ORITL TO GEOCENTRIC EQUTORIL COORDINTE SYSTEM TRNSFORMTION z i i i = (coωcoω in Ωcoiinω) (in Ωcoω + coωcoiinω) iniinω ( coωinω in Ωcoi coω) ( in Ωinω + coωcoicoω) in icoω in Ωini coωini coi z o o o GEOCENTRIC EQUTORIL TO ROTTING COORDINTE SYSTEM TRNSFORMTION Th quatoial plan coincid with th plan of th pap. Th ath otat anti-clockwi with angula vlocit Ω. and a a attachd to th ath and otat with it. z i and z a coincid. z i z Ω i i Satllit Obit (2) D. M. M. Dawoud
z = co( Ω T ) in( Ω ) T in( Ω co( Ω T T ) ) 1 z i i i ` T i th tim lapd inc th ai coincidd with th i ai. Th valu of Ω T at an tim t, pd in minut aft midnight UT i givn b: ΩT = α g, +. 2568447 t dg. Wh α g, i th ight acnion of th Gnwich midian at h UT at Julian da JD and i givn b: 2 α g, = 99.69983+ 36.7689T c +. 3878Tc dg wh Tc i th lapd tim in Julian cntui btwn h UT on Julian da JD and noon UT on Janua 1, 19. T c = ( JD 24152) / 36525 dd.5 to th JD valu ud in thi quation bfo ubtituting in th pviou quation ( inc it i calculatd at h UT). JULIN DYS ND JULIN DTES Standad tim i Unival tim UT (man ola tim at Gnwich obvato na London). tonom u Julian da and Julian dat. Julian da tat at noon. Julian dat tim fnc i 12 noon UT on Janua 1, 4713 C Satllit Obit (21) D. M. M. Dawoud
Eampl: Noon on Dcmb 31, 1899 wa th bginning of Julian da 2,415,2 Noon UT on Dcmb 31, 1984 wa th tat of Julian da 2,446,66 :: hou UT on Janua 1, 1985 wa Julian dat 2,446,66.5 JULIN DTES T THE EGINNING OF ECH YER FOR (1986-2) Ya Julian dat Ya Julian dat 24 + 1993 48 987.5 1986 46 43.5 1994 49 352.5 1987 46 795.5 1995 49 717.5 1988 47 16.5 1996 5 82.5 1989 47 526.5 1997 5 448.5 199 47 891.5 1998 5 813.5 1991 48 256.5 1999 51 178.5 1992 48 621.5 2 51 543.5 Dat DY NUMER FOR NOON ON THE LST DY OF ECH MONTH Da No. Lap a Dat Da No. Lap a Jan 31 31.5 31.5 Jul 31 212.5 213.5 Fb 28/29 59.5 6.5 ug 31 243.5 244.5 Mach 31 9.5 91.5 Spt 3 273.5 274.5 p 3 12.5 121.5 Oct 31 34.5 35.5 Ma 31 151.5 152.5 Nov 3 334.5 335.5 Jun 3 181.5 182.5 Dc 31 365.5 366.5 Satllit Obit (22) D. M. M. Dawoud
Eampl of Julian dat calculation: 1. Find th Julian dat JD coponding to 3 h UT on Oct 11,1986. Oct 11 i da numb 273.5 + 11 = 284.5 Stat of Oct 11 (h UT) i 284 t 3:: UT i (3/24) =.125 da Da and tim will b 284.125 dd thi to th Julian dat fo Jan 1, 1986 W gt: 2,4, + 46,43.5 + 284.125 = 2,446,714.625 2. Find th Julian dat JD coponding to 15:: h UT on Mach 1, 1999. Mach 1 i da numb 59.5 + 1 = 69.5 t 15:: UT i.125 da aft noon Da and tim will b 69.5 +.125 = 69.625 dd thi to th Julian dat fo Jan 1, 1999 W gt: 2,4, + 51,178.5 + 69.625 = 2,451,248.125 Satllit Obit (23) D. M. M. Dawoud
LOOK NGLE DETERMINTION Dfinition: Look angl a th coodinat to which an ath tation antnna mut b pointd to communicat with th atllit. Local vtical Noth El z Eat zimuth (z) Th angl maud atwad fom gogaphic noth to th pojction of th atllit path on a locall hoizontal plan at th ath tation. Elvation (El) Th angl maud upwad fom th hoizontal plan to th atllit path. Satllit Obit (24) D. M. M. Dawoud
Satllit Obit (25) D. M. M. Dawoud THE SUSTELLITE POINT Th point wh a lin dawn fom th cnt of th ath to th atllit pa though th ath ufac. L Th noth latitud of th ubatllit point. l Th wt longitud of th ubatllit point. ] [ co 9 2 2 2 1 z z L + + = + + = fouth quadant thid quadant ond quadant quadant fit l tan tan 9 c tan 18 ) ( tan 1 1 1 1 L l Subatllit point
