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0!.H!.x!6!6!4"4P"""""0#08# h#  # # # "#"# $$$($ P$X$  `$p$$ $$$ $$$ $$ $%@%P%p%%%% d%4(& `&p&&B&&& .&'0'8'P'X'$`' '' $'''( (@(P( dX(4( ())B )h)p) .))))))$)  * "(* 0* $8* `* h*p*x* * ,*(*(*(+0+ H+`+ x+ + + ++ +R+((,(P,(x,(,,,,R, <H- <- <- <. H.X. `.p.... .. 3sqZPxME "@ 14@$L@&L@(L@*L@,L`.`0`2`4`6`8`:`<`>`@`B`D`F`H`J`L`N`P`R`T`V`X`Z`\`^```b`d`f`h`j`l@n @p @r  @$LSl@&L O3b@(L!El@*LA to@,L!El`.A to`0Az`2to G`4Az`6to O`8'El`:A to`<`>e GN`@)`Bh an`DC (d`F%Az`Hto O`J@`Lde`N Lon`PGE`R`Tv`Vemen`Xlev@n emen@p lev@r onen XB`. GEO`0x `tor`onen`H` O3b`` P0 @$L@&L@(L@*L@,L`.`0```````` 0  `  h `````````````` ` XY"   0 <8 <x j Z(  2 (  > X p.** 0&@&hFF, ,P00..6@6x44 @`00((((P(x((88(`hp ""$$ 6(  ` p        R H ` p  / / 0/ H/`/ h/$x/$/$/$/0 0(000 480"p0 x0.0*0*0 1 81@1H1P1X1`1h1p1x1111111111111112222 2 (2 @2 "P2"x2"2$2 62 (383P3 X3h33 R333 24d@4 >4 445 556H6X6`66 6 66666 7"7$87>`7 777 7 7788L8$`8p808p(909p908:ph:0:;$; @;P;X;p;x;L;$;p;0h<p<0=p8=0=p=0H>x>$> >>>>>  ?>?(P?x? >?(?? ?&@ 0@@@ X@(h@(@@(@(@ A6(A6`AXAXAHBPB`B pB B B,BNB(C,0CN`CC C DC(D8DD@D(DD D8D E*E HE(XE(EE(E(EF6F PF P`FF ZFG6 G XG PhGG ZG H(H0H@H PH `HhHH H H Az_Elev_SR_Calculation5d=sqrt [h^2 + 2*Re*(h + Re)*(1-cosA*cosB)] in km6Azi=Asin(-sin(B)/(SQRT[1-cos^2(A)*cos^2(B)]) in degdEle=Acos((Re+h)/d * SQRT[1-cos^2(A)*cos^2(B)]) in deg (this equation's result is always positive!)SEle=Atan((1/tan(Beta))-(Re/(((Re+h)*sin(Beta))))) where Beta = acos(cos(a)*cos(B))where:,h=SC height above earth's surface = 35796 km"Re=earth equatorial radius=6380 kmA=ground station latitude7B=difference in longitude between ground station and SC d=slant range]F,DT! @H]`Earth equatorial radius (km)]z@xGEO SC height(km)]@O3b SC height(km)] $]]GND STA latitude (DegN)]GND STA longitude (DegE)] 8Difference in longitude between GND STA and GEO SC (Deg)]88Difference in longitude between GND STA and O3b SC (Deg)]PSlant range GND STA to GEO SC]hSlant range GND STA to O3b SC]!Elevation angle GND STA to GEO SC]!Elevation angle GND STA to O3b SC]Azimuth angle GND STA to GEO SC]Azimuth angle GND STA to O3b SC]'Elevation angle GND STA to GEO SC (deg)]'Elevation angle GND STA to O3b SC (deg)]%Azimuth angle GND STA to GEO SC (deg)](%Azimuth angle GND STA to O3b SC (deg)]@GEO SC Longitude]XO3b SC Longitude]pGEO SC min elev]O3b SC min elev]!One element to calculate GEO elev]!One