1'"א/. א *K68×^אWbאJG*Kא cאK_9 A×^א" א/. א Fb ABCא 9T1×KF# a'mאא/. K 71 • *Yא/. א 8* >%*-א )*q א .#אG_א #:K0 • ^א?^א*א/. א K 180˚?6(_9 • א cא*א/*8 T1א/,*,*א \! K0 • T1?Ħ1#+ġא/. א K#9×?א m'א .* K /*F*Kא/. א _ 'K aK 4 9_א a א ,+*. × @0#S K ،3@E D0)#אĦGא/. א K א/. א ABC א/. א _ PXZ F# *+Kא/. א ?ZTZ، a b c T1ZTZ^א* F# A B Cא/. א _K ZTZT1ZTZ?^א*0 WF • א ĩ6.ī PZ 'm *$א Lat ) co-Lat l – ˚90 ) • א ī ZX 'm.6א א ,+h ) ZD L – ˚90 ) • א ī PX 'm.6א א Dec )PD 3 ± ˚90 ) • א cאĩ P.6 א cא א ,* 0אLHA 0Ò א cאאLHA)%<*Ġ ~ ˚360 ) • א cאĩ Z.6א cאא ,Az 0+ א cאאAz )%<*Ġ ~ ˚360 ) • א cאĩ X.6א cא @אĞ$א ,+*X 72 6FVא/. א *>a E?א 0+אğ,*08א V*xTo? L*;)0 @*!א/. א א ,0#Ĩ M9?ú*K;א @*!، A:*8א$ġ+# ?א/*;N-א *01 א 0,0qא/7، א EL× ? א Ħ8(T^א*9אא/. T1 KD אğ* א&W ħ 6א/. א WV A B Cא T1 א .a b c ZT - A,G$*; 0%]א +*$H*;^א*א/. א .A B C ZT Cos (a) − Cos (b)Cos (c) Cos (A) = Sin (b)Sin (c) Cos (b) − Cos (c)Cos (a) Cos (B) = Sin (c)Sin (a) Cos (c) − Cos (a)Cos (b) Cos (C) = Sin (a)Sin (b) 73 א ğ* א .*W 0G 6א/. א WV A B Cא b c Ħ1 ،א cאאS@08 Aa<#QÒ+* A,G J$*; 0%]א +*$P*,ğא a a 'm Cos (a) = Cos (b)Cos (c) + Sin (b)Sin (c)Cos (A) Cos (b) = Cos (c)Cos (a) + Sin (c)Sin (a)Cos (B) Cos (c) = Cos (a)Cos (b) + Sin (a)Sin (b)Cos (C) QE J א&T1א .a b c ZT #@#; * א&Hħ*;א cאB C Ħ 74 אğ* א .* . W 6א/. א WV A B Cא b c Ħ1 ،א cאא/*B8 &+9* A,G J$*; אH[0Ğ*;א cאא/*8א&Co Sin (A) = Sin (B) = Sin (C) Sin (a) Sin (b) Sin (c) F#G*(_3( W hTא0Ğ]א ,*+9F#Ħ@ZVĦ8*#9א/P#3"א/,*6q א *8MĜ?ī،0 ħVa;#אsq*QĠאx@:0 +. א א @s F4 K×1'"א/. א *K68×^אWbאJG*Kא cאK_9 A×^א"א /. א Fb ABCא 9T1×KF# a'mאא/. K QE J 6K?א cאB C Ħ ،א Ħmא/*b c Ħ8 #@@6 * א ,*H8*; א cאA ،א a a 'm 75 אğ* א אW 8 6א/. א WV A B Cא ^אB C Ħ ،א m'אS@08 a<#QÒ +* A,G J$*; א&%cא(א&>H (BaCb)، (cBaC)8*;א c'm ،א b'm Sin (b)Tan (A) Tan (a) = (aCbA) Sin (C) + Cos (b)Cos (C)Tan (A) Sin (c)Tan (B) Tan (b) = (bAcB) Sin (A) + Cos (c)Cos (A)Tan (B) Sin (a)Tan (C) Tan (c) = (cBaC) Sin (B) + Cos (a)Cos (B)Tan (C) Sin (c)Tan (A) Tan (a) = (AcBa) Sin (B) + Cos (c)Cos (B)Tan (A) Sin (a)Tan (B) Tan (b) = (BaCb) Sin (C) + Cos (a)Cos (C)Tan (B) Sin (b)Tan (C) Tan (c) = (CbAc) Sin (A) + Cos (b)Cos (A)Tan (C) 76 QE J א&T1א .a b c ZT #א cאK B C Ħ VF#0#*;א cאA A:*8i*@wא$ *; אħV6@G [0Ğאğ* א&0ħ T1Fא/. #K Sin (A) = Sin (B) = Sin (C) Sin (a) Sin (b) Sin (c) אğ* אW ,*Ġ 6 א/. א WV A B Cא ^אA B Ħ ،א m' א/*a 68 K*+9& A,G J$*; אH[0 Ğ*;א m'א/*68א&b b o Sin (A) = Sin (B) = Sin (C) Sin (a) Sin (b) Sin (c) QE J 6K?א cאA B Ħ ،א Ħmא/*a b Ħ8 #$@@6 * א ,*H8*; א cאC ،א c'm 77 אğ* א ,*;: W 6א/. א WV A B Cא ^א*Mא .A B C ZT A,G J$*; 0%]א +*$T1;*Hא/. א .a b c ZT Cos (A) + Cos (B)Cos (C) Cos (a) = Sin (B)Sin (C) Cos (B) + Cos (C)Cos (A) Cos (b) = Sin (C)Sin (A) Cos (C) + Cos (A)Cos (B) Cos (c) = Sin (A)Sin (B) 78 אğ* א ,*W 8 6א/. א WV A B Cא ^אb c Ħ8* Ħ1، B C Ħ 6K;*HÙ8*G-N;*$A,G J ? א a'm ،א cאA 1 1 Cos ()B + C Sin ()b + c a 2 2 Tan = 2 1 1 Cos ()B − C Cos ()b + c 2 2 1 1 Cos ()C + A Sin ()c + a b 2 2 Tan = 2 1 1 Cos ()C − A Cos ()c + a 2 2 1 1 Cos ()A + B Sin ()a + b c 2 2 Tan = 2 1 1 Cos ()A − B Cos ()a + b 2 2 79 1 1 Cos ()B + C Cos ()b − c A 2 2 Tan = 2 1 1 Sin ()B + C Cos ()b + c 2 2 1 1 Cos ()C + A Cos ()c − a B 2 2 Tan = 2 1 1 Sin ()C + A Cos ()c + a 2 2 1 1 Cos ()A + B Cos ()a − b C 2 2 Tan = 2 1 1 Sin ()A + B Cos ()a + b 2 2 80 א 6QאĠ* \ אKğא h*9 %א$א ,+* אKğא h*9א 0#0 %א$א ,+* X0G >אFא aא&>fO#01#>9*?א ħVPtא Fb ،$#6Ka27א&%א$ א ,+*E Kęi*9* ,0?א ħV27א X0@K Pt 0 7E*SG*89*;( 8W( @א& א _(7 E*@ *8 <#Sh EØ ' ?א& E 4i*0<E E 83 Wi*0G*Z j#3o@א lא/א> ˚ Lat < 23 .5 @o f60ī 23.5˚Nl #>;>אFא aא ,+*'PP 4;אaqאNWS N 8@ \ ;>%oא o60ī*+K ،lאH:#א(א ,+*'QQ ?אĠא #א!Ħ86א ,+Jא @Ùh '@8 ZZ o%<;\א Kl ShEא&%א$א ,+*?אNא ĝ_(7 _ @אNא K ،_8t+*,03'א א!a9*7 ]א&% א$א ,+*K #60ĩא^*60-א&%א$א ,+*א *+7 S@0*אĞ@08# 4,#;אaqאNWS N c8אא>$*ĩ *9 lא א! ( *8 ، (90˚- Lat * Sa ØF#EN_#>א&%א$ א ,+*2#א& ,* oVaØ Sq** : 6 א& WVNVא60F*KאĞ$א ,+*,* KX3O*"*+K ! *Sq* oVaØ <*9<#SaØ (X, X1, X2) *Sq* oVaØ >*9<#SaØ (X4, X5, X6) 84 *Z Wi*. j#3o@א lא/ ˚ Lat > 23 .5 < ˚ 5. 66 @o f60ī 66.5˚N l#>;>אFא aא ,+*'PP 4;אaqאNWS N 8@ \ ;>%oא o60ī*+K ،lאH:#א(א ,+*'QQ 4אĠא #א!Ħ86א ,+J א @@8 ZZ'Ùh o%<;\א K l g8ShEא&%א$א ,+*?אNא ĝ_(7 _ @אNא K ،_8t+*,03'א א! g8a9*7א&%א$א ,+*K #60ĩא^*60-א&%א$א ,+* א *+7 S@0*אĞ@08# 4,#;אaqאNWS N c8אא>$*ĩ*9 lא א! ( *8 ، (90˚- Lat * Sa ØF#EN_#>א&%א$ א ,+*2#א& ,* oVaØ Sq** : 6 א& WVNVא60F*KאĞ$א ,+*,* KX3O*"*+K ! Dq* oVaØ <M<#SaØ (X2) Dq* oVaØ >M<#SaØ (X4) ªTEא&%א$א ,+*א&8א Sh#>א PtE NLא&8אoH *(א K27ENL (X, X1) 8א EPt FN <#Sh (X5, X6) 8אoH E27 FN )* 85 >א Wi*8 j#3o@א lא 3 Lat > 66 .5 ˚ 0 @א 3]א *+7 3@_ f#>;>אFא aא ,+*'PP 4אĠא #א!Ħ86א ,+J א @3@*+K ، ZZ'Ùh oאH:#א(א ,+*'QQ 4;אaqאKNWS N 0ShE'א&%א$א ,+*Wא-א/O#0א *+7 F;0אK08#@Ğ k*EN'#א^*60-א&%א$א ,+*',#;א aqא*8 ، NWS N * ĜN _ *a9א 27א F#E ،Ptא&%א$א ,+*Wא-א/O#0א +7* 80 א Sh#>، אĞ@08# 8אoH K)* E>0'אH%א$א ,+*";אq aא/Y<2#cKא א!K Zi**ĩ 86 א h#א9א/*Q Kא h*9א 0#0 %א$א ,+*SĜj5* • א 27א Pt E4 25a9*אĞ$א ,+*k*F [8'#א^D0';אaqא& "א 67א #*k'#א^6K60?אX$Ğ אY$Ğ ';אaq א& "'Y'،X 4 W 60F#F?8Nא Ğ$א ,+*!$*ĩ?t lא א!K Q'd' < Q'N → Dec < ( 90˚- Lat ) Q c < QS → Dec < ( 90˚- Lat ) WVאiא j7א a9*ğ$^Tא 27א Ú$%&Pt* Dec + Lat < 90˚ 87 • EaØ#א%אĞ$א ,+*2#א& EaØ?×K#א%M : 6 א&א&א& "א 67א #אĞ$א ,+*Û60W X* _#אa<*5H lא א!، 08@+*אĞ$ א ,+**~_8#@% 60W Y a<*5H lא א!، EaØFªT#א%אĞ$ א ,+*X 2# א& EaØ?×K#א%M : 6 א& ، *8*+@08 ,@ X$א ,+*Fb Y EaØ#א%2#M א& ! EaØ?t#א%M : 6 א& K WVאiא j7א EaØF#E4$^T#א%אĞ$א ,+*2# א& EaØ?×K#א%M : 6 א& aØF#EF4@Ĩא aØ?×K27א Pt Dec + Lat < 90˚ ( ) א j7א EaØF#E4$^T#א%אĞ$א ,+*2# א& !EaØ?t#א%M : 6 א& aØF#EF4@Ĩא aØ?t!27א Pt Dec + Lat < 90˚ ( ) 88 • 25אĞ$א ,+*?3Gא D8 E27 3G@א WPt "א 67א #אĞ$א ,+*!*,60W X F#0 ،#א^3@D0 o4 אH:#א(א ,+*3G?27DGªT ،Q'Qא Pt E27 3G@א WPt EaØFªT*+K#א%אĞ$א ,+*X 2# א& EaØ*,E#א%M : 6 א& F4@Ĩ KD8aØ*,ED(5aØ WVאiא j7א T^$ 27אĞ$א ,+*?3Gא D8 E27 3G@א i*hG WPt Dec = 0˚ 89 • אĞ$א ,+*א א>#Oא 3] F#4אĞ$א ,+*;א>#Oא k*N[[3'#א^D0';אaq א& "א 67א #k*EN'#א^*6K60-?אĦĞא ,+*Y ، XĦ ';אaq א& ، *8 * EN_ a9*א 27א *8Pt ,@ Y ، XĦX ، 0 '#א^ 60 אĞ$א ,+*2#D+K`8 X א& ، 08@+*'#א^ 60אĞ$ א ,+*K*8 Y+ : 6 א& ، 0 6K4א@S+*;א>אO#iא cE، P[3;א;M9a9*7א Ka9*h+*^א;o lא א!، @oאH:#א(0 @$א M9 9*7ENl א 08a9*h@+* @א 3] 6KF #Eא @X#$;א>O#aא 4 ،[3 W 60F#F?8NאĞ$א ,+* $*ĩ*,×K lא א!K Q'd' ≥ Q'N → Dec ≥ ( 90˚- Lat ) Q c ≥ QS → Dec ≥ ( 90˚- Lat ) WVאiא j7א F#4$^TאĞ$א ,+*;א>#Oא 3] Dec ≥ 90˚- Lat 90 • אĞ$ א ,+*א א>#Oא 3]2#א& : D "א 67א #אĞ$א ,+*Û60W X* _#אa<*5H lא א!#9;א>#O א 3]2# א& ، 08@+*אĞ$א ,+**~_8#@%60W Y a<*5H lא א!#9 ;א>#Oא 3] : 6 א& K #FאĞ$א ,+*;א>אO #iא 3]2# א& i*(TkVPtNDG4@Ĩ Dec + Lat ≥ 90˚ ( ) F#*+@08אĞ$א ,+*;א>אO#iא 3] : 6 א& Ni*(TkV27NDG4@Ĩ Dec + Lat ≥ 90˚ ( ) 91 • >אĞ$א ,+*א אaqא :0אħN "א 67א #אĞ$א ,+*Û60W X* _#אa<*5H lא א! @D)6)+0 Qd < QZ → Dec < Lat 0 3' אĞ$א ,+*DK)*@Z א אaqא :0א ħN S% @א M27 M*ě*8F#0 א ، 90˚ i**ĩ 27 S% @ א o a Pt M*ě*8 F#0 א TK " ، 270˚i**ĩ Pt א/.67 Ħ1# q*(K א cא @א c אא ,0 ę Az 0+ 6KP*,?ī? E Tan (Dec ) Cos (HA ) = Tan (Lat ) @M9א*ğ ī?>!אDK)*@Z$Ğא 0#0א h*9 @0'>8*;אaqא& K א j7א T^$/ >אĞ$א ,+*א אaqא :0א2#ħN א& Dec < Lat ( ) 92 • >אĞ$א ,+*8@3א ,+M<)*@Z ZJ o4א cאOא # א! "א 67א #אĞ$א ,+*#60W Xא lא א!a<*5V)+0 Q'd' = QZ → Dec = Lat 8 F#א j7א T^$/>א Ğ$א ,+*8@3א ,+ZJ Dec = Lat ( ) 93 • ±#8אĞ$א ,+*;>%E "א 67א #אĞ$א ,+*E X 58i*0<E')4 ;>%אE - א lא/860@ \אa<*5H + א lא/úTĚ 60 אa<*5H 94 • ±#8אĞ$א , +*;>%¤V h l* 0@ : 6 א&א&א& "א 67א #אĞ$א ,+*A@ X M*ě*8i*0<Eg א& א Pt4_8t Z X'@ ,+"V¤ *41 ;>%א¤H l*א/8#3 4 X'' @ W F ?8N #F א # j*3¦V 4G; #9 Nd' Y X$ א ,+* : 6 א& Y#( ? ×K אj*3¦H א/0 Nh P#3 W F Z'Q' = Lat d'Q' = Dec Nd' = 90 - (Dec + Lat) Nh = h، 90 - (Dec + Lat) > h WVאiא j7א T^$ #±אĞ$א ,+*;>%¤V hl* 0@ : 6 א& (Dec ± Lat) - 90˚ > h + א lא/860@ \אa<*5H - א lא/úTĚ 60 אa<*5H 95 • ±#8אĞ$א ,+*)4Q ^אAz 0Ú "א 67א # אĞ$א ,+* )4Q ^א 0(5 0Ú D Z ، X1@ #; 0 )4Q ^א08 0Ú 8 X2@ oM<#^ אOא א!، 4 W F ?8N #F 60אĞ$א ,+*?×K lא א! 8@ \ אWĜ* 4+ ،a<*5H 8אĞ$ א ,+* ^אA:*8*9Ĝ?ī ،*9^*XN#Q(0Úא$א/*; א * W0 Cos (Dec ) Sin (Az ) = Cos (Lat ) E Tan (Lat ) Cos (HA ) = Tan (Dec ) WVאiא j7א T^$ #±אĞ$א ,+* )4Q ^אAz 0Ú Dec > Lat ( ) 96 • א #>א cא _ X$א ,+* E×א&%א$א ,+*SKOTo*א o0#0^אOא א !0 ،ĦE o×E*SG^אO א א!א #E - א lא/860@ \אa<*5H + א lא/úTĚ 60 אa<*5H E\ א5H*>א-"*P*,OאE 97 א #> א cא _ א #Ġ^אOא א!)JÚ3GP#@%O*ÛĢא א!Z ، ? א/ +?K i**ĩĢF W+ ،*9@ 6K+0(4?60אĞ$א ,+*o lא א!8* 67א * _W - א #> א cא _ 3GO*Ûא ,+Dec > Lat J - א #> א cא _ %@#3GPא ,+Dec < Lat J - א #> א cא _ @3Gא ,+Dec = Lat J @hğ #>אĞ$א ,+*Ġ^אOא א!א #E@$)+0^אDא ,* 0א0Ò *8 ، LHA * D3*,_א/ ,RA 0 'א c?א @X+_אĦ0E-;<Fb ، LST _Ò )+0א/3'א/,**Ú$%& 0 P*,#:0א c?א @X+_א_ Ò J(# #> W א*+$Ğ D3 +0(#9F#6Q א/,K 0 98 *WV W .Oא +FJ)+0א/ Dec 60 X@#$א * W_90 Aldebaran 16° 32 ′ 14 ″ N Alkaid 49° 14 ′ 29 ″ N Altair 08° 54 ′ 27 ″ N Rigel 08° 11 ′ 09 ″ S Spica 11° 14 ′ 12 ″ S J o@ PtNlא @Ki*3 Alkaid X Dec + Lat ≥ 90˚ & same name Lat ≥ (90˚ – 49° 14 ′ 29 ″) N Lat ≥ 40° 45 ′ 31 ″ N WVאiא @i*3PtN Alkaid X o@ 0iN*Û.K` 40° 45 ′ 31 ″ Nl F# ;א>#Oא 3]2# א& K J 8* @, א!oW Ħ8 30˚ Nl?