Теория определения положения центра референц-єллипсоида по наблюдениям искусственных спутников земли

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  • TEOPH~ OHPE)~E. I IEHH.q HOfIO) I (EHHJ~ L[EHTPA PEq)EPEHI_ [ -3 .q f IH I ICOH~A HO HABJ I IO~EHH~IM

    HCKUCCTBEHHbIX CFIYTHI/ IKOB 3EM.rIH

    l Ioc~tmeHo BOCbMI4,/~eC~tTHIIflTH.IIeTRIO npoqb. )I-pa B. I L Ia J taMoaa

    MILAN BU R.~A

    Hcc.r uncmumym eeode~uu, FIpaea*)

    [-[yCTb B MOMeHT S FpRHrP-iCKOFO 3Be3~HOFO BpeMeHH H3BeCTHb[ B gaHHOM reo~e-

    3rtqeCKOM DyHKTe M 3eMHOfi 11OBepX.HOCT~t TO~IOt~eHTprtqeCKr[e 3~BaTOpHa3lbHble

    Koop~rtHaTbI ~', ~$' 14 Tor lo l leaTprtqecKoe paCCTO~[HHe A' oripe~ie.aeHHOrO HcKyccTBeH-

    Horo cnyTrmra 3eMaa Sp (HC3). Koop,~aHaTbt ~', 6' MOryT 6b~Tb no~yneHbt rib Ha6mo~eHrtfi Sp B M; paccToaHrte A' 6y, aeM npe,ano~araTb Bb~mcsteHm,~M no

    ~Z Z'

    / , i

    A......~ ~_~: - -~. " - .., 7"--~ : .-" .2,. /

    . . . . : : : , x / v a

    Pac. I.

    CrtrtxponnbIM aa6.am)~e- HHRM ~ t~' B /~1 14 B He-

    KOTOpOM 14HOM reo,~e3H-

    qeCKOM nyHgTe B TOil a~e

    peqbepeatbcr~cTeMe, ~O- CTaTO'mO y~laaeaHOM OT M. 1-lyerb ~aa TOrO a~e

    MOMeHTa S HBBeCTHb~ 3~eMeHTht s i oc~y3tH- pyrotttefi op6aTbt HC3,

    onpeae~amtuue noao- ~Ken~e rlocaegHe~ OTHO- CHTedIbHO reot~euTpuqec-

    ro ro arnaxopa. B nyu- KTe M 6y~eM Cqi~TaTb K3BeCTHblMI4 reo~c314qecKHe Koop~tHaTbt B, L, HOpMaJIbHylO Bb~COTy Hq rt BbICOTy KBa3areortaa ~ B CaCTeMe nprmaToro peqbepeHt~-3aarmco~a E, C FI3BeCTHbIMH napaMeTpaMH a, e 2. I.[eHTp O' 3TOFO 3~nl4nco~a B 06tt leM He

    COBna,~aeT c I~eHTpOM Macc 3eMnrt O (pac. 1). Ero noao~Kemte OTHOCFtTeabHO O

    onpe~ena~T npaMoyroabHbIe npocTpancTBeHnI, Ie ~oop~uaT~,~ AX o, A Yo, AZo B reo- qeHTprt'~ecro~ CaCTeMe X, Y, Z. OcI, Z 3aecb HanpaBaeI-ia no nonapHO~ OCa rmept~mt

    3eMmt nono:~rtTe~I, no x ceBepHoMy rtoat-ocy, X napanne~,HO naoc~oc'rrt rprmrtnCKO- ro acTporIoMrt~ecKoro MepagHaHa rt noaoa~rtTesn, Ho B CTOpOHy Fprtmtqa, Y nono- ~HTem, nO X BOCTOI~y. HanpaBnemte Ma~O~ OCrt Z ' 3a.rrrmco~a B O6ttleM He COBna-

    ,~aeT c HanpaB~eHrteM Z rt naOCI~OCT~, (X'Z') rtcxo~Horo reo,~e3a~ecKoro MepH~rtaua He napaaaeabna nnOCKOCTrt (XZ). HanpaBaeart~ oce~t X', Y', Z' reo~e3rt,~ecro~ peqbeperI~-CrtCTeMbt nycTb onpe~esra~OTC~t B CaCTeMe X, Y, Z TpeM~t yrnaMrt 9~.rtepa e, ~k, e9 [4].

    *) Agpec: Politick2~ch v~zfifi 12, Praha 1 - - Nov6 MEsto.