element to calculate O3b elev]x component of GEO vector]y component of GEO vector]z component of GEO vector]x component of O3b vector]0y component of O3b vector]Hz component of O3b vector]`"*Offangle between O3b vector and GEO vector]x&*Offangle between O3b vector and GEO vector]]]B8O3b_GSO$t%v'2B9O3b_GSO$t%v'4B10O3b_GSO$t%v'NB11O3b_GSO$t%v'P0Convert longitude to between 0 to +/-180 degrees 4 h 4 '4kp N h N 'Nk@ P h P 'PkLLoop to calculate Slant Range, Elevation angle, azimuth angle, and off angle 0 4 N '6 4 P '8+Calculate SR between GND station and GEO SC ( & ( &  , 2$x , 6$x  ': : 0A1 SR_Ele_Az$t%v,z+Calculate SR between GND station and O3b SC * & * &  , 2$x , 8$x  '< < 0A1 SR_Ele_Az$t%v,z8Calculate elevation angle between GND station and GEO SCele_GEO = Application.WorksheetFunction.Acos(((Re + h_GEO) / d_GEO) * ((1 - Cos(deg2rad * A) ^ 2 * Cos(deg2rad * B_GEO) ^ 2) ^ (1 / 2))) This equation calculates positive values only , 2$x , 6$x |!~%'V V $'>dp V$ & & (  V$ $'>k  > ,'F F 0A1 SR_Ele_Az$t%v,z8Calculate elevation angle between GND station and O3b SCele_O3b = Application.WorksheetFunction.Acos(((Re + h_O3b) / d_O3b) * ((1 - Cos(deg2rad * A) ^ 2 * Cos(deg2rad * B_O3b) ^ 2) ^ (1 / 2))) , 2$x , 8$x |!~%'X X $'@d X$ & & *  X$ $'@kX @ ,'H H 0A1 SR_Ele_Az$t%v,zCalculate azimuth angle between GND station and GEO SC, needed to adjust the result from the Az equation based on four different scenarios FZ MbP?  , 2$x , 6$x N/A 0A1 SR_Ele_Az$t%v,zd , 6$ , 2$x , 6$x 'jr2check to make sure az term did not exceed -1 and 1 j j 'jd'jk k $ j |!~% 'B 2 4 N B ,'J 2 4 N eh B , 'J 2 4 Ne B , 'J 2 4 N e B , 'Jk J 0A1 SR_Ele_Az$t%v,zk jNote: The above AZ calculaton is tested with the results of http://www.satcom.co.uk/article.asp?article=1Calculate azimuth angle between GND station and O3b SC, needed to adjust the result from the Az equation based on four different scenarios HZ MbP?  , 2$x , 8$x N/A 0A1 SR_Ele_Az$t%v,zd , 8$ , 2$x , 8$x 'lr2check to make sure az term did not exceed -1 and 1 l l 'ld0 'lk k $ l |!~% 'D 2 4 P D ,'L 2 4 P eh D , 'L 2 4 P e D , 'L 2 4 P e D , 'Lk L 0A1 SR_Ele_Az$t%v,zkrCalculate the off angle between O3b and GEO using dot product cos(o3b_GEO_offangle) = (vectorA dot vectorB)/|A||B|FEach of the O3b and GEO vectors to GND station should have 3 componetspComponents x and y are derived from SR, azimuth angle and elevation angle x=SR*cos(Ele)*sin(az), y = SR*sin(Ele)OComponent z is derived using az, x and law of sines z= (x*(sin(90-Az)))/sin(Az) 0A1 SR_Ele_Az$t%v%zN/A 0A1 SR_Ele_Az$t%v%zN/AN/A 0A1 SR_Ele_Az$t%v,zd : , F$x , J$'Z : , F$'\ J & 2$'^d Z ,Z J $ , J$'^k < , H$x , L$'` < , H$'b L & 2$'ddP ` ,Z L $ , L$'dk Z ` \ b ^ d  Z \ ^  ` b d  |!