א @Ģ Rigel Aldebaran Ħ+X *a9א 27א 27*+SPt KD8?×KMØ Ģ4אĞ$א ,+**a9א 27א Dec + Lat < 90) F#F?8NP t) 9אא j7 *8 ,@ 0 Rigel Aldebaran Ħ+X@ WF Star Name Dec + Lat Aldebaran 16° 32 ′ 14 ″ + 30° < 90° Rigel 08° 11 ′ 09 ″+ 30° < 90° F#F?8ND8aØ?×KD(5aØF#E4 60אĞ$א ,+*@8 a<*5V\ lא א!E Lat same name as Dec F 9א @0 Aldebaran X F D0#אa<*5H lא א!K 99 J 1?א @X#$א ,*8ī8@3א ,+DKOTo ZJא h*9 8* @, א!W K 08° 54 ′ 27 ″ N l o Dec = Lat & same name א @#60W Altair Xא lא א!#9F#0+0(a<*5Vא @X א/K P#3 ī69 ?08 J? א!W N l˚29 ?>£א @Ki* Spica Alkaid Ħ+X /W o6(;*V[ ?īl W p6K£<M@ OTo?א W (T Dec + Lat < 90˚ & contrary name *8 , @ D@wD£<F#E Alkaid X@ j#3o'0@א lא *+7 ħV*1H*80 j#3oא lא 408#@Ğ M*ě*8 6(` 40° 45 ′ 31 ″ S lאH:#א(K Lat < (90˚ - 49° 14 ′ 29 ″) S Lat < 40° 45 ′ 31 ″ S or any North Lat. *8 ,@ D@wD£<F#E Spica X@ j#3o' 0@א lאħV*1H*808#@Ğ j#3oא lא *+7 40 M*ě*8 6(` 78° 45 ′ 48 ″ NlאH:#א(K Lat < (90˚ –11° 14 ′ 12 ″ ) N Lat < 78° 45 ′ 48 ″ N or any South Lat. WVאīi?>£א @_3oĦ8i* Spica Alkaid Ħ+X Nl ″ 48 ′ 45 78° *8 ، 40° 45 ′ 31 ″ S * ī_? א!oW N l ˚29 ?>£א @Ki*Ħ+X 100 78° 45 ′ 48 ″ N > Lat < 40° 45 ′ 31 ″ S J o@ F#l א @Spica X 2# א& ħVא&8 o@ F#l : ħV Dא&K 8 Dec + Lat ≥ 90˚ & same name Lat ≥ (90˚ - 11° 14 ′ 12 ″) S Lat ≥ 78° 45 ′ 48 ″ S WVאiא @2#F# Spica X א& ħVא8N o@ M*ě*8 .K` 78° 45 ′ 48 ″ S l א 3]אK _8#@Ğ Dec + Lat ≥ 90˚ & contrary name Lat ≥ (90˚ - 11° 14 ′ 12 ″) N Lat ≥ 78° 45 ′ 48 ″ N WVאiא @F# Spica X : 6 א& ħVא8N o@ M*ě*8 .K` 78° 45 ′ 48 ″ N l א 3]א *+7 K_ 101 J 08? ?א @X#$א ,*j5Ģ8>א אaqא :0א8ħN* @, א!oW K 29˚N l Dec < Lat & same name WVאiא @Aldebaran X א @j5F*Ģ Altair Xא/> ، F#F#9א/t!60? א l 8@ \אKa<*5H *Ú$Ğ60%<;6(_9* J j5*Sא Sh#>א&88* @, א!oW K 22˚ Nl Dec + Lat ≥ 90˚ & same name Dec ≥ (90˚ – 22˚) N Dec ≥ 68˚ N WVא6Kiא&%א$א ,+*WאiN*Û.K` 68˚N 60-;אq+א Sh#> א!W N l˚22 ±#80G*V_ 9* Jא @¤V Aldebaran X l*˚47 : 6 א& 8* @, א!oW K 32˚ N l (Dec ± Lat) - 90˚ > h (16° 32 ′ 14 ″ + 32˚) - 90˚ > h 16° 32 ′ 14 ″ – 90˚ > h 41° 27 ′ 46 ″ > h WVאiא @¤V±#8D@īN Aldebaran X l*˚47 : 6 א& 0 ¤V%<;4Q(F l * S#8D@ī* : 6 א& *8 41° 27 ′ 46 ″ _9 ,@ Ġ lא א!K 102 ±#80G*V_9* Jא @E WVאiא @ E H = (Dec ± Lat) - 90˚ H = (08° 11 ′ 09 ″ + 29° 15 ′) - 90˚ H = 37° 26 ′ 09 ″ - 90˚ H = 52° 33 ′ 51 ″ 60F*Ĩא @?t! X lא א!,F#0א @3GP#@% Xא ,+hğ ZJ M<# א cא _ 0 F#E^אא ,hğ0+^א K180˚*,ED J *#9א>אE 103 4Q(% J^א 0(5 Az 0Ú St*א @Alkaid X 8* @, א! o4 l E Cos 49( º 14' 29' )' Sin (Az ) = Cos 14( º 25' 00' )' Sin (Az ) = .0 674101 Az = 42 º 23' Sin (Lat ) Sin (h) = Sin (Dec ) Sin 14( º 25' 00' )' Sin (h) = Sin 49( º 14' 29' )' Sin (h) = .0 328690 h = 19 º 11.4' 104 א 6Qא , *;Y א #)P*,J0א c? 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M9EFא #3a W*+9Ħ0:*:Ħ • ]ZF#EF*8א K+0 • ]EF#א'a*0F#5אF*,GHא/K070 )DěVא aØ;*V"Ù ;>אFא aא&>A:V 6%? *9<#fO#01אa#K*S Y*0א c?، 0 3 4א aØא c@0א S0 EL*א aא&>fO#*Ka<;01#>9* 3Qא V+ ،$#0: 9אא $#0 4אĞ$א ,+*א/,aØP*,"$Aא >אM9F ، W4 ú@:*@Gb ~$*ZTZ 4 K א $#0א +7,_א W 9*h א aØא Ħ80@c *?<# Ħ0 +7\א0 0ğ o4^אĦO ،ZÙ_9*8א +0 E*S@#א'a*0F#5אF*,GHא/K070 א $#0א + W א aØא Ħ80@c *?<# Ħ0 + o4^אZÙ_9،ĦO*8 א EN*SG*+K+0#א'a*0F#5אF*,GHא/K070 א $#0א @W _+X א aØ א Ħ80@c * ?<# Ħ0 @3אH אOא _08 o4^אĦO ،Z_9*8א +0 EN*S@#א'a*0F#5אF*,GHא/K070 א #Z a *-א +0 א #א'F#5אa*0ğ א $#0א +7,_א J8*ZÙ 9*h #א א $#0א + Ù J8*ZÙ#א א $#0 א @Ù J8*Z _+X#א 109 *8 KħV0G*Za ;#א +7\א00ğ، א S? ×EL 6%אKğ*-א*8 0,ğ ,@ ħV א* f"،F*,GH *.$*hG;*V _ Y*0א M9??cאGp ،Kğ $**@, W*+9Ħ K1 ;>אFא aא&>O#01א s(*G'3(" \+7 0\ "א>;אę ،q,]א *F#G א .*_G F#E?: א >אFħVs¤ ،+h@Fא +7\אE00ğ *i*9 4,#א אaqא ,+*,8 K+h@Ù E K2 א +7\אi*9*00ğ 4,#א אaqא ,+*، E*+@08>א aא&>01 #* 9<#fO o#, 4אH:#א(א ,+*، א c860īא˚ E 23.5 i* ? ,#א אaqא ,+*، DG4@Ĩ ġ*@1ØV#*^אK$*hGViא +7\א00ğ א h*9 4,#א אaqא ,+*، M9,FbאKğ o#,4 אH:#א(א ,+* ?#Ki*+h@F : א # [K <A@ <B@ 8 C@ K$*hGVlא +7\א00ğ ab ≠ AB 4 110 )*@8 :*4 KW*ĝVF;O#Ģ*Fmא +7\אa#K0ğ Y*0א c?، #9 SK*א h* 9 4,#א אaqא ,+*، 9FT0ħV*1H*8אא/,# ?,#o א H:#א(א ,+*، )M9Ğ*Jĩא*5H KĦE#3o"0 G W iN E 00ĝ \Ûl 4,#א אaqא ,+* ,8 E+h@,*#: : א +7\א8 ، 00 ğ ÙZ`E_5TGא/א>אF_X09H אúToHא/ E cK hGV4*$ : א K\+7 GØ i*0G*Z M9F l Wא +7\א E ،00A o#,4אH:#א(א ,+*8@ \ א , א/#:3 G،3 V*S0: א +7\א/#:8، 3 FT0ÙZ`E_5TG,#א אaq א ,+* ?,#oאH:#א(א ,+*K V: אĞ$ א/א> א , א +7\א00ğ א אaqא ,+* h@Ù + א +7\א/#:3 ;אaqאH:#א(א ,+* @h+ 8 ! E 00ĝ i*,Û*@ o#,4אH:#א(א ,+*,8 h@+ h *: L 15 °O;*E i*#*S@3QG ،3:#%א#9iא $#0א +7,_א/#: *: 24 K 360 ° =15 ° / hour 24 א $#0א +7,_ א/#: W א aØא Ħ80@c *?<# Ħ0 +7\א/#:3 o4^אĦO ،ZaØ_9*8 א 0+0 *: 24 *,E E*SG*+K ،3:##א 'a*0F#5אF*,GH א/VË( ،070 *>9*א #aא&:*:Y*0("0א #)Jא +7,_א/#: ، א $#0 א +7,_א /#: @hğא/>א cא _א , _ +7\א/#:K3 mean day m.hours m.minutes m.seconds 1 = 24 = 1440 = 86400 111 *8 ħV h@א aא ,+*?א& M*ě*84א F#0: ،[3א/@K<#h+*"א 67א * _W • True Sun א +7\אMean Sun E، TS F00ğ א +7\א/#:EMS F3 • 3G γאH אOא 08_ • 3G Pא cK* @96.ĩ[3;אoaqאH:#א(א ,+*K • o PQ^אO@ א #،'o PQ^אO@ א , _K • o PM^אOא א! א #،'o PM^אOא א! א , _K • o PTSא cאOא/*>8* +7\אK00ğ • o PMSא cאOא/*>8* +7\א/#:K3 • o Pγא cאOא/*>8@3אH אOא K_08 • א #Yא #א!ī MS TS Ħ86.6*; א #)KJ 112 א #)JאÒ_א/#: Local Mean Time (LMT) O#kא #Y o4אH:#א(א ,+*א cא א/*: @א 8V P[3א( ?oא cאOא , _ א! 'o 4 PM א cאO א/*> 8* +7\ א/#:M*ě*8 PMS 3א × ،Pt S@*#8א- ^@*: 24 –00 Eא aØא L-@ hğ א/> א cא _ א , _ +7\ א/#:3 ،E _9,* א cא א ,* 0 א0Ò +7\ א/#:K 12 ±3 LMT = LHA ± 12 )J@0א/#: Greenwich Mean Time (GMT) O#kא #Y o4אH:#א(א ,+*א c א א/*: @א 8V P[3א( ?oא cאOא , _ o 4 PQ' @t א cאO א/*> 8* +7\ א/#:M*ě*8 PMS 3א ×،Pt S@*#8א- ^@*: 24 –0?0 Eא aØא L- @ hğ א/> א cא _ א , _ +7\ א/#:3 ،E _9,* א cא א ,* 0 t@ +7\ א/#:K 12 ± 3 GMT = GHA ± 12 א Ħ8(T א #)JאÒ_א/#: J( LMT@0א/#: GMT LMT = GMT ± Long H O#3א J ،_(7 O#3א 8t_ 113 א #)JאÒ_ א h*9 Local Apparent Time (LAT) א cאא/*: @א 8V P[3א( ?oא cאO א , _ א! 'o 4 PM א cאO א/*> 8* +7\אM*ě*8 PTS 00ğא × ،Pt S@* #8א-^@*: 24 –00 Eא aØא L - @ hğ א/> א cא _ א , _ +7\ אE _9، 00ğ,* א cא א ,* 0 א0Ò +7\א، 12 ±00ğ hğ @א/>א cא _ א # +7\אFb 00ğא #)JאÒ_א h*9 LAT = LHA ± 12 h m ,* 00 12 ;אJ(#9، i*+qא/c K )J@0 א h*9 Greenwich Apparent Time (GAT) א cאא/*: @א 8V P[3א( ?oא cאO א , _ o4 PQ'@tא cאOא/*> 8* +7\אM*ě*8 PTS 00ğא ×،Pt S@* 8 #א-^@*: 24 –0?0 Eא aØא L -@hğא/>א cא _ א , _ +7\א00ğ ،E_9,*א cאא ,* 0 t@ +7\ אK12 ±00ğ GAT = GHA ± 12 א Ħ8(T א #)JאÒ_ א J( LAT 9*h @ א GAT9*h LAT = GAT ± Long 114 *; א #)J Equation of Time (Eq.T) EE א +7\א/#:SKę3*'א +7\א00ğ E(T8,4+*; א #)J ، א úEL SG4* O#kא #Y o4אH:#א(א ,+*א cא @א P[3 אĦ8a<#QÒ;אEq_^א6KO? א +7\א/#:3א +7\א00ğ ،+*; א #)J a<* ?א Ħ82א #)Jא h*9 א Ù7E Dא/c א +7,0 א #)Jא/#:א Ù7E V ED0א ,* א K*@"*S+¦L Eq.T = GAT - GMT WĦ K/Qf_9 • K אúToHא/cKא @*Dě ?1 : א +7\א00ğ 4א אaq א ,+* O#Q 4 א +7\ א 00Aא/@:"+h K*S • K א/FT0 א @*Dě K6G? א +7\ א 00A o#,4 אH:#א(א ,+* O#Q 4 א +7\א/#:K3 QfF#Eא/K Ħא ĩL.6*; א #)EJ,*! אi>8א-"א *$#א _ 15 68 ، : 1 ، #0G# 13 0×+,; 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Day Jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dec 1 -0:03:11 -0:13:27 -0:12:28 -0:04:06 0:02:49 0:02:18 -0:03:42 -0:06:23 -0:00:15 0:10:06 0:16:24 0:11:17 2 -0:03:39 -0:13:35 -0:12:17 -0:03:48 0:02:56 0:02:09 -0:03:54 -0:06:19 0:00:05 0:10:25 0:16:26 0:10:55 3 -0:04:07 -0:13:42 -0:12:04 -0:03:30 0:03:03 0:01:59 -0:04:05 -0:06:15 0:00:24 0:10:44 0:16:27 0:10:32 4 -0:04:35 -0:13:49 -0:11:52 -0:03:12 0:03:09 0:01:50 -0:04:16 -0:06:10 0:00:43 0:11:03 0:16:27 0:10:08 5 -0:05:02 -0:13:54 -0:11:39 -0:02:55 0:03:15 0:01:40 -0:04:27 -0:06:04 0:01:03 0:11:21 0:16:26 0:09:44 6 -0:05:29 -0:13:59 -0:11:25 -0:02:38 0:03:20 0:01:29 -0:04:37 -0:05:58 0:01:23 0:11:40 0:16:25 0:09:20 7 -0:05:55 -0:14:03 -0:11:11 -0:02:20 0:03:25 0:01:18 -0:04:47 -0:05:51 0:01:44 0:11:57 0:16:22 0:08:54 8 -0:06:21 -0:14:06 -0:10:57 -0:02:04 0:03:29 0:01:07 -0:04:57 -0:05:44 0:02:04 0:12:15 0:16:19 0:08:28 9 -0:06:46 -0:14:09 -0:10:42 -0:01:47 0:03:32 0:00:56 -0:05:06 -0:05:36 0:02:25 0:12:31 0:16:15 0:08:02 10 -0:07:11 -0:14:10 -0:10:27 -0:01:30 0:03:35 0:00:44 -0:05:15 -0:05:28 0:02:45 0:12:48 0:16:10 0:07:35 11 -0:07:35 -0:14:11 -0:10:12 -0:01:14 0:03:38 0:00:32 -0:05:24 -0:05:19 0:03:06 0:13:04 0:16:04 0:07:08 12 -0:07:59 -0:14:11 -0:09:56 -0:00:58 0:03:39 0:00:20 -0:05:32 -0:05:10 0:03:27 0:13:19 0:15:57 0:06:41 13 -0:08:22 -0:14:11 -0:09:40 -0:00:43 0:03:40 0:00:07 -0:05:39 -0:05:00 0:03:48 0:13:34 0:15:50 0:06:13 14 -0:08:45 -0:14:09 -0:09:24 -0:00:28 0:03:41 -0:00:05 -0:05:47 -0:04:49 0:04:10 0:13:49 0:15:42 0:05:44 15 -0:09:06 -0:14:07 -0:09:07 -0:00:13 0:03:41 -0:00:18 -0:05:53 -0:04:38 0:04:31 0:14:03 0:15:32 0:05:16 16 -0:09:28 -0:14:05 -0:08:50 0:00:02 0:03:40 -0:00:31 -0:06:00 -0:04:26 0:04:52 0:14:16 0:15:22 