    Stadia geoph, at geod. 9 [1965] 225

  • M. Burga

    Ec.rlH B MOMeHT S 6hi.rill 6hi H3BeCTHbl KpoMe 3.rleMeHTOB Q, i Tax~ce apryMeHT

    nepnrez ~ ocKynHpymme~ op6rrrbi , 3naqeHrte aCTaHHOfi aHoMa~rt14 v rt reot~eaTpa-

    qecKoe paccToaHrm A ~:~ paccMaTpaBaeMoro nonoxeHng Sp, To Koop~rmaT~,i

    t~enTpa E, MOXHO 6~IaO 6~I BblqaCnHTb nO qbopM.

    AXo = A[cos u cos (s - - S) - - sin u sin (12 - - S) cos i] - - N ' cos B cosL - -

    -- A' cos 6' cos (~' - - S) - - coN' cos B sin L + $N sin B ,

    (1) AY o = A[cosus in ( f2 - - S) + s inucos(O- - S )cos i ] - -N 'cosBs inL - -

    - - A' cos 6' sin (a ' - - S) + a~N' cos B cos L - - aN sin B ,

    AZo = A sin ,t sin i - - N sin B - - A' sin Y -- N' cos B(~b cos L - - e sin L) ,

    rae N '=N+ Hq+ ~q, N= a(1 - -e - ' s in 2B) --~, N=N' - -Ne 2, u = ~ + v. Co-

    OTHOILIeHHH (1) He co~epxaT q.rleHbl r tops~Ka 692N ', t~2N ' 14T~I., H OHH HOJlyqeHbI 14CX0-

    .28 H3 H3BeCTHblX COOTHOIIIeHH~ He6ecHo~l MexaHHKH [1], TeopH~ napaJ i J taKca 62IH3-

    K14X rle6ecHbtX Te~l [2], 14 C yqeTOM 3aB14C~tMOCTe~I MCX~ly reojIe314qecro~ !4 reol~eHTp~-

    qeCKO~ CrtCTeMaMH [4].

    O~rlaK6, npHMeHeHHe (1) Ha npaKTaKe an~ t~e2te~ OCHOBHOI4 reo~le3vttt, Korea

    Tpe6yeTc~ cpaBHHTe,~bHo BbmoI

  • Teopu.g onpe3eaenua noaoy .cenua genmpa pe~epemt-gaauncouc)a . . .

    HOM KOJIriqeCTBe Ha6aro~IeHa~ l~e:Iecoo6paBHblX HC3 c ps~a Ha]Ie~Knblx reo~teBa-

    ~ecKmx CnyTHrU

  • M. Burga

    a l = Z;, sin Si - - Z ' is in Sk, a , = Z~cos S~ - - Z~eos Sk,

    a3 = X'i sin Si - - X;, sin S~ + u cos Si - - Y; cos Sk,

    b t = a 2 , b 2 = - -a~, b3 = X ;eosS~- -X 'kcosSk- Y/s inS~ + Yk'sin Sk ,

    ct = (X ; + X'k) sin (Sk -- S~) + (Y; - - Y[) cos (Sk - - S~),

    c2 = (Y[ + Y/,) sin (Sk - - S~) - - (X;, - - X'~) cos (Sk - - S~), c3 = 0 ,

    P4 = P2N sin B -- paN' cos B sin L , P5 = P3 N' cos B cos L - - p~,~ sin B , (6) P6= N 'cosB(p ls inL - -p2cosL) , p=a,b ,c .

    H3 (5), rge He yqTem,t Haeabl, co~epxatuHe AX2o, AXo A Yo, e AX o a-ca., rtMeeM

    tgf2 = AB -1 + d t AXo + dzAYo + d3AZo + d,e + ds$ + d609 , (7)

    tg i = DC-1 + et AX ~ + e2 A Yo + e3 AZo + e~e + es~k + e6a) ,

    d t = B-2(atB - - Abt ) = B-2( - - V'7 '2.i~k - - , kL , '2 ..{_ #) ,

    d 2 = B-2(a2 B - -Ab , ) = R-2[y '7 '2 , ,2 h) _ ~ I~ i~ k ~-XkZ i -~- ,

    d3 = B-2(a3B- -Ab3) = - -B -2C(Z~ - - Z ; ) , O = (A 2 + B2) * ,

    e~ = (CD) - ' (Aa I + Bbt) -- C -2Dc~ = (CD) -~ (X'iZ'k 2 + X'kZ'i 2 + h) - -

    - - C -2DCl ,

    e2 = (co) (Aa2 + 8b,) -- C-2Oc = (CO)-' (Y;Z'/ + r;Z 2 - - g ) - - - - C -2Dc2 ,

    e 3 = (CD) - ' (Aa3 + Bb3) = (CD) - '{Z ' i (X'k z + r~2) + Z,k(X;2 + y;2) +

    + (Z; + Z;,) [(X'iY;~ -- X'kY~) sin (Sk - - S~) - -

    - - (X;X'k + Y 'Y ; ) cos (Sk - - S , ) ]} ,

    g = Z;Z;,[-(X~, - - X;) sin (S~ - - S,) + (It/' + Y~) cos (Sk -- S i ) ] ,

    h = Z'iZ~C(Y ~ -- Y;) sin (Sk -- Si) - - (X; + X~) cos (Sk -- S i ) ] .