~%'f f ,'h h 0A1 SR_Ele_Az$t%v,zk P 0A1 SR_Ele_Az$t%v,zL_GEO = L_GEO - 1 P 'P 0o Long_offset_Calculation Macro5d=sqrt [h^2 + 2*Re*(h + Re)*(1-cosA*cosB)] in km6Azi=Asin(-sin(B)/(SQRT[1-cos^2(A)*cos^2(B)]) in degdEle=Acos((Re+h)/d * SQRT[1-cos^2(A)*cos^2(B)]) in deg (this equation's result is always positive!)SEle=Atan((1/tan(Beta))-(Re/(((Re+h)*sin(Beta))))) where Beta = acos(cos(a)*cos(B))where:,h=SC height above earth's surface = 35790 km"Re=earth equatorial radius=6380 kmA=ground station latitude7B=difference in longitude between ground station and SC d=slant range]F,DT! @H]`Earth equatorial radius (km)]z@xGEO SC height(km)]@O3b SC height(km)] $]]GND STA latitude (DegN)]GND STA longitude (DegE)] 8Difference in longitude between GND STA and GEO SC (Deg)]88Difference in longitude between GND STA and O3b SC (Deg)]PSlant range GND STA to GEO SC]hSlant range GND STA to O3b SC]!Elevation angle GND STA to GEO SC]!Elevation angle GND STA to O3b SC]Azimuth angle GND STA to GEO SC]Azimuth angle GND STA to O3b SC]'Elevation angle GND STA to GEO SC (deg)]'Elevation angle GND STA to O3b SC (deg)]%Azimuth angle GND STA to GEO SC (deg)](%Azimuth angle GND STA to O3b SC (deg)]@GEO SC Longitude]XO3b SC Longitude]pGEO SC min elev]O3b SC min elev]!One element to calculate GEO elev]!One element to calculate O3b elev] 4'n N'p P'rB8O3b_GSO$t%v'2B9O3b_GSO$t%v'4B17O3b_GSO$t%v'RB18O3b_GSO$t%v'T 4'N 4'P 4 h 4 '4kp N h N 'Nk@ P h P 'PkZ'F F R?  n p n p 4 N '6 n pe 4 N '6 n pe 4 N '6k@ ( & ( &  , 2$x , 6$x  ': , 2$x , 6$x |!~%'V V $'>dx V$ & & (  V$ $'>k( > ,'FC17O3b_GSO$t%v1st Az N? 'Nd N? 'Nk NB10O3b_GSO$t,vZ'H H T?  n r n r 4 P '8 n re 4 P '8 n re 4 P '8k * & * &  , 2$x , 8$x  '< , 2$x , 8$x |!~%'X X $'@d X$ & & *  X$ $'@k @ ,'HC18O3b_GSO$t%v1st Az P? 'Pd0 P? 'Pk PB11O3b_GSO$t,vo Separation_Angle_Calculation]X]p]]]%Minimum Separation Angle (deg)]%GEO elevation angle (deg)]%O3b elevation angle (deg)]$O3b elevation angle (deg)] . 0 . 0+ 0 .'.' A1 SR_Ele_Az$t%v%zB17O3b_GSO$t%v N/AB34O3b_GSO$t,vN/AB35O3b_GSO$t,vN/AB36O3b_GSO$t,vN/AB37O3b_GSO$t,v'd( 0 0A1 SR_Ele_Az$t%v%zB18O3b_GSO$t%v 0A1 SR_Ele_Az$t%v%z .