0:04:47 17 -0:09:48 -0:14:01 -0:08:34 0:00:16 0:03:39 -0:00:44 -0:06:05 -0:04:14 0:05:13 0:14:29 0:15:12 0:04:18 18 -0:10:08 -0:13:57 -0:08:16 0:00:30 0:03:37 -0:00:57 -0:06:11 -0:04:01 0:05:35 0:14:41 0:15:00 0:03:48 19 -0:10:27 -0:13:52 -0:07:59 0:00:43 0:03:35 -0:01:10 -0:06:15 -0:03:48 0:05:56 0:14:53 0:14:47 0:03:19 20 -0:10:46 -0:13:47 -0:07:42 0:00:56 0:03:32 -0:01:23 -0:06:19 -0:03:34 0:06:18 0:15:04 0:14:34 0:02:49 21 -0:11:04 -0:13:40 -0:07:24 0:01:08 0:03:28 -0:01:37 -0:06:23 -0:03:20 0:06:39 0:15:14 0:14:20 0:02:19 22 -0:11:21 -0:13:34 -0:07:06 0:01:20 0:03:24 -0:01:50 -0:06:26 -0:03:05 0:07:00 0:15:24 0:14:05 0:01:50 23 -0:11:37 -0:13:26 -0:06:48 0:01:32 0:03:20 -0:02:03 -0:06:28 -0:02:50 0:07:21 0:15:33 0:13:49 0:01:20 24 -0:11:52 -0:13:18 -0:06:30 0:01:43 0:03:15 -0:02:16 -0:06:30 -0:02:35 0:07:42 0:15:42 0:13:33 0:00:50 25 -0:12:07 -0:13:09 -0:06:12 0:01:54 0:03:09 -0:02:29 -0:06:31 -0:02:18 0:08:03 0:15:50 0:13:16 0:00:20 26 -0:12:21 -0:13:00 -0:05:54 0:02:05 0:03:03 -0:02:41 -0:06:32 -0:02:02 0:08:24 0:15:57 0:12:58 -0:00:09 27 -0:12:34 -0:12:50 -0:05:36 0:02:14 0:02:57 -0:02:54 -0:06:32 -0:01:45 0:08:45 0:16:03 0:12:39 -0:00:39 28 -0:12:46 -0:12:39 -0:05:18 0:02:24 0:02:50 -0:03:06 -0:06:31 -0:01:28 0:09:05 0:16:09 0:12:20 -0:01:08 29 -0:12:58 -0:05:00 0:02:33 0:02:42 -0:03:19 -0:06:30 -0:01:10 0:09:26 0:16:14 0:12:00 -0:01:38 30 -0:13:08 -0:04:42 0:02:41 0:02:35 -0:03:31 -0:06:28 -0:00:52 0:09:46 0:16:18 0:11:39 -0:02:07 31 -0:13:18 -0:04:24 0:02:26 -0:06:26 -0:00:33 0:16:21 -0:02:36 אĞאOא ,*3E8_)+0*; א #)J אא @J0(#8$#0 *, GMT 00 00: ، Wbא*9EJ@K *, o?:* *-א ،$#0 O#ĜFiN [%#,:* *-@ h א c%ħV Lא(?א *S+, 8$#0 1 Z ، 24 4 S*'א $#0א ،א:A[* *S8*?)+0*; א #)38Jא Ħ86א ,3?، $#0א/P#3א $#0א * _ D، 8 6QĜ 4)+0*; א #)J&:* ?:* *-א K $#0 120 )Jא/@3 Zone Time (ZT) E א #) JאÒ_א/#: J (' LMT@א/#: j# Ě3 GMT א O#3، h /*JG*Kא +7\א/#:O#*Ka<; '3E3א&>OTo 360˚l 24 :* #:3 m ، Sא}*@G`8 G!<#*א \+7 q*(; 4 _ m8*SGb ، 25 48˚O#ko@ ^@0 :#F o@א O#3אZ ،25 47˚<*Ó ˚46 25 ،9א0ę ħVO#ko? 6@ E . 8 ،0@^q*(;8<OToo J(-*@א/#: א Y*:#9א Fb ، Y*0 )+0א #)JאÒ_א/#: oÙt8ÙtE א Ù0tE$c,DG4@Ĩ ،O#3 א #)o ÙtE*+ K J O#kא א! ، F#N O#k o 360 ;#%#8 9א א& i* 0+ 4א2TkH ، ?9@*%*(- Ea,0 :3א&>Ĩ*S@3@6K ',E ، 0@^3@ 24 ħVlא>˚j#3o? 15 א 0ę ، O#3 J0(#E*@9F#א J(4+,3@6א/@ZT 3 א #)Jא/G_ א/# ، א ú DG 4א #)JאÒ_ א/#: Ġ LMTא O#3 א/@Q +@3 א c@0 ، ģ J( ?@א/#: 8; ! 0?א ,* *-K */@3א ! 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' א#3Ġא-א/1# S:&*8 ' א *aא5H*>א- @א @K*S@08*+0 6 125 א #)Jא @X+_אÒ_ Local Sidereal Time (LST) O#kא #Y o4אH:#א(א ,+*א cא א/*: @א 8V P[3א( ?oא cאOא # א! o4 PMא cאOא/*> 8@3 אH אOא M*ě*8 Pγ_08א ×،Pt S@* #8א-^@E 0א aØא hğ@-L א/>א cא _ א # @3אH אOא 08_ ،E_9,*א cאא ,* 0א0Ò @3אH אO א K_08 LST = LHAγ א #)Jא @_+X t@ Greenwich Sidereal Time (GST) O#kא #Y o4אH:#א(א ,+*א cא א/*: @א 8V P[3א( ?oא cאOא # o4 PQ @tא cאOא/*> 8@3 אH אOא M*ě*8 Pγ_08א ×،Pt S@* #8א-^@E 0א aØא hğ@-L א/>א cא _ א # @3אH אOא 08_ E_9، Ħ p,*א cאא ,* 0 GST = GHAγ @t @3אH אOא K_08 א Ħ8(T א #)Jא @X+_אLST _Ò א #)Jא @_+X *K43E GST @t * W_ LST = GST ± Long 126 *8 ħVh@ 6K$#S?א #)Jא @X+_אLST _Ò ،א cאא ,* 0אLHA 0Ò ،א/3' א/,FªT@: RA 0א #)Jא @X+_א LST _Ò X$א ,+* X J( @,* 6K#+ġ?א cאא ,* 0אLHA 0Ò ،א/3'א/ ,x RA 0אאĞ$א ,+* K LST = RA LST = LHA + RA At Noon 08@+* @א hא S0×L*אĞ$א ,+*o X^אOא א!Fb)+0א cאא ,* 0 h h אx LHA 0Òאא*8 ، 24 0 *,E$Ğ * F#E_)+0א #)Jא @X+_אLST _Ò ,* 3+' א/,x RA 0א אĞ$ א ,+* @ M9 א Wb ، hא A:V%@* א #)J א @X+_א LST _Ò J( @ ^אF*K *Ú$%Oאğ*!#96א/3'א/,RA 0 xאא$Ğ W@ א #)Ĝ JאKi F8 אĞ$א ,+* X M<#א cא _DK"i*SXא h*9א ħV0#0א Pt )Y*0א cאא ,* 0אx LHA 0Òאא8 ،$Ğ G,@°א T)א xTo?*@@īL* א cאo Ħ8א cאOא # א!oא cאOא/*>Ğ*8$א ,+* ، 8* * _ א #)Jא/ _ #>אĞ$א ,+*o X^אOא א!א/*K D@_1 LHA = LST - RA 127 *8 Ka;# ħV S# $ א cאא ,* 0א @ *S+0(Fi*mX@: SHA 0+X X$א ,+* dk°E*G*,E*J(" X א #)J א @X+_אLST _Ò ? א cאא ,* 0אLHA 0Ò xאא$Ğ W@ א #)FhT' ، J א cאא ,* 0א @SHA 0+X ،א/3'א/,0 h S@6K + RA+*א¢K 24 360˚ħ Vo RA = 360˚ - SHA SHA = LHA - LST 128 א #)Jא @X+_א #)Jא +7,_ E>א aא&>M9OTo ، $#6Ka *9<#fO#01א >o*+p×Ea^אOא א! ;#E Z 3@0G*ZM<# M94א aØא S(t:VL*א @Ħ8 Xא #>?V: א $#0א @X+_ ،א& G ĢD, 3G*@GÙ \+7 4א aØ א S(t:VL*א Ħ8\+7 א #>?V: א $#0א *8، _,+7 Y*0 Ħ 9F`8*@ ?א E?ī، Ħ*,ÙĦ#0 Ù, 9אאúToH 4א @ #א * _ W 8 6K!<ËĦJ("DGl?א +7\ א @hğ X o*+9<#^ אOא א!*i F א EF8DGb E 1'1# א&>F*9<#fO#*Ka<;l א F`8ªT@: E 2'1#א +7\ m s o×EN^אOא א!"hğ #>א @ o*E68 X ę D@#א _ W'%، 03 55.9 FħVא&>l JKĜ(*9<#fO#*SE<;Jĩ*@ 4א>O#*9א ę\+7 #א _ ˚ *8 ، 0.9856 * E_ 4א&> 0mEFħV%*ęl (iT0(*9<#fO#*SE< EF6 m s א o\+7^אOא א!@W4 F^?א $#0א @ę6_+X#א _ 55.9 03 ?^? א $#0א Wb_,+7א*>!hğ*G #> א @ X o 4^אOא א!9Fbאא @X :#0; m s m s i* M×0 hğ? M<#א ,*Ĩ8א> 55.9 03 "א $#0א&O 51.82 07 " h m s א $#0א .*G_9אF#0א>א $#0א @X+_ 4.09 56 23 ?א $#0א +7,_א/#:K 1d of mean solar time = 1d.00273790935 of mean sidereal time 129 Ħ0Eא #)Jא @X+_ Ħ א #)Jא @_+X A:*8 GST @tא$א/*; א * W0 h GST = GST 0 + 0.0657098244 * d + 1.00273791 * GMT 0 J(6.ī GMT@א/#:،d >) א $#0?א ,@ E 1Z d←*@ 1F 08@+* ī GST 0.6 )+0 א #)Jא @X+_א Q t@ @8אא ,@ #אOĞא * _ M9 א +0 K 2051 @:4$ 1980 @:Ħ8*Ħ@,$ Year GST 0 Year GST 0 Year GST 0 Year GST 0 1980 06 35 18 1998 06 37 50 2016 06 36 25 2034 06 38 57 1981 06 38 17 1999 06 36 52 2017 06 39 24 2035 06 37 59 1982 06 37 20 2000 06 35 55 2018 06 38 27 2036 06 37 02 1983 06 36 22 2001 06 38 54 2019 06 37 29 2037 06 40 01 1984 06 35 25 2002 06 37 57 2020 06 36 32 2038 06 39 03 1985 06 38 25 2003 06 36 59 2021 06 39 31 2039 06 38 06 1986 06 37 28 2004 06 36 02 2022 06 38 34 2040 06 37 09 1987 06 36 31 2005 06 39 02 2023 06 37 37 2041 06 40 08 1988 06 35 34 2006 06 38 05 2024 06 36 40 2042 06 39 11 1989 06 38 33 2007 06 37 08 2025 06 39 39 2043 06 38 14 1990 06 37 36 2008 06 36 11 2026 06 38 42 2044 06 37 17 1991 06 36 39 2009 06 39 11 2027 06 37 45 2045 06 40 17 1992 06 35 42 2010 06 38 13 2028 06 36 48 2046 06 39 20 1993 06 38 41 2011 06 37 16 2029 06 39 48 2047 06 38 23 1994 06 37 44 2012 06 36 19 2030 06 38 50 2048 06 37 25 1995 06 36 46 2013 06 39 18 2031 06 37 53 2049 06 40 25 1996 06 35 49 2014 06 38 20 2032 06 36 56 2050 06 39 27 1997 06 38 48 2015 06 37 23 2033 06 39 55 2051 06 38 30 א #)Jא @_+X GST @t אא ,@ ?Ħ0E*@@ī Z א #)Jא @X+_אO#k*1b8LST _Òא א!א dk_(7א 8t_8 ħV#Ĝא-^@E 15 ÷ Long F0 ?א #)Jא @_+X GST @t . LST = GST ± Long 130 א/60א _ 60#9א אaqא ,+* ú ،E ε F DG4א cאאfĦ8a<#QÒ#>;>אFא aא&>01 א +#;א *q 4,#א אaqא ,+* ، א cאĦ8,#;אoaqאH:#א(א ,+* ,#א אaqא ,+*א ,E ، 0#>)+0 ")@*אğ* ″1 21.448 ′ 26 23° ، #9 o "א @*) 0.4684 ″ OĨs P*,?ī @:، 6;>%א/60א _A:*8א$א/*; א * V'0 Y<* א ,@א/K8#3 ε = 23 ° 26' 21.448' ' - [0.4684 ( Y - 2000 ) / 3600 ] א O#3א ,+* +7\ K ú *8 O#3 א ×%_ EλF ، #9 א/,* א cא א/*: i*(5 4 ,# א אaq א ,+*?˚8V 360˚ - 0א( ?3GאH אOא γ_08 4א אaqא 4+hא #א!Ħ8 )3 א אaq א ,+* א #א!6K;*VD8*,[3 ،$Ğ*8?א/3'א/,0 7 +\" א $#0אÒ;א/60א _، 0 *8l#G T)א * 0'א F`8)+0א O#3א ,+*]F F#E;אG"i*+q \א 8'?א אaqא #אD0% א/3' א/,K 0 Tan(RA) Tan (λ) = Cos (ε ) 60א +7\ ×א/Dec 60 א @*!א/#G א0Z*-אH:#א ، *Ú$%& 0q V4 F<* א @Qא¢ #9oא/3' א/,60P*,ğ ، RA 0א E[%#, Dec \+7#א)6K+0 ? 3' א RA \+7 ، א/60א 6 אaqא ,+*Wb ، εאW6Q P1V 0%] 3' א +7\" 6 א/60א _6QĜ 4 6 60א K\+7 Tan (Dec ) = Sin(RA)Tan (ε ) 131 .*W E 1 F O 8* @, א! 60X,EË 099 ˚ 56 ' WO#ko 4א #)JאÒ_א/#: h m s LMT F*68 15 $#0 55 04 11 +*)+0א #)Jא/#: GMT @t @Eא K h h m s LMT 11 04 55 ,15 April h m s Long ÷15 06 39 44 +W ------h m s GMT 17 44 39 ,15 April .*V W E 2 F O,]*; א #) Eq .T J K 2008 Y<* 15 $#0 :@ K 2008 ،,0 F O%"6oG D0 *; א #)J ,@א o`G E ,0א +0א/*8 KY<* 15 ®<* Eq.T = - 08 m 55s .*6X: W E 3 F Oא #)Jא/#: GMT @t Y<* 1$#0 2008 א! o 4 h m s ħVÙ7 F* 048˚ 5.6' EO#k 12 24 10 +*)+0א #)JאÒ_א h*9 m s LAT 8* @, א! @Eא WV hא +FJ*; א #)K -12 20 J h m s GMT 10 24 12 ,1 March h m s Eq.T 00 12 20 (Eq.T -) MT > AT ------h m s GAT 10 11 52 ,1 March h m s Long ÷15 03 12 22.4 +E ------h m s LAT 13 24 14.4 ,1 March h m s .*WV W E 4 F Oא +J(FJא/@*8#* 6$# ZT 18 23 00 3 ,@ ħV >א! WO#ko 4 '16 ˚137 +*)+0א #)Jא/#: GMT @t E@א Kh h m s ZT 18 23 00 ,6 May h ZN 09 +W ------h m s GMT 03 23 00 ,7 May 132 .*60X,E Ë W E 5 F O א cא א ,* 0 t@ +7\ אO;*E JG* GHA 00ğ *8 J( +0( F#E 37˚ 16.4' -*%< א/@ZT 3 8* @, א! O#k o 4 m s 039˚ 49' E E@א WV hא +FJ)+0*; א #)K +02 53 J h m s GHA ÷15 02 29 5.6 ± 12 ------h m s GAT 14 29 5.6 h m s Eq.T 00 12 16 (Eq.T +) MT < AT ------h m s GMT 14 26 12.6 ZN 03 h +E ------h m s ZT 17 26 12.6 .*hğ[,V W E 6 F Oא/>א cא _ J( F\+7א E Sh 8* @, א! O#ko 4 m s WV 048˚ 5.6' Eא +FJ)+0*; א #)K +01 42 J h m s LAT At Noon 12 00 00 h m s Eq.T 00 01 42 (Eq.T +) MT < AT ------h m s LMT 11 58 18 h m s Long 03 12 22.4 - E ------h m s GMT 08 45 55.6 ZN 03 + E ------h m s ZT Noon 11 45 55.6 h m .*hğ60X,EË W E 7 F Oא/>א cא _ @*8 Altair X J0(# א/# ZT 18 21 ،Ë$*8<_m8א c0SX 0+א !