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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/0ęú3GF#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<V *אĞ$א ,+* Altitude E<Vú *אĞ$א ,+* O#kDG4 א #Yא/*Y 4א אaqא :0א/*>Ğ*8a$ א ,+* 8Vא( ?;אaqא#4N)'אĞ $ hc *8* E< c 90˚- 0˚?Y* ، @hğ>אĞ$א ,+* 4;אaq ^אOא א!DGbE<V* * D,04+@ אE<H *א cא _c *8D o` HcאM*ěH א *+7 N_ אę S_8#@Ğ,]אSĞאP(N KD א א ,+L X$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$א ,+* 4;אaq ^אOא א!Fbא א ,+0L@ ,4+א א ,+Lא cא _c *8D Kmer.ZD c א E<VĦ8(T *אĞ$א ,+*M8א ,+L ZD = 90˚ ± h H אĞ$א ,+*: 6א& J אĞ$א ,+*2#א& 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 3KK' ?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 3KK'?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#3K; #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<H h h * א @h*$א& _ ;אaqאN، א אaqא :0א 0,0q א cאא ,Az 0+ ;אaqאH:#א(א ,+*، ;אaq^אO א/Dec 60 א @h*$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 ,+* )3S0* א/*>8a@3אH אOא 08_ א lא ,+* β 21 אHא0Z *-א& 0 Horizon System אHא0Z *-א& 0 X$א ,+*#81#E Xא:3 @*!א WY*0 • אE<H h* • א cא א ,AZ 0+ אHא0Z*-אH:#א0q Equinoctial System אHא0Z*-אH:#א0q X$א ,+*#81#E Xא:3 @*!א WY*0 • א cאא ,* 0אLHA 0Ò ، א/3'א/,RA 0 • א/Dec 60 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_ $*hG?6#:#אq_ Sin (Dec ) = Sin (h)Sin (Lat ) + Cos (h)Cos (Lat )Cos (Az ) Sin (h) − Sin (Lat )Sin (Dec ) Cos (LHA ) = Cos (Lat )Cos (Dec ) i*0G*Z א WV$*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*.