+ 0A1 SR_Ele_Az$t%v%z .+ 0A1 SR_Ele_Az$t%v%z .+ 0A1 SR_Ele_Az$t%v%z .+ . '.k 0$'$'$'$'  . $  $' $' $' $'k  B34O3b_GSO$t,v B35O3b_GSO$t,v B36O3b_GSO$t,v B37O3b_GSO$t,v'ko-Calculate min separation angle across GEO arcX]F,DT! @]Earth equatorial radius (km)]z@GEO SC height(km)]@O3b SC height(km)] $] ]( ]@ ]X ]p ] ] ] ] ] ] ]8 ]P ] ] ] ] ] ] ] ]0 ]H ]` ]x ] ] ] ] A2:E201$vB@H B@G2Summary$t%v' B8O3b_GSO$t,vB9O3b_GSO$t%v'B10O3b_GSO$t%v'0Convert longitude to between 0 to +/-180 degrees  h  'k  h  'kx LLoop to calculate Slant Range, Elevation angle, azimuth angle, and off angle 0   '+Calculate SR between GND station and GEO SC ( & ( &  , $x , $x  '8Calculate elevation angle between GND station and GEO SCele_GEO = Application.WorksheetFunction.Acos(((Re + h_GEO) / d_GEO) * ((1 - Cos(deg2rad * A) ^ 2 * Cos(deg2rad * B_GEO) ^ 2) ^ (1 / 2))) This equation calculates positive values only , $x , $x |!~%'  $ 0+d  $ & & (  $ $ 0+k 0$ , 0+  ' 0$' . . $  . $'k .G3Summary$t%v' B17O3b_GSO$t,vG4Summary$t%vB18O3b_GSO$t,v 'd'     ' '    AA"B20O3b_GSO$t%v A1Summary$t%v,zB20O3b_GSO$t%v'A2:A201 SR_Ele_Az$t%v G2:G201 SR_Ele_Az$t%v ~% ~%'  A1Summary$t%v,zB2:B201 SR_Ele_Az$t%v G2:G201 SR_Ele_Az$t%v ~% ~%'  A1Summary$t%v,zD2:D201 SR_Ele_Az$t%v G2:G201 SR_Ele_Az$t%v ~% ~%'  A1Summary$t%v,zE2:E201 SR_Ele_Az$t%v G2:G201 SR_Ele_Az$t%v ~% ~%'  A1Summary$t%v,z   ' B17O3b_GSO$t,v d  AA"B20O3b_GSO$t%v A1Summary$t%v,zB20O3b_GSO$t%v'A2:A201 SR_Ele_Az$t%v G2:G201 SR_Ele_Az$t%v ~% ~%'  A1Summary$t%v,zB2:B201 SR_Ele_Az$t%v G2:G201 SR_Ele_Az$t%v ~% ~%'  A1Summary$t%v,zD2:D201 SR_Ele_Az$t%v G2:G201 SR_Ele_Az$t%v ~% ~%'  A1Summary$t%v,zE2:E201 SR_Ele_Az$t%v G2:G201 SR_Ele_Az$t%v ~% ~%'  A1Summary$t%v,z   ' B17O3b_GSO$t,v k8Summary$tB@  '  '  A Summary$t%v? $A Summary$t,vkC Summary$t%v? $C Summary$t,vk  ?A :E $vB@H B@A $vB@H B@A Summary$t%v'C Summary$t%v'    A Summary$t,v C Summary$t,vd>A  Summary$t%v  'C  Summary$t%v  'A  Summary$t%v  A Summary$t,vC  Summary$t%v  C Summary$t,vk=  '  '   e   A Summary$t%vA Summary$t%vh A Summary$t,vk<C Summary$t%vC Summary$t%vh C Summary$t,vkH< A Summary$t%v? $ A Summary$t,vk;C Summary$t%v? $ C Summary$t,vkH;  A :E Summary$t%vB@H B@A Summary$t%vB@H B@A Summary$t%v'C Summary$t%v'    A Summary$t,v C Summary$t,vd9A  Summary$t%v  ' A  Summary$t%vA Summary$t,vdH9A  Summary$t%v  A Summary$t,vk8C  