א * +0*9 #א #)Jא/#)' />א @K X m s :#$0 >א @ 03 55.9 OĨ X F#0:$*8<_m8 ،$#6) d m s m s Ĩ$Eא> 8 ، E4 × 03 55.9 F 15 43.6 J(F# #>א @X " h m s א $#0א א '8 ĩ@*$א ,* *8 18 05 16 J0(#א/G_א/ # K ZT 133 h m .*V W E 8 F O,]א #)Jא @X+_אLST _Ò #$ 10 : +× 2009 ,* 24 02 J0(#8 ZT; א #K 48˚ E O#ko J h m s ZT 02 24 00 ,10 Sep. h ZN 03 - E ------h m s GMT 23 24 00 ,9 Sep GST = GST 2009 + 0.0657098244 * d + 1.00273791 * GMT GST = 06 h 39 m 11 s + 0.0657098244 * 252 + 1.00273791 * 23 h 24 m 00 s GST = 22 h 40 m 33.59 s LST = GST + Long (E) LST = 22 h 40 m 33.59 s + (48º÷15) LST = 22 h 40 m 33.59 s + 03 h 12 m 00 s LST = 01 h 52 m 33.59 s .*J(60X,EË W E 9 F Oא/@ZT 3 27א +7\#$ 23 ×א 2009 א! o 4 h m J( F# ZT 06 23 F* 032˚ E O#kא/@ZT 3 27א +7\ א! K 027˚ E O#ko 4 h m s ZT 1 06 23 00 , 23 Feb. h m s D.Lo 1 00 08 00 + D.Lo E ------h m s LMT 06 31 00 h m s D.Lo 2 00 12 00 + D.Lo W ------h m s ZT 2 06 43 00 , 23 Feb. 134 .*J(60X,EË W E 10 F Oא/@ ZT 3 cאOא +7\#$ 11 # #0 2010 א! o 4 h m s J( F# ، ZT 11 53 03 F* 048˚ 07' EO#kא/@ ZT 3 cאO א +7\ א! K 147˚ 12' EO#ko 4 h m s ZT 1 11 53 03 , 11 Jul. h m s ZN 1 03 00 00 - Long E ------h m s GMT 08 53 03 , 11 Jul. h m s Long 1 03 12 28 + Long E ------h m s LMT 12 05 31 , 11 Jul. h m s LMT 12 05 31 , 11 Jul. h m s Long 2 09 48 48 - Long E ------h m s GMT 02 16 43 , 11 Jul. h m s ZN 2 10 00 00 + Long E ------h m s ZT 2 12 16 43 , 11 Jul. .*J(60X,EË W E 11 F Oא/@ ZT 3 cאO א +7\#$ 23 ×א 2009 א! 4 h m s F#E ZT 11 45 23 F* 052˚ E O#ko)+0*; א #)xJאא K$#0 h m s ZT Noon 11 45 23 h ZN 03 - Long E ------h m s GMT 08 45 23 h m s Long ÷15 03 28 00 + Long E ------h m s LMT 12 13 23 h m s LMT 12 13 23 h LAT Noon 12 ~ ------h m s Eq.T 00 13 23 (Eq.T -) MT > AT 135 h m .*J(" W E 12 F Oא/@ZT 07 00 3 ? #$ 11 # #0 2010 א! o4 V، 048˚ E O#k,])+0 א cאא ,* 0 א @0+X WV SHA \+7א +J(FJא Sh h m s ĦĢ"א ,* *8 11 53 00 J0(# א/G_א/#، Fא #)Jא @X+_אLST _Ò h m s K 02 27 52 *, h m s ZT 07 00 00 , 11 Jul h m s Local Noon 11 53 00 ~ ------h m s LHA 04 53 00 h m s ~ 24 00 00 ------h m s LHA 19 07 00 h m s LHA 19 07 00 h m s LST 02 27 52 ------h m s SHA 16 39 08 h m s .*J(" W E 13 F Oא/@Y<* 8$# ? ZT 09 30 00 3 2007 א! 4 V، 054˚ 06' E O#ko,])+0א/3'א/, RA 0 \+7 W@ א #)KJ h m s ZT 09 30 03 , 08 March h m s ZN 04 00 00 - Long E ------h m s GMT 05 30 00 , 08 March :@ *Z 2007 K@:8_E`E30,8@: ،,0 F O%"6oGD0 *; א #)J ,@ א ,30א .* . o`G Eא +0א/*8 KY<* 8®<* Eq.T = - 10 m 57 s h m s GMT 05 30 00 , 08 March h m s Long 03 36 24 + Long E ------h m s LMT 09 06 24 , 08 March 136 h m s LMT 09 06 24 , 08 March h m s Eq.T 00 10 57 (Eq.T -) MT > AT ------h m s LAT 08 55 27 ± 12 ------h m s LHA 20 55 27 GST = GST 2007 + 0.0657098244 * d + 1.00273791 * GMT GST = 06 h 37 m 08 s + 0.0657098244 * 67 + 1.00273791 * 05 h 30 m 00 s GST = 16 h 32 m 11.42 s LST = GST + Long (E) LST = 16 h 32 m 11.42 s + (054º 06'÷15) LST = 16 h 32 m 11.42 s + 03 h 36 m 24 s LST = 20 h 08 m 35.42 s h m s LST 20 08 35.4 h m s LHA 20 55 27 ------h m s RA 23 13 08.4 .*W E 14 F O %)60+0א אaqא ,+*F א/60א _ E ε K 1991 @, ε = 23 ° 26' 21.448' ' - [0.4684 ( Y - 2000 ) / 3600 ] ε = 23 ° 26' 21.448' ' - [0.4684 ( 1991 - 2000 ) / 3600 ] ε = 23 ° 26' 21.448' ' - [- 0.001171 '' ] ε = 23 ° 26' 25.66' ' 137 .*O#k[, W E 15 F Oא +7\א ,+* K 2012 L 5L 15 $# E λF :@ K@: 2012 ،0, F O%"6oGD0 *; א #)J ,@א o`G E ,0א +0 א/*8 K#* 15 ®<* Eq.T = 03 m 41 s GMT 00 h 00 m 00 s Eq .T 00 h 03 m 41 s (Eq.T +) MT < AT ------GAT 00 h 03 m 41 s ± 12 ------GHA 12 h 03 m 41 s GST = GST 2012 + 0.0657098244 * d + 1.00273791 * GMT GST = 06 h 36 m 19 s + 0.0657098244 * 136 + 1.00273791 * 00 h 00 m 00 s GST = 15 h 32 m 30.5 s GST 15 h 32 m 30.5 s GHA 12 h 03 m 41 s ------RA 03 h 28 m 49.5 s * 15 52˚ 12' 22.5'' ε = 23 ° 26' 21.448' ' - [0.4684 ( Y - 2000 ) / 3600 ] ε = 23 ° 26' 21.448' ' - [0.4684 ( 2012 - 2000 ) / 3600 ] ε = 23 ° 26' 15.83' ' Tan(RA) Tan (λ) = Cos (ε ) Tan(52 ° 12' 22.5' )' Tan (λ) = Cos 2( 3° 26' 15.83' )' λ = 5 4° 34' 03' ' 138 .*O#k[, W E 16 F Oא +7\א ,+* K1995 L 2L 2$# E λF :@ *Z 1995 K@:8_E`E 30,8@: ،,0 F O%"6oGD0 *; א #)J ,@ א ,30א .* . o`G Eא +0א/*8 *>®2 ×אK Eq.T = - 13 m 35 s GMT 00 h 00 m 00 s Eq.T 00 h 13 m 35 s (Eq.T -) MT > AT ------GAT 23 h 46 m 25 s ± 12 ------GHA 11 h 46 m 25 s GST = GST 1995 + 0.0657098244 * d + 1.00273791 * GMT GST = 06 h 36 m 46 s + 0.0657098244 * 33 + 1.00273791 * 00 h 00 m 00 s GST = 08 h 46 m 52 s GST 08 h 46 m 52 s GHA 11 h 46 m 35 s ------RA 21 h 00 m 27 s * 15 315˚ 06' 45'' ε = 23 ° 26' 21.448' ' - [0.4684 ( Y - 2000 ) / 3600 ] ε = 23 ° 26' 21.448' ' - [0.4684 ( 1995 - 2000 ) / 3600 ] ε = 23 ° 26' 23.79' ' Tan(RA) Tan (λ) = Cos (ε ) Tan(315 ° 06' 45' )' Tan (λ) = Cos 2( 3° 26' 23.79' )' λ = − 4 7° 21' 08' ' ~ 360 ˚ λ = 312 ° 38.9' 139 .*W E 17 F O ,]60א K 2012 L 1L 18 $# Dec \+7 :@ K@: 2012 ،0, F O%"6oGD0 *; א #)J ,@א o`G E ,0א +0 א/* 8 K*@ 18 ®<* Eq.T = - 10 m 03 s GMT 00 h 00 m 00 s Eq.T 00 h 10 m 03 s (Eq.T -) MT > AT ------GAT 23 h 49 m 57 s ± 12 ------GHA 11 h 49 m 57 s GST = GST 2012 + 0.0657098244 * d + 1.00273791 * GMT GST = 06 h 36 m 19 s + 0.0657098244 * 18 + 1.00273791 * 00 h 00 m 00 s GST = 07 h 47 m 17 s GST 07 h 47 m 17 s GHA 11 h 49 m 57 s ------RA 19 h 57 m 20 s * 15 299˚ 20' ε = 23 ° 26' 21.448' ' - [0.4684 ( Y - 2000 ) / 3600 ] ε = 23 ° 26' 21.448' ' - [0.4684 ( 2012 - 2000 ) / 3600 ] ε = 23 ° 26' 15.83' ' Tan (Dec ) = Sin(RA)Tan (ε ) Tan (Dec ) = Sin( 299 ° 20' )Tan( 23° 26' 15.83' )' Dec = 20° 42.2' S 140 h m .*W E18FO ,]60א 1998 L 9L 4$# Dec \+7 *, K@ 20 30 :@ K@:8_E`E30,8@:_G*Z 1998 ،,0 F O%"6oGD0 *; א #)J ,@ h m א ,30א .*F*Ĩ، E 0Gא #)Jא/o`G @ 20 30 P#3א +0א/*x 8אא #)38J m s א Ħ86א ,3? +0 א: 5 4®<*E Ħ8a<#QÒ @، ×+ 6Q Eq.T = 01 04 4 GMT 20 h 30 m 00 s Eq.T 00 h 01 m 04 s (Eq.T +) MT < AT ------GAT 20 h 31 m 04 s ± 12 ------GHA 08 h 31 m 04 s GST = GST 1998 + 0.0657098244 * d + 1.00273791 * GMT GST = 06 h 37 m 50 s + 0.0657098244 * 247 + 1.00273791 * 20 h 30 m 00 s GST = 19 h 25 m 01 s GST 19 h 25 m 01 s GHA 08 h 31 m 41 s ------RA 10 h 53 m 57 s * 15 163˚ 29' 15'' ε = 23 ° 26' 21.448' ' - [0.4684 ( Y - 2000 ) / 3600 ] ε = 23 ° 26' 21.448' ' - [0.4684 ( 1998 - 2000 ) / 3600 ] ε = 23 ° 26' 22.38' ' Tan (Dec ) = Sin(RA)Tan (ε ) Tan (Dec ) = Sin( 163 ° 29' 15' ')Tan( 23° 26' 22.38' )' Dec = 07 ° 01' 30' ' N 141 .*W E19FO ,]אHא0Z*-אH:#א (Dec & RA )0q L 10 L 2$#\+7 1999 :@ *Z 1999 K@:8_E`E30,8@: ،,0 F O%"6oGD0 *; א #)J ,@ א ,30א .* . o`G Eא +0א/*8 K8#K 2®<* Eq.T = 10 m 25 s GMT 00 h 00 m 00 s Eq.T 00 h 10 m 25 s (Eq.T +) MT < AT ------GAT 00 h 10 m 25 s ± 12 ------GHA 12 h 10 m 25 s GST = GST 1999 + 0.0657098244 * d + 1.00273791 * GMT GST = 06 h 36 m 52 s + 0.0657098244 * 275 + 1.00273791 * 00 h 00 m 00 s GST = 00 h 41 m 05 s GST 00 h 41 m 05 s GHA 12 h 10 m 25 s ------RA 12 h 30 m 40 s * 15 187˚ 40' ε = 23 ° 26' 21.448' ' - [0.4684 ( Y - 2000 ) / 3600 ] ε = 23 ° 26' 21.448' ' - [0.4684 ( 1999 - 2000 ) / 3600 ] ε = 23 ° 26' 21.92' ' Tan (Dec ) = Sin(RA)Tan (ε ) Tan (Dec ) = Sin( 187 ° 40' )Tan( 23° 26' 21.92' )' Tan (Dec ) = - 0.05784051 7 Dec = 03 ° 18' 37' ' S 142 .*W E 20 F O ,]אHא0Z*-א ( Az & h )0N L 1L 15 $#\+7 2009 h m א ,* J0(#8 ZT 10 45; א #K 29 ˚ 22 ' N & 048 ˚ 00 ' E J ZT 10 h 45 m 00 s ,15 January ZN 03 h -E ------GMT 07 h 45 m 00 s , 15 January :@ ، 30,8@:O 2009 F O%"6oGD0 *; א #)J ,@א ,30 א&Ĩ، E ħ* h m Fא #)Jא/o`G @ 07 45 P#3א +0א/*x8אא #)38Jא Ħ86א ,3? m s +0א@،*@ 16 15 ®<*EĦ8a<#QÒ 6Q Eq.T = -09 25 4 GMT 07 h 45 m 00 s , 15 January Eq.T 00 h 09 m 25 s (Eq.T -) MT > AT ------GAT 07 h 35 m 35 s ± 12 ------GHA 19 h 35 m 35 s Long ÷15 03 h 12 m 00 s +E ------LHA 22 h 47 m 35 s *15 341˚ 53' 45'' GST = GST 2009 + 0.0657098244 * d + 1.00273791 * GMT GST = 06 h 39 m 11 s + 0.0657098244 * 15 + 1.00273791 * 07 h 45 m 00 s GST = 15 h 24 m 35 s GST 15 h 24 m 35 s GHA 19 h 35 m 35 s ------RA 19 h 49 m 00 s * 15 297˚ 15' 143 ε = 23 ° 26' 21.448' ' - [0.4684 ( Y - 2000 ) / 3600 ] ε = 23 ° 26' 21.448' ' - [0.4684 ( 2009 - 2000 ) / 3600 ] ε = 23 ° 26' 17.23' ' Tan (Dec ) = Sin(RA)Tan (ε ) Tan (Dec ) = Sin( 297 ° 15' )Tan( 23° 26' 17.23' )' Tan (Dec ) = - 0.38541451 Dec = 21 ° 04' 38' ' S Sin (h) = Sin (Dec )Sin (Lat ) + Cos (Dec )Cos (Lat )Cos (LHA ) Sin (h) = Sin (−21 °04 38' )'' Sin 29( °22 )' + Cos (−21 °04 38' )'' Cos 29( °22 )' Cos (341 °53 45' )'' Sin (h) = (− .0 176359391 ) + .0( 772934342 ) Sin (h) = .0 59657495 h = 36 ° 37.5' Sin (Dec ) − Sin (Lat )Sin (h) Cos (Az ) = Cos (Lat )Cos (h) Sin (−21 °04 38' )'' − Sin 29( °22 )' Sin 36( ° 37.5' ) Cos (Az ) = Cos 29( °22 )' Cos 36( ° 37.5' ) Cos (Az ) = − .0 93245392 Az = 158 °49 '2. 144 א 6Q א ,*8' 3E 0*- 4א/. א א #)N8J אHאHאE< H * /א #)Jא #D0F אĞ$א ,+* E 147 .