ELEVTION EVLUTION Satllit Local hoizontal d El Subatllit point (L, l ) Eath tation (L, l ) Cnt of ath co( γ ) = co( L )co( L )co( l l ) + in( L )in( L ) d 2 = 1 + 2 co( γ ) Satllit Obit (26) D. M. M. Dawoud
El = ψ 9 Uing th law of in : d = in( ψ ) in( γ ) co( El ) = in( γ ) = d 1+ in( γ ) 2 2 co( γ ) Th quation pmit th valuation of th lvation angl fom a knowldg of th ubatllit point and ath tation coodinat. ZIMUTH CLCULTION Th atllit, ub-atllit point and th ath tation li on th am vtical plan. Thfo th azimuth angl can b maud fom th noth diction going atwad towad th ub-atllit point. Th gomt ud fo th calculation dpnd on whth th ub-atllit point i at o wt of th ath tation and which hmiph contain th ub-atllit point and th ath tation. Thi calculation i implifid fo th idal gotationa obit. Satllit Obit (27) D. M. M. Dawoud
Pol C Y Pol C Y X X Nothn hmoph, wt of Nothn hmoph, wt of X C Y Pol Y C Pol X Southn hmoph, wt of Southn hmoph, wt of Eith point o point can b th ath tation; th oth mut b th ub-atllit point. i clo to th pol that i na to both point. Point,, and th pol fom a phical tiangl with pola angl C and angl X and Y at th vtic and. Satllit Obit (28) D. M. M. Dawoud
C = l l o C = 36 l l Whichv mak C 18 dg Ca 1: t lat on point in th nothn hmiph. L >L i chon to b clo to th noth pol. Th baing X and Y ma b found fom: tan[.5( Y cot(.5c)in[.5( L X )] = co[.5( L + L L )] )] tan[.5( Y + cot(.5c)co[.5( L X )] = in[.5( L + L )] L )] X =.5( Y + X ) +.5( Y X ) Y =.5( Y + X ).5( Y X ) Th lationhip btwn X, Y, and th azimuth z dpnd on th idntit of point and and on Satllit Obit (29) D. M. M. Dawoud
thi gogaphical lationhip. Th a givn in th following tabl. Fomula fo calculating th azimuth. t lat on point in th nothn hmiph Sub-atllit point Eath Station Rlation zimuth wt of 36 - Y wt of X wt of Y wt of 36 - X oth point in th outhn hmiph Sub-atllit point Eath Station Rlation zimuth wt of 18 + Y wt of 18 - X wt of 18 - Y wt of 18 + X Satllit Obit (3) D. M. M. Dawoud
CLCULTION OF LOOK NGLES FOR GEO-STTIONRY STELLITES Sub-atllit point i at th quato. thfo L =. Th go-nchonou adiu = 42242 Km Th ath' adiu = 637 Km Th cntal angl γ i givn b: co( γ ) = co( L )co( l l ) Th ditanc d fom th ath tation to th atllit i givn b: d = 42242[1.2274.31596 co( γ )] 1/ 2 Km Th lvation angl i thn givn b: in( γ ) co( El ) = [1.2274.31596 co( γ )] 1/ 2 Satllit Obit (31) D. M. M. Dawoud
zimuth calculation i impl than th gnal ca, bcau th ub-atllit point li on th quato. W f to th following figu fo thi calculation. χ α E a = l l c c = L L S a G Coniding th half pimt of th tiangl = =.5( a + c + γ ) Th angl a at th vt ma b obtaind fom: in( )in( ) tan 2 α γ c ( ) = 2 in( )in( a) and α = 2 tan 1 in( γ )in( L in( )in( l l Satllit Obit (32) D. M. M. Dawoud
γ α E E α γ c c S a G G a S SSP outh-wt of ES SSP outh-at of ES S a γ G c α E G c α E a γ GS SSP noth-wt of ES SSP noth-at of ES Equation fo calculating azimuth fom phical tiangl angl α SSP Sub-atllit point ES Eath Station Situation Equation 1. SSP South-wt of ES z = 18 o + α 2. SSP South-at of ES z = 18 o - α 3. SSP Noth-wt of ES z = 36 o - α 4. SSP Noth-at of ES z = α Satllit Obit (33) D. M. M. Dawoud