Summary$t%v  ' C  Summary$t%vC Summary$t,vd@8C  Summary$t%v  C Summary$t,vk7k7  '  ' k7{ESC} |B@A1$vB@Ho`7X7Attribute VB_Name = "Module1" Sub Az_Elev_SR_Calculatio`n() F.ProcDataInvoke _Func \n14d' 'ed=sqrt [h^2 + 2*Re*(h Re)*(1- cosA*B)] in km7Azi=Asin(-B)/( SQRT[1^2(A)5)1degw=A(((Re+h)`/d *  (this equ's result always positive!'3tan((1/Beta))-:4/(=*\ ))Rwhere -aQad(B)*:bh=SC height above earthKsurfac3579b6CKRe=/orial radius=6380T=ground( st8 AtudeB=diff'n@Dlongi betwPeen aSC@xlantng@ Const pi93.1415926535897R/B&}'E7/0 (kmEh_GEO=# 'GAI O3b 8063# 'A; 2@I */ 180A/ Dim I As Integer, JHAADouble0'GN D STAW (DegN@1AL^ ] E B>$ 'D65% A# nA + dSE Eto y*d_Ttce,le2auv#^an~g5ta z'`muth  id_@ZJL (`B$ (( 8ES'!mHL1&LZGLUO$ `%M m`vfSM ar Onleme`ca3}e24a ='2e  xM'x c omponofRvectorSysyy3b 'zyx/| yys| }~zs| }_Off3@z'fv0Cdno2// 8_07ter>mCCBrL_sign, L/tAuWorksheets("GSO").Re("B8"GLo_k9b%= 10ol11`0Q Then = -(360 - L` E@If  J8A}a ~ q)x LoopQ 'Btb, )q, azi7j off#k For0= 1 To8 20r/s= Abs(L1 ?#  VKSROeu׊ Ä= (^ b0 2*U+ 0(11@Cos!m* Eu+Ԁ#= `"N/A"@E_az_term(-uG?^| C) 'check/make sure az did n@ot exc@4 -1:d 1T@[,) > 1G\\` =$ Ea`@-K'`'@k+}]s `v (A >= 0 A@L <= L?&x Dj/ &j  j >C %* 360@| XL 18  ) +D!"I%!`|).`g a'@Note: A above AZL c$isUs2twis of http://www.satcom.co.uk/article.asp?dn=`J?a`aSC??:BL@O@LQqoo2L// 3q`L LaXL{q\ / {LLL1x9 b L0 LьZILI=T"T2Lnϑ.ALLp*L`n= KTLPB` BLQLQU ULQL3bL%eL_b0!L|Joff|QDQkug dot product o QjQ7(vectorAB)/|A||B|LEach_AP! pSoshould ha0V30mpon0@1Qonts xy a0derivWSR,`79 vB x0=SR* p)*q+az), y') z ^#az,lawes z= (x*(Q90-AzЯ/A@"//'E (k6m-ch$Y6# ' $ t`8063# '?Fv@`/ 180 Dim I As Integer, JA!Doub`b'GND STA+ (DegN L.uEBB 'D65% A#_ nA + dSE Eto *vd$'tce`a '`uv#^ct D<`a# '`muth id  (`B$ ((YsN 2 <?69#oCm2N#pwCM.F, mPT0v)M-I/1bn`leLmeW0ca3ye24 'O91}e sign, L _70CRLSSgn(L$5 quvp A#ɍGSOגB8V"o_k9a f #= oi1701b8If L >c Then = -(360 - 8z ~ A&0uB#4= 9 nWhi@kv>= ( + 0.1 < Ors T0 P 0  Ckbs(LGa lse-X1 A#1_AP-o_+`@ Sks2* (9S+ p0`- C%* A1+v =я(/\$ht B2 1* AtTu0- `"PRSw0áT'5( ::C: "1p 3]̡*05 -,D8Wen3>0"!= Q 3u3@3 B33= 3p /s/3 3E83pT3o 3U33QA d_O3@b = (h^ 2 +* Re *T+4)81 - Cos(deg2rad$A. $B))) ^ (1 / 2) Beta= Application.WorksheetFuncAc^A%b If Z0 Then eleopi Else Atn(QTanF(#\- (/ ((+ tSiq+nd If 8_y?/ Vxs("_GSO").Range(@"C18")"1st Az"fLe+ 0.065h -LWend CAt@SR 0good0To 200, 1 C)GAb Fo*r`1=4"c }J@Pf I(, JT0Ne@xt J I% I! 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