*J([,V W E 1F Oא/@ZT 3 א! o4 F#E*+@0 29 ˚ 20 ' Nl א \+7 E Cos (ZD ) − Cos (Co .Lat )Cos (PD ) Cos (LHA ) = Sin (Co .Lat )Sin (PD ) Cos 54( °29 )' − Cos 60( °40 )' Cos 76( ° )'7.5 Cos (LHA ) = Sin 60( °40 )' Sin 76( ° )'7.5 Cos (LHA ) = .0 547380 LHA = 56º 48' 45' ' LHA 56º 48' 45'' h m s ÷15 03 47 15 ------h m s LHA 03 47 15 h m s ZT AT Noon 11 45 00 h m s ) 6א cאLHA 03 47 15 - O ------h m s ZT 07 57 45 148 .*J([,V W E 2F Oא/@ZT 3 א! o4 F#E*+@0 26 ˚ 14 ' Nl א \+7 E Cos (ZD ) − Cos (Co .Lat )Cos (PD ) Cos (LHA ) = Sin (Co .Lat )Sin (PD ) Cos 63( °29 )'9. − Cos 63( °46 )' Cos 98( °25 )'1. Cos (LHA ) = Sin 63( °46 )' Sin 98( °25 )'1. Cos (LHA ) = .0 575809 LHA = 54º 50' 37' ' LHA 54º 50' 37'' h m s ÷15 03 39 22 ------h m s LHA 03 39 22 h m s ZT AT Noon 11 50 00 h m s 8א cאLHA 03 39 22 + O ------h m s ZT 15 29 22 149 .*V W E 3F O,]א #)J"@א *$o F#E*+@0 26 ˚ 25 ' Nlא +7\ E Cos (ZD ) − Cos (Co .Lat )Cos (PD ) Cos (LHA ) = Sin (Co .Lat )Sin (PD ) Cos (102 °00 )' − Cos 63( °35 )' Cos 75( °54 )'1. Cos (LHA ) = Sin 63( °35 )' Sin 75( °54 )'1. Cos (LHA ) = − .0 364126 LHA =111 º 21' 14' ' LHA 111º 21' 14'' h m s ÷15 07 25 25 ------LHA 07 h 25 m 25 s h m s ZT AT Noon 11 44 00 h m s ) 6א cאLHA 07 25 25 - O ------h m s ZT 04 18 35 150 אHאHאE< H N8* א #)J E 151 h m .*E h m s ZT AT Noon 11 44 00 h m s ZT 08 28 00 ͂ ------h m s LHA 03 16 00 * 15 49º 00' 00'' א א ,+ZD L ؟ ĩ*$א Co.Lat l '40 ˚60 א א PD 3 '18 ˚69 א cאא ,* 0אLHA 0Ò '00 ˚49 Cos (ZD ) = Cos (Co .Lat )Cos (PD ) + Sin (Co .Lat )Sin (PD )Cos (LHA ) Cos (ZD ) = Cos 60( °40 )' Cos 69( °18 )' + Sin 60( °40 )' Sin 69( °18 )' Cos 49( °00 )' Cos (ZD ) = .0 708183 ZD = 44 °54 '9. ~ 90 ˚ h = 45 ° '2.5 152 h m .*E h m s ZT Transit 01 24 54 h m s ZT 04 25 00 ͂ ------h m s LHA 03 00 06 * 15 45º 01' 30'' * 1.00273791 LHA 45º 08' 54'' א א ,+ZD L ؟ ĩ*$א Co.Lat l '45 ˚60 א א PD 3 '12.1 ˚51 א cאא ,* 0אLHA 0Ò '8.9 ˚45 Cos (ZD ) = Cos (Co .Lat )Cos (PD ) + Sin (Co .Lat )Sin (PD )Cos (LHA ) Cos (ZD ) = Cos 60( °45 )' Cos 51( °12 )'1. + Sin 60( °45 )' Sin 51( °12 )'1. Cos 45( ° )'9.8 Cos (ZD ) = .0 785737 ZD = 38 °12 '7. ~ 90 ˚ h = 51 °47 '3. 153 א cאא ,N8 0+ אE א cאא ,O#k_9 Az0+א #Y 4;אaqאN، א cא @א ,+ZJ *:? א אaq א :0 א 0,0q 4 א אaq א :0 א/*>N8 *S8*,ğ ،$Ğ*8 a E .*V W E 6 FO,]א> א cאא ,0+ Ħ 2003 L 5L 28 $# \+7 E Cos (PD ) − Cos (ZD )Cos (Co .Lat ) Cos (Az ) = Sin (ZD )Sin (Co .Lat ) Cos 68( °36 )' − Cos 30( °00 )' Cos 60( ° 40' ) Cos (Az ) = Sin 30( °00 )' Sin 60( ° 40' ) 154 − .0 0593801567 1 Cos (Az ) = 0.4358922068 Cos (Az ) = − .0 136227 Az = 97 °49 '8. .*W E 7 FO %א>א cאא ,0+ K#] א/Ħ 2015 L 6L 13 $# Ø7 E Cos (PD ) − Cos (ZD )Cos (Co .Lat ) Cos (Az ) = Sin (ZD )Sin (Co .Lat ) Cos 73( °54 )'3. − Cos 49( °10 )' Cos 64( ° 44' ) Cos (Az ) = Sin 49( °10 )' Sin 64( ° 44' ) − .0 001857826 Cos (Az ) = 0.6842302209 Cos (Az ) = − .0 002715 Az = 90 ° '3.9 ~ 360 ˚ Az = 269 °50 '7. 155 אHאHאE< H N8* א cאא ,0+ /א>E >א F`8KאĞ$א ,+* אE 156 .*W E 8 FO %א>E Sin 58( °46 )' Sin (100 °) Sin (B) = Sin 83( °22 )' B = 57 °58 ' B + Az Co .Lat + PD Cos Sin ZD 2 2 Tan = 2 B − Az Co .Lat + PD Cos Cos 2 2 57 °58 '+100 °00 ' 58 °46 '+83 °22 ' Cos Sin ZD 2 2 Tan = 2 57 °58 '−100 °00 ' 58 °46 '+83 °22 ' Cos Cos 2 2 ZD Cos (78 °59 ')Sin (71 °04 ') Tan = 2 Cos ()()− 21 °01 ' Cos 71 °04 ' 157 ZD Tan = .0 596784 2 ZD = 30 °49 '7. 2 ZD = 61 °39 '4. ~ 90 ˚ h = 28 °20 '6. .*W E 9 FO %א>E Sin 60( °45 )' Sin 80( °00 )' Sin (B) = Sin 70( °53 )'5. B = 65 °24 '9. 158 B + Az Co .Lat + PD Cos Sin ZD 2 2 Tan = 2 B − Az Co .Lat + PD Cos Cos 2 2 65 °24 '9. +80 °00 ' 60 °45 '+70 °53 '5. Cos Sin ZD 2 2 Tan = 2 65 °24 '9. −80 °00 ' 60 °45 '+70 °53 '5. Cos Cos 2 2 ZD Cos (72 °42 '5. )Sin (65 °49 '2. ) Tan = 2 Cos ()()− 07 °17 '5. Cos 65 °49 '2. ZD Tan = .0 667395 2 ZD = 33 °43 '1. 2 ZD = 67 °26 '2. ~ 90 ˚ h = 22 °33 '8. 159 א #)N8J א cאא ,0+ Ħ0E?īא #)M*ěV !< OTo?J אĞ$א ,+*، 6K 0# Ĩ?60אo$Ğ lא א!، A,G *@Gb$)#אĦGא/. א F אğ* א .* . ،0 ،،، E F##$ @* T1?Ħ1א/. +9* א א $*ĩ3 lא א! ، א cאא/*8 +9¢* 9_ א cאא ,0+، א Ë LאO#Qğ S0*8* !א _، @, F#G*(iN $A אA: N[0Ğא[ א cאא/*8א&o ، א 9L_א cא @אĞ$א ,+* F א cאħV6@G Z? E، B F אğ* א ,*N*? E 8-א/. א N *;א cאא .* .א/8#3، 9_ א cאא ,* 0 אA:*8 0Òא$*;KÙ8*G-N Ùoא0Gi ?א #)Jא/dk8P#3א cאא ,* *S*1V0 J(4א cאM*ěV[,ęO אĞ$א ,+* ، א @* D1#4 "א ,+*(، 0 S%F*K FVא 27 ) 6א cאO d3Eא cא א ,* 0אJ(?0Òא cאS% F*KFV ،Oא Pt 8א cאú*mE O D0 O#Q 4א #)Jא/KP#3 160 .*W E 10 FO %א #)Jא/G_א/# ZT "א/@*א #א) o4 N l ' 14 ˚ 26 #$ JG*KĦ 2001 L 11 L 22 א cאא ,0+ WV 122˚O;*E \+7א +60FJ h m s א J(، 20˚ 08.3' S \+7א Sh"9אא K ZT 11 24 00 $#0 ĩ*$א Co.Lat l '46 ˚63 א א PD 3 '8.3 ˚110 א cאא ,Az 0+ '00 ˚122 א cא א ,* 0אLHA 0Ò ؟ Sin (Co .Lat )Sin (Az ) Sin (B) = Sin (PD ) Sin 63( °46 )' Sin (122 °00 )' Sin (B) = Sin (110 ° )'3.8 B = 54 °07 '1. B + Az Co .Lat − PD Cos Cos LHA 2 2 Tan = 2 B + Az Co .Lat + PD Sin Cos 2 2 54 °07 '1. +122 °00 ' 63 °46 '−110 °08 3. Cos Cos LHA 2 2 Tan = 2 54 °07 '1. +122 °00 ' 63 °46 '+110 °08 '3. Sin Cos 2 2 161 LHA Cos (88 ° '5.3 )Cos (− 23 °11 '1. ) Tan = 2 Sin ()88 ° '5.3 Cos 86( °57 )1. LHA Tan = .0 585924 2 LHA = 30 °22 ' 2 LHA = 60 °44 ' /15 º h m s LHA = 04 02 56 A:V8א[א cאא ,* 0אLHA 0Ò א EL× ?א #)Jא/ _ E4\+7 o א cאOאÒ_/@א/@*، א #) J א/*M*ěVF*Ĩ ،*x<o@ _1א +7\˚122 #9 %@# ،_(5P Ħ א!F`8א EÍ\ +7 oא cאOא*8 ،8_Ò * E_ א cא א ,* 0אM9"0Òאğ* ?א #)Jא/ _ E4\+7 oא cא، O d3E D0? )Jא Sh O#Q J(4 א/@3א/M*ěNP#3א +7\א/ l"א/,` K h m s ZT AT Noon 11 24 00 h m s ) 6א cאLHA 04 02 56 - O ------h m s ZT 07 21 04 162 .*p M*ěV!<Ë W E 11 FO @]אĞ#^א( L 4L 12 $# Betelgeuse 2012 ? @אH:@>א #א) o4 WV K 255˚ 26' D9*ěVF* 31˚14 ' Nlא +FJ h m s )60+0 א @J(، 07˚ 24.5 ' N #9 Xא cא O *8 16 30 37 X@ J0(#א/G_ א/# ZT *:_ Ëא !؟ ĩ*$א Co.Lat l '46 ˚58 א א PD 3 '35.5 ˚82 א cאא ,Az 0+ '26 ˚255 '34 ˚104 א cאא ,* 0אLHA 0Ò ؟ Sin (Co .Lat )Sin (Az ) Sin (B) = Sin (PD ) Sin 58( °46 )' Sin (104 °34 )' Sin (B) = Sin 82( °35 )'5. B = 56 °34 '1. B + Az Co .Lat − PD Cos Cos LHA 2 2 Tan = 2 B + Az Co .Lat + PD Sin Cos 2 2 56 °34 '1. +104 °34 ' 58 °46 '−82 °35 '5. Cos Cos LHA 2 2 Tan = 2 56 °34 '1. +104 °34 ' 58 °46 '+82 °35 '5. Sin Cos 2 2 163 LHA Cos (80 °34 ')Cos (−11 °54 '9. ) Tan = 2 Sin ()80 °34 ' Cos 70( °40 )9. LHA Tan = .0 491412 2 LHA = 26 °10 '2. 2 LHA = 52 °20 '4. /15 ˚ h m S LHA = 03 29 22 A:V8א[א cאא ,* 0א LHA 0Ò *S+,G X@ N 1.00273791 4 *> א 2 Ħ8 א c? א @X+_א c?א +7,_א/#: ، M*ěVF*Ĩ א @P#@%#9 255˚ 26' X 8_ ، Ħ א!F`8 א @o ^*ě 8 ( Xא cאOא*8 ،_Ò * E_×א cאא ,* 0א0Ò" M9אğ* ?א #)J א/*_1 o@ X@>^א _ ، D ú*m D0 D3 :#EJ(4 O#Q J(4א/@3א/P#3"א/,` K h m s LHA 03 29 22 ÷ 1.00273791 ------h m s LHA 03 28 47 h m s ZT Transit 16 30 37 h m s 8 א cאLHA 03 28 47 + O ------ h m s ZT 19 59 24 164 א cאא ,N8 0+ א #)J Ħ0E?ī א cאא ,0+ X$א ,+* N8 א #)A:*8 ،Jא[א cאא ,* 0א0Ò LHA W ،$X 2P*,ęא ,* * J(Ħ8-א cאOא #)Jא/ 6K0#Ĩ ،l ?60אo$Ğ lא א!، #F Ħ1*@^אF#G*($A,@ ،*+S@08a<#Qf א/. א F אğ* א .*H E 0G* ;א m'א .* #9א א ,+ ،L Q T1א/. #، ? 6@G Z 3 F#G*(0א/. א F אğ* א &H E ħ*;א cאא/8#3، 9_ א cאא ,K0+ h m .*M*ěV% W E 12 FOא +7\א ,* ZT 14 49 8^אL 5L 12 $#O 2012 "@א *oa9 WV 30˚ 03 ' Nlא +60FJא J(، 18˚ 18.3 ' N\+7 h m ^אOא W"\+7 א *8 12 51 $#0 J0(#א/G_א/#K ĩ*$א Co.Lat l '57 ˚59 א א PD 3 '41.7 ˚71 א cאא ,* 0אLHA 0Ò ؟ 165 h m s ZT AT Noon 12 51 00 h m s ZT 14 49 00 ͂ ------LHA 01 h 58 m 00 s * 15 8א cאO ''00 '30 ˚ 29 Cos (ZD ) = Cos (Co .Lat )Cos (PD ) + Sin (Co .Lat )Sin (PD )Cos (LHA ) Cos (ZD ) = Cos 59( °57 )' Cos 71( °41 )'7. + Sin 59( °57 )' Sin 71( °41 )'7. Cos 29( °30 )' Cos (ZD ) = .0 872523 ZD = 29 °14 '8. Cos (PD ) − Cos (ZD )Cos (Co .Lat ) Cos (Az ) = Sin (ZD )Sin (Co .Lat ) Cos 71( °41 )'7. − Cos 29( °14 )'8. Cos 59( °57 )' Cos (Az ) = Sin 29( °14 )'8. Sin 59( °57 )' − .0 1228461523 Cos (Az ) = 0.4229011078 Cos (Az ) = − .0 290484 Az = 106 °53 '2. ~ 360˚ Az = 253 ° '8.6 166 h m .*WE 13 FO % א cאא ,0+ X@ א ,+*א& Spica Oc א ,* ZT 23 18 ? L 6L 6$# 2015 " א #o J WV 29˚ 15' Nlא +FJ )+0 60 א @X h m J(، 11˚ 14.2' SO;*E oa<#א cאW" O א *8 20 14 $#0 J0(#א/K_G ĩ*$א Co.Lat l '45 ˚60 א א PD 3 '14.2 ˚101 א cאא ,* 0אLHA 0Ò ؟ h m s ZT Transit 20 14 00 h m s ZT 23 18 00 ͂ ------LHA 03 h 04 m 00 s * 15 8א cא46º 00 ' 00"O * 1.00273791 46º 07' 33" Cos (ZD ) = Cos (Co .Lat )Cos (PD ) + Sin (Co .Lat )Sin (PD )Cos (LHA ) Cos (ZD ) = Cos 60( °45 )' Cos (101 °14 )'2. + Sin 60( °45 )' Sin (101 °14 )'2. Cos 46( ° )'5.7 ZD = 60 ° '3.8 Cos (PD ) − Cos (ZD )Cos (Co .Lat ) Cos (Az ) = Sin (ZD )Sin (Co .Lat ) Cos (101 °14 )'2. − Cos 60( ° )'3.8 Cos 60( °45 )' Cos (Az ) = Sin 60( ° )'3.8 Sin 60( °45 )' − .0 4381503254 Cos (Az ) = 0.7566547685 Az =125 °23 '1. ~ 360˚ Az = 234 °36 '9. 167 א/60א/60א/N8 60 אE 168 h m s .*J(" W E 14 FOא/@L 5L 30 $# ? ZT 18 40 02 3 2015 א! o4 E h m s ZT Transit 14 54 47 h m s ZT 18 40 02 ͂ ------h m s LHA 03 45 15 * 15 LHA 56º 18' 45'' א א PD 3 ؟ ĩ*$א Co.Lat l '26.3 ˚63 א א ,+ZD L '35 ˚50 א cאא ,* 0אLHA 0Ò '18.8 ˚56 Sin (Co .Lat )Sin (LHA ) Sin (B) = Sin (ZD ) Sin 63( °26 )'3. Sin 56( °18 )'8. Sin (B) = Sin 50( °35 )' B = 74 °26 '8. 169 LHA + B ZD + Co .Lat Cos Sin PD 2 2 Tan = 2 LHA − B ZD + Co .Lat Cos Cos 2 2 56 °15 '+74 °26 '8. 50 °35 '+63 °26 '3. Cos Sin PD 2 2 Tan = 2 56 °15 '−74 °26 '8. 50 °35 '+63 °26 '3. Cos Cos 2 2 PD Cos (65 °20 '9. )Sin (57 ° '7.0 ) Tan = 2 Cos ()()− 09 ° '9.5 Cos 57 ° '7.0 PD Tan = .0 650752 2 PD = 33 °03 '2. 2 PD = 66 °06 '5. ~ 90 ˚ Dec = 23 °53 '5. 170 h m s .*J(" W E 15 FOא/@L 3L 30 $# ? ZT 08 59 47 3 2015 א! o4 E h m s ZT AT Noon 11 52 44 h m s ZT 08 59 47 ͂ ------h m s LHA 02 52 57 * 15 LHA 43º 14' 15'' א א PD 3 ؟ ĩ*$א Co.Lat l '45 ˚60 א א ,+ZD L '15.9 ˚48 א cאא ,* 0אLHA 0Ò '14.3 ˚43 Sin (Co .Lat )Sin (LHA ) Sin (B) = Sin (ZD ) Sin 60( °45 )' Sin 43( °14 )'3. Sin (B) = Sin 48( °15 )'9. B = 53 °13 '2. 171 LHA + B ZD + Co .Lat Cos Sin PD 2 2 Tan = 2 LHA − B ZD + Co .Lat Cos Cos 2 2 43 °14 '3. +53 °13 '2. 48 °15 '9. +60 °45 ' Cos Sin PD 2 2 Tan = 2 43 °14 '3. −53 °13 '2. 48 °15 '9. +60 °45 ' Cos Cos 2 2 PD Cos (48 °13 '7. )Sin (54 °30 '5. ) Tan = 2 Cos ()()− 04 °59 '3. Cos 54 °30 '5. PD Tan = .0 937766 2 PD = 43 °09 '6. 2 PD = 86 °19 '2. ~ 90 ˚ Dec = 03 °40 '8. 172 E E 173 .*WE 16 FO %א>E Sin (Dec ) Sin (h) = Sin (Lat ) Sin 13( ° )'2.7 Sin (h) = Sin 31( °14 )' h = 25 °57 '7. .*WE 17 FO %א>E Sin (Dec ) Tan (Dec ) Sin (h) = Cos (LHA ) = Sin (Lat ) Tan (Lat ) Sin 23( °18 )'2. Tan 23( °18 )'2. Sin (h) = Cos (LHA ) = Sin 33( °45 )'5. Tan 33( °45 )'5. h = 45 °23 '4. LHA = 49 °52 '6. 174 )J אH:3* א 4+h X$א ,+* J( Ħ0 אH:3* א 4+h X$א ,+*، #9א #)Jא 6Q M@א4Q(ħV$Ğ ^אiN ،8N @w0Ú?א WV*+0אF*KאĞ$א ,+*:0 א j7א/P#3 WO#Qğ F#F#9 ،א/K 60× ?א 8l@ \ אKF*KFb ،a<*5H iN ]A,G אE 175 .*J( % WE 18 FOאH:3* א 7)0א 4+h X@ א אW Caph [0mĠ N 60 '13.8 ˚59 8* @, א! o4 WV 2014 L 8L 1$# 29˚ 15 ' Nlא h m s +J( FJ^אOא @*8 03 15 05 X J0(#א/G_א/# ZT ?א $#0א * _ ،Z %א>M9א*3:H K Sin (Lat ) Sin (h) = Sin (Dec ) Sin 29( °15 )' Sin (h) = Sin 59( °13 )'8. Sin (h) = .0 568675 h = 34 °39 '5. א א ,+ZD L '20.5 ˚55 ĩ*$א Co.Lat l '45 ˚60 א א PD 3 '46.2 ˚30 א cאא ,* 0אLHA 0Ò ؟ Cos (ZD ) − Cos (Co .Lat )Cos (PD ) Cos (LHA ) = Sin (Co .Lat )Sin (PD ) Cos 55( °20 )'5. − Cos 60( °45 )' Cos 30( °46 )'2. Cos (LHA ) = Sin 60( °45 )' Sin 30( °46 )'2. Cos (LHA ) = .0 333461 176 LHA = 7 º0 31' 15' ' /15˚ h m s LHA = 04 42 05 LHA 04 h 42 m 05 s ÷ 1.00273791 ------LHA 04 h 41 m 18 s 03 h 15 m 05 s , 2Aug ZT Transit h +24 h m s ) 6 א cאLHA 04 41 18 - O ------ h m s ZT 22 33 47 , 1Aug Cos (Dec ) Sin (Az ) = Cos (Lat ) Cos 59( °13 )'8. Sin (Az ) = Cos 29( °15 )' Sin (Az ) = .0 586356 Az = 35 °53 '9. 177 178 א 6Q א .*? א 27א Ptא #: א #: Transit X0G >אFא&>Fb ، $#6Ka*9 <#fO#l א&%א$א ,+* SK)*@Z*א h*9 א 0#0 ?א ħV27א o ×E Pt^אOא א!، @*#cKFאĞ$א ,+* 4 o^אOא א! ، *FOאĞ$"1' א #:، 0 Ħ8*DKY#(:#E(F# M*ě *8i**ĩ *S@0F# ،D8D(5א O*+7אc *+K ،P#@Ğא?W '±#8אĞ$ א ,+* )E @*#:אĞ$א ,+*Ġ^אOא א!، Fb)+0^אDא ,* 0אE LHA 0Ò@$، *8 * D3*,_א/,RA 0 ' )+0 א #)Jא @X+_אW? ، LST _Ò ī? ,*J(P א #: ?OTo א T) א * W0 LHA = LST - RA 181 ?OTo א T) א ,*ī 8@@* א cא אa<#QÒ @א o Ħ8 P[3^אOא א!o א cאOא/*>Ğ*8$א ,+* ، 8 ħV*S#א-^@ī0? א #)Jא/ _ #>אĞ$ א ,+* Ġ^אOא א!א/*Wb ،D@_1אE*GF*K°א T)#%]אS a<*5Hא}F אĞ$א ,+*) o^*ě :#E^אOא א! ، *,#%] א $ *8 8J(# >)+0א cא א ,* 0אWV*+@08 ،0ÒאF*K א @*E° :* ] אSa<*5H א}FאĞ$א ,+*Í #:8 Í o^אOא א! ، W ,#%] א `*8 o 8J(#@ \א >?J(6% א #:،א/*8;#Q 6KP*,J(#9*@9J(#? 3' אĞ$א/,0 ^אD א ,* 0 אJ( ،0Òא ,אKO "* א @X#$]),+א cא א ,* 0א @*ě W ، 1.00273791 4 ħV*S#Ĝ8 א-^@N 0 *>א Ħ82א c?א @X+_א c?א +7,_א/#:?G Z '08 א#3Ġא-אğ,*08א ,*K8 *"*Oא +، X0G Ùtא ,'")D3 +0א/,Fb ،+0א&3] , D3:#E J( 8# א ، W A: V6%?א[)+0א/3'א/,0 א c?א @X+_אÒ_ @ 9א א #)J א ، W?ÍFb p ،i**א0ęĦEP*,ğ J(F#א cא O א @*E°?אP*,ğא&EO، א ?To 6K+0(%#GD? א/3'א/,0 א c? א @X +_אA:N _ÒאS*"אP*,ğא .*_G J(#א #:א/KP#3 K?ī*+K א cאאa<#QÒ @א o Ħ8 P[3^אOא א!oא cאOא/*> Ğ*8$א ,+* ، ?J( Zא #:، "*E 182 א 27א Rising & Setting Pt א 27א Ĝ0a9*Pt @א hא S0F#L*אĞ$א ,+* @ א א!،8* @, א&%א$א ªTEL K¥(094* +7\א +، #Fא 27 א *8Pt ,@ V S0* @א hא S0\ĩL*אğ* א 0* ¥אĞ$א א!، E M9א WVa9*hא?6K+0(#+ġF*K lא א!60אK 90 ˚?6($Ğ "א 67 MTאĞ$א ,+*X "1'א Pt @א&א 8t_ א! F#، NWS M8א ,+ZX L @9אא 1#',*˚ 90 ، ^אDא ,* 0א*86.+E0Ò cא ZPX ، ī*[email protected]א #M8 PX Yא 3، 8* *>א cא PZX ^אאĞ$א ,F# Ħ" ،0+ א #$*ĩ#9 PZ Y lא א!K 3E? ī 0)#אĦGא/. א F אğ* א .*P*, Eğ 0G א cאא ,* 0א LHA 0Ò X$ א ,+*0 ،D8D(5hğ X M96.ĩא cאQG א aØא 0@c Sh#>אĞ$ א ,+*2#א&، Y#( QG4+,Eא EJ(?*S 38،<#Sh#:אĞ$א ,+* ¦6Q J('*S+Ę*+@08 ،D(5J(4א #:*@Q(F#G K D8J(4 183 Cos (a) = Cos (b)Cos (c) + Sin (b)Sin (c)Cos (A) Cos (ZX ) = Cos (PZ )Cos (PX ) + Sin (PZ )Sin (PX )Cos (LHA ) Cos 90( °) = Sin (Lat )Sin (Dec ) + Cos (Lat )Cos (Dec )Cos (LHA ) QCos 90( °) = 0 − Sin (Lat )Sin (Dec ) ∴Cos (LHA ) = Cos (Lat )Cos (Dec ) Cos (LHA ) = −Tan (Lat )Tan (Dec ) @j#3 oא lא *+7 O*"0א&%א$א ,+*Wא-א/O#0א *+7 QG+0(Fb ،0 )#Yא @*: 6Ħ8*F#E<*S *: 12 ħV-* F#E، א cאא ,0+ D(5hğ$X M*ě*8א O*+7א F#E*+@08 ،_(7 M*ě*8 D8@א O*+7א K _8t *"*Oא&%א$א ,+* Wא-א/O#0אY#( QG+0(Fb ،08#@Ğא @0Ħ8*F#E<*S :* *: 6ħV F#E،-* א cאא ,0+ M*ě*8 D(5hğ$XאP#@ Ğא 7)_، 08@+* F#E M*ě*8 D8@אP#@Ğ א :*GKW*+K K _8t i** ، 27אĞ$א ,+*?3Gא 27 Pt 3G@א Pt D0F#* @,*! אW ، i ?א @*0א @Kh FVא/*; א ,*3E8_)+0א cאא ,* 0א0Ò J(# א 27 א Pt א @h %א$ א ,+* ،*8 F<*א א ,+L $X E@א h,*˚ 90 ، 9אĢN" א #א)'א/g8 o?8NWV ،9*7א #א6א/aZ 4)+0א א ,+L"אH ī،<*? M9<*QoVא #אW_*+06 אGH,*> א q#m_ 6+א úTtא#Ğ l< GV4,*>א m#(א *;$?א&%א$א ,+*، úToVX0G א .*"א úTtא0ę ،#Ğ 6+ 6%4א&%א$א ,+*E E 184 6KoE?;>%אğא>aא tmאĞ#"אH K<* P*,@)+0אGH,*>، 0 [:*@E*SG i*0,';>%אğא>i*;k ،a'א tmא K #Ğ V4 E 185 úToVא/@h א #¥א&_، #9א cא @cKאĞ$א ,+*אĦ8* a<#QÒא א!cKא&>l، E M9א cא)*x+0(4Q F#*@אĞ$ @א&، E Cos (ZX ) − Cos (PZ )Cos (PX ) Cos (LHA ) = Sin (PZ )Sin (PX ) Cos (ZD ) − Cos (Co .Lat )Cos (PD ) Cos (LHA ) = Sin (Co .Lat )Sin (PD ) 186 Y#( O#kא Sh#> 1#9 א>Y#( QGא ú ، <#Sh EDG4א aØא 0c@א5Ħ8a<#QÒ 2 אĞ$א ,+* O#kDG4@Ĩ D، 8א aØא c@0א S0F#L*א Ğ$א ,+*#א%אi 2#א& ، + 8* >%א&ħ K+0(4 6?60 א%<; $Ğ lא א! ، DG*+K E Ĩ#א)25J0 א&%א$א ,+* 0 ،*S8 KDG+*^א;Y#(O#k א E <#Sh $ # א o`68*/*82 7# א WħV*1H*8 ،Pt Y#(O#kFbא E<#S h E<*8 *אĞ$א ,+* )0ę ،D3:#EJ cE;א;)+0אE 187 O#ka;*^ ªTG*@GV:* *-א @8V<*Sא(א0 ،Y<*S5*SG?i E )+0א/60א +7* _ *8 \+7 a;*c ?$#8א H אOא Y#(o`0 ،Y<* 20_08א @*8<*S 4i*<Ea;*c #$אPTGHא 0Q #0G# 21 _، 0 א/*Û+0(4Q(*S@060 0 Y#(O#kF#0 ،D א @K?ī*4Q(<*S 8*:+א>Kא \+7 S0*א *+7 *8_ ،F*Q@ Y#(O#k6D0א @i*0<E<*S 4 #$אH אOאĠ : 22_ 3E Ħ ، ×+'א +7\;אoaqאH:#א(א ,+*?א +7* _ ħVאF# ،P#@Ğ)+0א/Jt8(60א Q *,0 ، O#k q@א @O#k'<*Sא Ki*hG60 E#א!6א P#@%*SK\+7;אoaqאH:#א(א ,+*، Y#(O#ks(*@0א @S*>4 #$אPTGHא 21#7 ;,+×، 0 א/08#@%+0(4Q(*S@060 O#kF#0 ،D )#Yא @+0(4G;"<*S KD Z א/60אW8_8#@Ğ *8 Y#(o`0 ،F*Q@א @*8<*S E4 ،a;*c#;א +7\ @3 8אS* @אH אOא F# ،Y<* 20_08)+0א/Jt8( 60א Q O#k*S@0*,0 א @O#k'<*Sא Ki*hG60 *%<;ÙZ`8*+0 lא א! Y#(O#k4א 9Fb ، <#Shאא&Ùo 4 ØVאZl *-)+0א/60 א *+7 oÙt8Ùt ،_ lא א!، #9Fאא 8Ùt* @, 60+ א +7* _ 4א @ #א * _W • c;א;O#kא #KY+*^א;-)+0א lא *+7 J(_)+0א lאK_8#@Ğ • O#kא #+0(4Q(Y D +0(4Q(@ lא *+7 K_ • O#k6א #J(*+KY)+0א lא +7* _^א;-)+0א lאK_8#@Ğ • O#kא #+0(4G;Y D +0(4Q(@ lא8K #@Ğ_ • ,*Y#(O#kא Y#(O#k'<#ShאoH F#E*+@0 i*hG )*)+0א/o60 א +9TKl*,*א Q K • Ģא \O*"i**ĩא/60אK_8#@Ğ 4 : 60א/.*O#kF#Oא @*8 <*S ,@ ħVא \+7 o@ S5OTo O*Û 30 ˚l #0 ،#0G * Û *S0 F# D@×K_ o@ S5OTo*+@08 ،O*Û 15 ˚l;,+× 0 O#kFb_8#@% *S 0F#א @<*S o@ #9F#O*Û 15 ˚lא&K ×K 188 `, FV SG O#k*> א Ģ " #$ אPTGH א 0Q SG Q( ،_*> א Ģ " #$ אPTGHא *8#7 ,@ V F*:?¦*@0א @Q א *+7 _ aא&>V [N ،01 M<*א , ] א/ *5 א `,Ĩ 0# o`E $E#א)25J0א S8\+7*، 4: 60א/.*ú;*QO #$אPTGHא Q(×+,; 21 #7*$א ,@، V4 Y#(O#kF<*א @S*>" 9אא $#0 #+0(4G;"F D، ?9אF`8{ Nא +7\"9א א o`J("27:$#0 8* @, 0*$א ,@، 0 FאúToH"#א)J0א 27א °@Pt EV? *א #)Jא +7,_ א/#:، א ģ ?א #)Jא h*9אK_0ğ 25J(FVא +7\א/`Ģ ، o"א $#0א D0F#Eא/aא J(Ħ8 0@cא cאO )Jא ،?ī*6( 27 \0 Y#(O#kF#*@א @K?ī*6(<*S J(FV^אOא J(o4@Ĩ ،\+7א ĢNSh 4*$א ,@ @G \א #)J א/#: W، MT úTĚא #)Jא h*9אAT _0ğ، א #J(Fא cא8O* @, h V D0;אi*+q @א ,* O*"*+K 12א/c א o¢$#?Ùt*ĪV ،0,+7 j#3o@ א O#3א ę0,0q,])+0*; א #)KJ *+K W; o[,ę lא א!، * @, Ġ Nl˚30 4: 60א/.*Fb ،O )25Jא +7\א/`ú;*Qo #א _ #$ P J(Ħ"،*@ 10 א +7 \א/$ @G o\א 1#O%_*+0،×+,; 2$# ú;*Ql*25$א +7\ א/`oא/$ @j#3o *Ûl ~0 K oא l 25$#א +7\א/`o 25$#א +7\א/$ #* 29 *@ 28 10˚ N #0G# 3 *@ 22 15˚ N #0G# 6 *@ 18 20˚ N #0G# 9 *@ 14 25˚ N #0G# 11 *@ 11 30˚ N #0G# 13 *@ 8 35˚ N #0G# 15 *@ 5 40˚ N #0G# 16 *@ 3 45˚ N 189 190 אH א E Ħ,*א @S*>א 60 אH א#9O א #:*Ħ8 O ،[:*@E 0K K"ĦאH אO"א V4 אO א EF*c,*:* *-א @S*>' :* *-א K 60 E?ī אH אO EDG4א hא L @9*א O#3א ,+*/cKא +7\ >%˚ĢN ، 180˚ 0אH אG"O \א W'%،@:6K?$# 0 FħV א a א&>#2t ,E01א _ '8<$# 365 O#*Ka<;א Ĩ\+7*,84+ * ,@ א/א>،9א*6 K@:*@ 6K,0>8':@#א-، 0 E"6*K$#*1V# Eא ,@،xא#6ĢN אH אG"O \א K 6K ?$#0:@ א ,@ # אH אOא 08_ # אH אOאĠ K@: _ 0, 22 September, 22:24 20 March, 12:34 2005 23 September, 04:04 20 March, 18:26 2006 23 September, 09:52 21 March, 00:08 2007 22 September, 15:45 20 March, 05:49 2008 22 September, 21:19 20 March, 11:44 2009 23 September, 03:10 20 March, 17:33 2010 23 September, 09:05 20 March, 23:22 2011 22 September, 14:50 20 March, 05:15 2012 GMT @J0(#E 191 * *'+,G*i E?,*:* *-א @S*>8,* *-א 60"#_ אH אOא 08_אĠ _ ، 0 @60$א +7\ @9?א O#k F#0 ،Ħ#0:* *-א @*: 12 <*S S.* ,* *-א 9،60א! 0?א @*0 א @FÙ ،hא&"א #א)'KF#N ، +? OToאOĞא * _/#א)P25J0א \+7 o@ To?m ،30 ˚Nl D O#k:* *-א @<*S a*$) ?#$אH אOא Y<* 20_08، א ĢÍ M@ E,*:* *-א @S*>':* *-א K60 א *>® # א 27 # א O#k Ptא @S*> 11 : 59 17 : 56 05 : 57 Y<* 16 12 : 00 17 : 56 05 : 56 Y<* 17 12 : 02 17 : 57 05 : 55 Y<* 18 12 : 05 17 : 58 05 : 53 Y<* 19 12 : 06 17 : 58 05 : 52 Y<* 20 12 : 08 17 : 59 05 : 51 Y<* 21 E WÙ, ħV'% a #אW_90,0q<6 Ģ J,]25א S8\+7* *א 0* ¥א ،\+7 F* &*9cK /\0 S@ o*، _א #)Jא #cKFא cN\+7אO : 6 א&F#Eאğ*א 0* +7\ )oJ,N א&، E>א/,*א cאcKĦ8)¥א S*\+7*א Q@8*0 )3 )¥ א +7\א *;O"א/#:' Y#( ħVú*mE0:#(0(; 16א @S*> @א 27 h א Pt، 9א?O#ka;*^DG`5:* *-א @<*S *: 12 ? 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EF\+7 V 6QE *St o[,ę * S0 א l;>60%א K \+7 ' א *6K+0( ' a? א/60א EVO*"l S(*+*" אo،SĞא K*+SToVO*"*+S@082 7 א/Dec ± Lat) ≥ 6˚ _G) - ˚90 7 א/Dec ± Lat) ≥ 12˚ _T) - ˚90 7 א _ ˚Dec ± Lat) ≥ 18) - ˚90 ?W oFĦא oo #9 54° 33 ′ 39 ″ N l ĢF?īl M@ א 7 א/k_T#אO*$א ,@*+@08 o @ Ģ 60° 33 ′ 39 ″ N l א 7 א/G_ k#אO*$א ,@ ، N W o " l iN*Û4:#"*0$@?א ,@ a<*5V+0([,ę;>0% 6א K\+7 198 :א/27א/Amplitudes Pt א ,Y#(_9? ;אaq א א!*cKĦ8אĞ$א ,+*3GD8D(5hğ א 27א 0Pt k*E'א אaq א :0א&ħ';אaqא&،Ĝ,]א , Amp 4 V E Sin (Dec ) Sin (Amp ) = Cos (Lat ) ī?אO#Qğ 4)+0א cאא , Az 0+ X$א ,+* @WD8D(5hğ ?OToא T)*-א * W0 HF 60+אJ ،_8#@Ğ 60+א *+7 Az = 90 ° ± Amp E_ HF 60+א *+7 J ،_ 60+אAz = 270 ° ± Amp E_8#@Ğ @Z o-*א Fbl)+0א ,60Ùt8ÙtEאĞ$א ,+*9mאא Ùt' א +7\א +א #א0[K M9P253GM*ěVÙtEª Tא&%א$?#$ħV K *x#0+0(ÙtEX0G o * ,@ ħV א M*ě*827E*SGhT?ī\+7א O*+7א 7)_ M*ě*8PtEא O*+7א Q OTo_8t_א 08'א 0 0Q 60F#א Û\+7* _08@+* M*ě*827E*SGpאP#@Ğא M*ě*8PtE_(7אP#@Ğא QOTo_8t_אĠ א 7*( 0 S0F#*%@8#_،"#_אH א 0O E@$)+0א/DG p 60?א @*0א @h 27E א M*ě*8 \+7א M*ě*8PtE27א KPt * "*Oא @X#$א L×א/EJ8*Z60 *8i* ,@ V ZªTG *@Gb*S0 *-)+0א , p6 @ *9X o@ 27E ;fl 4א א$?G \א @PtE3 G @ \א @3? א&،X0G F*:V א/* 8i*ī( F#T Ĝ"$#X@אěH*9*- 4א #!K )3FĢ'אo$ĞאH:#א(א ,+*DK)*@Z"א 4D(5J(Ħ8*aØ )Jא E{*Pt WªT،S%ħVS%?D0O O*"א + Ĝ אX0Gi : O א Ùtא 3 ،D0%<; 4 D0] א *Wa P*,@)+0א , 0 Ĝ,]א , @)P25JאĞ$א ,+*K 199 _ j*:V hğ\+7^אx* 8* @, א!oW Ûl* _"*$אH א Ħא 08_ אĠ _ ، אĦ8TGHא 0Q _א To?m #7 Y#(O#kDא @S*> ، א א ,+L hğא #:K Y#(:א/27א/KPt אH אOא Dec = ˚0 _08 אPTGHא 0Q Dec = 23 .5 ˚ N _ אH אOאĠ Dec = 0˚ _ אPTGHא Dec = 23 .5 ˚ S #7 200 אH א Ħ 25א 3G? \+7א 27 P253GÙtEא +7\ 4א& @oא l 4א>O#Qא ,@Ùt8 ;>60%א +7\ ، 4: 60א/.*O o@ Nl˚30 ?$#8 אH אOא 08 _ 0 cEא )+0 א/60 א *+7 Fb ، _ 27 א @ \+7 ħV ú א 0<E O*+7 i* 4 #$ אPT GH א 0Q 0 ، _ E : א/*8 *x +0( 4Q( 2 7 ,@ Ġ א l א/K#> ، 27.34˚ _9 W 8 *8 s(*@E ' s(*@ )+0 א/60 א *+7 6QE FV ħV _ @ אH אOאĠ _ G<0 \א/W8 S7 27FúTĚא @\+7 M9úא/M*ě*8a אcE ' i*0<E P#@Ğא )+0 א/60 אĞ@8# _ +7\ 4 #$ אPTGH א 0 ، #7 E#; א , )E ، 27.34˚ *x+0(4Q W8 *8 s(*@E's(*@)+0א/60אħV_8#@Ğ EFV#; 0 -8 @ אH אOא K_08 ?א @*0א @Fbh א M*ě *827E\+7א M*ě *8 PtE i**ĩ27 א Pt"#_אH אO א 08_אĠ 0 ، _ F#E)+0א ,E,*א Q *8 GV<*א$)60+0א +7\ @ 9?א 8DGÙ K Ħ#0* !א _ FĦ 9א N 4א @ #א )0،%'א , ] "W ħV a #אW*S@ 6 25J(ú Jא \+7 EDG 4א hא ĩL\ @9*אğ*א 0* +7\א& א 7)_ א!، 0 *9cK \0 E א/,* א cא *cK Ħ8 א S* \+7* א 0* #א _′ 16 ;)0)#:0"א/#:،QG6.ĩ_9 )3א K\+7 201 J( FV J אH אO א $@E M@ )+0 60 א OTo J( " Ģ ( \+7 #$ אH אO ،?א @*;>G"Zú;*QF 25J(\ א *8\+7 ,@ ħV#)'א א!، J("FV#9א Ù?+27א/+?KĢF J("א OToPtא $#0 א #א ،*>2א #)9Jאú*K Ù0t)60+0א K\+7 4: 60א/.*Fb OאH אOא ĩ" ( 2014 @:_08*$א ,* 16:58 @ ? #$ F Ħ " Y<* 20 5 2 א +7\ " ; א #ĩ J*$ א ,* 02:52 @?G \א 0 $#0 cENאOא :*S@0\+7 o6אH:#א(א ,+*%60Ĩ@8#_ Ki* E0:#(0(; 13 ′ħV6Q Ø*8 J אJ(ú;*QElאH אcK25J('Oא *8\+7 ,@ ħV>א! f;א/#)' E 74אGH,*>א ,EL cK<#S"[א D(5\+7 @א&א 7)_ "אĦğ א #cNFא:O D"א3o<، 0ğ`אę<*,GH#א _′ 34 ;)0)#:0"א/#:، W t1 @%# 1010 0 *>،;>%א>K# 10˚a P*,?īא>V¦א253Gúא ( a )\+7 3G?א G 27*0א 8O*+7* @, j#3Ġא lא *+7 G0*0א*8P#@Ğ ,@ j#3Ġא lאĞ@08# "#_ אH אO' ØVאGVlא$)60+0א \+7 J(@א 27 א! 4,#:3א ?OTo א/*; א * W0 Sin (a) = .0 015 °×Tan (Lat ) 38 0א/*; F ªTא>אH¦אoa;*c8cú lא א!0 ′ 29.5 *+K K 60˚l o@ 0:#(%<; 1.5˚ *+@08 30˚l o@ 0:#(0(; KªT GVא$)+0 9אאH¦אú o@אH:#א(*}M*ěV Fא hğ\+7 S* (5 "#_אH אĜ OאM*ě*8F#N iא NVi**ĩ27 o@אH:#א(0 @3 ,*>א \+7 o4אH:#א(א ,+* 30' ,#א&c8א)*ØV'+qאGVlא$ )+0א/60 hğ@א 7 2،*8* @, 0א l N "#_אH אO Ĝאo úTo*8 ĝ 8<*o $*" Ģ ( *ĪViא 0 l ( Ģ J(6 אH אOא J( 8 _08 אH אO אĠ *8 _ ,@ O#3Ġא lא *+7 F#Ħ 0 +7 \)0+0@? א/Ģ ،60 א \ *8 ,@ j#3 Ġא lאK08#@ Ğ 202 .*V W E 1 F O,]א #)Jא/G_א/# Eh#:א J( F\+7א cאE O 8* @, א! m s WV 39° 49' 34'' E O#ko 4א +FJ)+0*; א #)K +10 43 J h m s LAT At Noon 12 00 00 h m s Eq.T 00 10 43 (Eq.T +) MT < AT ------h m s LMT 11 49 17 h m s Long 02 39 18 - E ------h m s GMT 09 09 59 ZN 03 + E ------h m s ZT Noon 12 09 59 h m .*J(" W E 2 F Oא/@p:#EJ([,V 2015 68 10 $#? 20 22 3 א ,+*א א Arcturus 8* @, א! WV ، 48° 00' E O#ko 4א +D3 FJ h m s h m s א /,F، 14 16 19 *, 0א #)Jא @X+_אK 09 48 29 _Ò h m s LST 09 48 29 h m s RA 14 16 19 ------h m s ) 6א cאLHA -04 27 50 O h m s ÷ 1.00273791 -04 27 06 h m s ZT 20 22 00 h m s LHA 04 27 06 + ------h m s h ZT 24 49 06 -24 h m s ZT 00 49 06 11 April 203 .*P25 J( [,V W E 3 F Oא +7\ $#0 17 # #0 2015 "א #oJ WV ، 29° 15' N lא +FJ 60א +7\"9אא F، 21° 13' N *, $#0 h m )Jא cא*8 11 54 O J0(#א/G_א/#K א א ,+L P27א ZD \+7 '50 ˚90 ĩ*$א Co.Lat l '45 ˚60 א א PD 3 '47 ˚68 Cos (ZD ) − Cos (Co .Lat )Cos (PD ) Cos (LHA ) = Sin (Co .Lat )Sin (PD ) Cos 90( °50 )' − Cos 60( °45 )' Cos 68( °47 )' Cos (LHA ) = Sin 60( °45 )' Sin 68( °47 )' − .0 191374 Cos (LHA ) = 0.813357 Cos (LHA ) = − .0 235289 h m s LHA = 103 °36 '5. 06 54 26 h m s ZT Noon 11 54 00 h m s LHA 06 54 26 ------h m s )Jא Sun Rise 04 59 34 27 h m s ZT Noon 11 54 00 h m s LHA 06 54 26 + ------h m s )Jא Sun Set 18 48 26 Pt 204 .*J( [,V W E 4 F O א 7 א _ א/ ,* _q o , " 2015 ×+,; 15 $#0 WV ، 23° 37' N lא +FJ 60א +7\"9אא F، 23° 15.9' S *,$#0 h m s )Jא cא*8 12 00 31 O J0(#א/G_א/#K א א ,+L 7 א _ א/,*ZD _q '00 ˚108 ĩ*$א Co.Lat l '23 ˚66 א א PD 3 '15.9 ˚113 Cos (ZD ) − Cos (Co .Lat )Cos (PD ) Cos (LHA ) = Sin (Co .Lat )Sin (PD ) Cos (108 °00 )' − Cos 66( °23 )' Cos (113 °15 )'9. Cos (LHA ) = Sin 66( °23 )' Sin (113 °15 )'9. − .0 150780 Cos (LHA ) = 0.841744 Cos (LHA ) = − .0 179128 LHA = 100 °19 '1. h m s LHA 15/ ° 06 41 16 h m s ZT Noon 12 00 31 h m s LHA 06 41 16 + ------h m s )J א 7 א _ ZT 18 41 47 205 .*W E 5 F O 2%א #)Ħ8Jא 27א @hא/q_ +7\ $#0 24 ;,+× 2015 " א/ o WV ، 21° 25' N lא +FJ 60א +7\"9 אא S $#0 '25 23° h m s ،J(Fא cא*8 12 20 05 O J0(#א/G_א/#K J( W Nא 27א @h א א ,+L 27א +7\א @ZD h '00 ˚90 א Lat l '25 ˚21 א/S Dec. 60 '25 ˚23 Cos (LHA ) = −Tan (Lat ). Tan (Dec ) Cos (LHA ) = −Tan 21( °25 ).' Tan (−23 °25 )' Cos (LHA ) = .0 169869 LHA = 80 °13 '2. h m s LHA 15/ ° 05 20 52 h m s ZT Noon 12 20 05 h m s LHA 05 20 52 ------h m s )Jא 27א @ZT 06 59 13 h 206 J( W ·*0G*Zא 27א/q_ א א ,+L 27א +7\א/ZD _q '50 ˚90 ĩ*$א Co.Lat l '35 ˚68 א א PD 3 '25˚113 Cos (ZD ) − Cos (Co .Lat )Cos (PD ) Cos (LHA ) = Sin (Co .Lat )Sin (PD ) Cos 90( °50 )' − Cos 68( °35 )' Cos (113 °25 )' Cos (LHA ) = Sin 68( °35 )' Sin (113 °25 )' .0 130571 Cos (LHA ) = 0.854276 Cos (LHA ) = .0 152844 LHA = 81 °12 '5. h m s LHA 15/ ° 05 24 50 h m s ZT Noon 12 20 05 h m s LHA 05 24 50 ------h m s )J א 27א/Sun Rise 06 55 15 _q h m s WVאiא J(Ħ8 2א 27א @hא/_q O;*\+7 58 03 00 207 .*W E 6 F O %:א/27 5hğ V gae X@)"א #oJ N l ' 15 ° 29 ،#$ WV 2015 Y<* 20א +FJ 60א @N *, X ′ 47.9 38° Sin (Dec ) Sin (Amp ) = Cos (Lat ) Sin 38( °47 )'9. Sin (Amp ) = Cos 29( °15 )' Sin (Amp ) = .0 718148 Amp = 45 9. ° .*M*ěV% W E 7 F Oא S8hğ\+7* @א #oJ N l ' 15 ° 29 ،#$ 25 ×א WV 2015א +FJ 60א \+7 E@א K 09° 14.1' S *,h Sin (Dec ) Sin (Amp ) = Cos (Lat ) Sin (−09 °14 )'1. Sin (Amp ) = Cos 29( °15 )' Sin (Amp ) = − .0 183937 Amp = 10 6. ° HF 60+א *+7 J ،_ 60+אAz = 270 ° ± Amp E_8#@Ğ Az = 270 ° −10 6. ° Az = 259 4. ° 208 .*PtM*ěV% W E 8 F Oא + א! @o N l ' 19 ° 29 ،#$ 15 ,3\ WV 2015א +FJ 60א + @Eא K 07° 11.1' N *,h Sin (Dec ) Sin (Amp ) = Cos (Lat ) Sin 07( °11 )'1. Sin (Amp ) = Cos 29( °19 )' Sin (Amp ) = .0 143445 Amp = 2.8 ° HF 60+א *+7 J ،_ 60+אAz = 270 ° ± Amp E_8#@Ğ Az = 270 ° + 2.8 ° Az = 278 2. ° 209 א/א%'א 0+ WWW iN א/א%'א 08 JK;K #5)_א F ON )@*;6א ,+ ،ġ )*E+# א F*0אH w ، 0Tא ? K ( J LF*3 3QO;* F 4 א/Tא E، 0 א S@7*8_ 3 * א @7، אK<@:H : F F*+0:+f JK;K 0q*m*"*2 א KE J;K F 4:#?,_ 8[א ,+*( ،E ;א>;7 3 * א Q *א @K 7;، 7 J;K F 4:#?,_ א #)J0א # ،E ;א>א ،;K 7 8+f ;K J*:6א F _q*3 א א * E ،;א>א @ *K-Ù8،\q c;#0%ħV6o F <#G .09 ;K$K J*א&)+*>א *@Q E، 0 א א>א 08 K-Ù8، $# f J+א&E F <*QG# א #אE، [K ;א>א 8 @7א #^' ، א #K J J א *dא ,0א F _o#3 א ,+*(א&>lא E )*m ،א/ א .*K-Ù8،0 J +*; א k F 9*ġcc\א @E $#X ،א/:,א 08 >א:*-א @K-Ù8،7 fÕ*! ;K J+א F ÙX א/#א)J0א )#א . ،אE 3 אħN، א KÙX F «#8kĦ J;K אtĞא0*א 0א 3אqא 0+"א) א&%א$ ،E ;א>א ،;K 7 F Õ*!* J א/ *;(א 0א #!T-א E، 0,+7 א/3 א&Ù ، א *K a9 J;K _ K;،M@ א *;> *F 8 א ,+*("א E، 60 ;א>א )*F @7א #^' ، +*KF JK#5+f J$K ę F M;# P*, L#א)J0א E، aTQ א/7אT:H_ !א&K 9 J א&Ùא/? Y#*( F;א>א א _ ;،E א>א +K-Ù8 ، ĦT 210 WWW i*0G*Zi*0G*Zi*0G*Z א/א%'א&%@ 0 Astronomical Algorithms by Jean Meeus (2nd edition, December 1998, − Willmann-Bell, Inc) . Astronomical Formulae for Calculators by Jean Meeus (4th − edition,1988, Willmann-Bell) . Astronomical Almanac for the Year 2014 by Nautical Almanac Office − (U.S.), Annual edition . Explanatory Supplement to the Astronomical Almanac by US Naval − Observatory & University of Virginia . Practical Astronomy with Your Calculator by Peter Duffett Smith , − Cambridge University Press; 3 edition (March 31, 1988). Mathematical Astronomy Morsels V by Jean Meeus, Willmann-Bell, − Inc, USA . Textbook on Spherical Astronomy by W. M. Smart (Sixth edition, − results by R. M. Green) . A Treatise on Spherical Trigonometry by John Casey, Merchant Books. − Spherical Trigonometry: For the Use of Colleges and Schools by I. − Todhunter, Fifth edition. Celestial Navigation in a Nutshell by Hewitt Schlereth, Sheridan − House, (July 15, 2000). Nautical Almanac ( 2014 & 2015 ) by US Naval Observatory,UK − Hydrographic. 211 f#*-א *P א/#1# א Q 3 KKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKK א 6Qא&O %tא0*א aא ,+* א aא ,+* KKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKK KKKKKKKKKK 9 א&)P*3א ,+* KKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKK KKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKK 9 oאH:#א(א ,+* KKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKK 10 ;אaqא cאOא ,+* KKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKK KKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKK 10 #א^*-א/KKKKKKKKK KKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKK 60 11 11 א ,+Jא @KKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKK Ùh 11 11 ;אaqא& KKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKK KKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKK 12 א אaqא :KKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKK 0 12 #א^ *-אE 212 hG*$אHא0Z*-א ,+* KKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKK KKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKK 21 אHא0Z*-א&KKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKK 0 22 אHא0Z*-אH:#אKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKK 0q 22 אHא0Z*-א ,+* KKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKK KKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKK 23 א hGĦ86# אHא0Z*-א ,+* KKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKK 23 א #א-א c@0א #א-א cא KKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKK 25 6#Ĝא cאא ,KKKKKKK KKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKK 0+ 26 .ĩ*>?א 6Qא&KKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKK O 27 א 6Qא .*G_ אk*:H*-א 0 j*:V)*7GV aא ,+* KKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKK KKKKKKKKKKKKKKK 33 j*:V 4;אaqא cאKKKKKKKKKKK KKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKK O 35 j*:V 4;אaqא& KKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKK 41 .ĩ*>?א 6Qא .*KKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKK KKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKK _G 47 א 6Qא .* #א)'א @X#$ 51 KKKKKKKKKKKKKKKKKKKKKKKKK KKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKK 0Sĩ )*q+א #K *-א @KKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKK 0+X 52 #א)'א @KKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKK KKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKK $#X 54 א 6Qא א8' א/. א א/. א KKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKK KKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKK 71 אğ* א&KKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKK ħ 73 אğ* א .*KKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKK KKKKKKKKKKKKKKKKKKKKKKKKKKK 0G 74 אğ* א .* . KKKKKKKKKKKKKKKKKKKKKKKKKKKKK KKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKK 75 אğ* א אKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKK 8 76 אğ* אKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKK KKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKK ,*Ġ 77 אğ* א ,*;: KKKKKKKKKKKKK KKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKK 78 אğ* א ,*KKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKK 8 79 213 א 6QאĠ*\ אKğא h*9 %א$א ,+* אKğא h*9 א 0#0 %א$א ,+* KKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKK 83 @oאH:#א( KKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKK KKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKK 83 @j#3oא lא/א> KKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKK 84 @j#3oא lא/ KKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKK KKKKKKKKKKKKKKKKKKKKKKKKKKKKKKK 85 @j#3oא lא 3 KKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKK 0 86 א h#א9 א/*Q Kא h*9א 0#0 %א$ KKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKK 87 א 27א KKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKK KKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKK Pt 87 EaØ#א%א2#$Ğא& KKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKK 88 25א3G?$Ğא KKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKK KKKKKKKKKKKKKKKKKKKKKKKKKKKKK 27 89 אĞ$א א>#Oא KKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKK [3 90 אĞ$א א>2#א&: KKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKK D 91 >אĞ$ 4א אaqא :0א&KKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKK KKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKK ħ 92 >א8$Ğ@3א ,+KKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKK J 93 ±#8אE . ĩ*>?א 6QאKKKKKKKKKKKKKKKKKKKKKKK KKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKK \*Ġ 99 א 6Qא ,*;Y א #)P*,J0א c? Kא& >KKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKK l 107 Y*0(aא KKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKK KKK KKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKK ?c 109 א #)JאÒ_א/#: KKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKK 113 )J@א/#: KKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKK KKKKKKKKKKKKKKKKKK 113 א #)JאÒ_א KKKKKKKKKKKKKKKKKK KKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKK 9*h 114 )J@א KKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKK 9*h 114 *; א #)KKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKK KKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKK J 115 )Jא/@KKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKK 3 121 214 o א *>®א _ KKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKK 124 א #)Jא KKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKK KKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKK _:*0 124 א #)J0א 0Q KKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKK _ 125 ,*Pא #)Jא KKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKK KKKKKKKKKKK _,+7 125 א #)Jא @X+_אKKKKKKKKKKKKKKKKKKKKKKKK KKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKK _Ò 126 א #)Jא @_+X KKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKK @t 126 א #)Jא @X+_א #)Jא KKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKK KKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKK _,+7 129 Ħ0Eא #)Jא @KKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKK _+X 130 א/60א _ KKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKK KK 131 א O#3א ,+* KKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKK KKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKK \+7 131 60א KKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKK \+7 131 .ĩ*>?א 6Qא ,*;KKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKK KKKKKKKKKKKKKK Y 132 א 6Qא ,*8' 3E 0*- 4א/. א א #)N8J אE 215 :א/27א/KKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKK Pt 199 אH א 25Ħא 3G?\+7א KKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKK KKKKKKKKKKKKKKKKKKKKKKKKKKK 27 201 .ĩ*>?א 6Qא .*? KKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKK 203 א/א%'א KKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKK KKKK 0+ 210 216 Ahmad Mohammad AL-Ansari P.O. Box: 521 C/O: 83001 ,Khaitan Kuwait 217