    Bupa~enr ia ~:Ia d4, ds, d6, e4., es, e6 no~tyHa~oTca no (6) nprt p = d, e.

    H3 COOTHOmeHH~ (7) aureKae'r , HTO 3~eMen'ru 12, i no~yqaroTca no 8a6.rl lo~enrlaM Ha OZrlOfi CTaH~I4R C o tur t6raMa, ne 3aBrtcau.~rtMrt o r OILII,{6OK CO6CTBeHrlO na6moze-

    Hrt~. 3Trt otur~6~rt cogepgaT rt neKoropyro qaCTb cr~ereMaTrwec~oro xapa~Tepa, r IpegcTaBaammylo co6ofi qbyart~am reogeam~ecKax KoopgaHaT ganao~[ CTaHI~I4H,

    3TIeMCHTOB op~eHT~[pOBK~[ gaaaoro peqbepeHLba~a~ncomxa ~ BpeMeHa aa6a Io~eaaf i . O~Haro, Tpe6yeMaa ZOttHOCTb O.rleMeHTOB f2, i BbIcoKa ~.rls Ke.rIefi npr tMeaerma (4 ) .

    )KestaTe~,rio 6hugo 6~,t rtMeTb 3Ta 3~eMeaTbt ga~e go ceryu~ ~yrr~, '~To6r~ no~y~rtTb

    (rio 60:tbtUOMy KOartnecT~y Ha6mozeHrt~ rt ypa~armamta) roopzrmaTbt AXo, A Yo, zlZ 0 c TOqHOCTblO ~eC~ITKOB M. qTO6b~ ~,136eraTb y~a3aHablX r io rpemnocTef i , KOTO-

    pbte MoryT COCTa~aSTb ~ecaTrn ceryH~ ~yrn , aa~xo COCTam~Tb cnet~aar~uym npo-

    rpaMMy Ha6:~m~emtfi ~ t~estax rto:~y,~eaHa 9:teMeeTo~ op6aT HC3. 3Ta ntporpaMMa

    928 Studia geoph, et geod. 9 [1965)

  • Teopua onpec)eaenu.,t noaoa~ceuua qeumpa pe~epeuq-gaauncouc)a...

    ~OStXHa 6blTb TaKOBa, qTO6bl CyMMapHoe B:BtaHrte He yqTeHabtx (He rt3BeCTHblX)

    3.rleMeHTOB opKeHTHpOBKrt nprtHaTOrO pedpepeHt~-a~armcortaa, npear Bcero Koop-

    gaHaT ero t teaTpa AX o, A Yo, AZo oxaocrtTem, HO t~ertTpa Macc 3eM:Ia, 6~,taO 6I, t

    npeHe6peraeMo MAYO. ~St~t 3TOI'O c~e~IyeT pacno~araTb CeTblO ~yH~aMeHTa.rlbHbiX

    reoge3rP~ecKr~X crtyTI~nKOBI, IX rIyHKTOB, t te : Iecoo6pa3no pacrlpe~eaeHn~,[x no (BCe~)

    3eMae. I"[OYIO~KeHH~ 3THX IIyHKTOB ~OJDKHb[ 6biTb H3BeCTHbI B e~artHO~ reo~e3r~qecKofi

    pedpepem~-crtcTeMe, OCHOBO~ rOTOpO~ cayxaT raK pa3 TOT peqbepentp3s~artr tco~,

    KoopgHHaTbI KeHTpa KOTOpOFO OTHOCHTe.IIbHO ~eHTpa Macc 3eM.qrt rto~.rlemaT

    oripe~e~eHa~O.

    HOcrynHao 3. 2. 1965 Pet~eu~emn: E. Buchar

    .,Tumepam ypa

    [1] M. ~. Cy66OTrta: Kypc rle6ecaofi MexaHrlKri, T. 1. FOC. H3.a. TeX.-Teop. mIT., M.-fl. 1941. [2] C. H. Bna~o: Kypc cdpepn,lecKo~ aCTpOHOMHrl. FOC. H3~. TeX.-Teop. nHT., M. 1954. [3] C. Popov ic i : Some Geodetic Uses of Non-Simultaneous Observations of Satellites. Studii

    s.i cercetgtri de astronomie, 9 (1964), 201. [4] M. Burga: K nonpocy onpe~eaeHaa aanpaa~eHnfi Ma.rlofl ocH pe~bepeau-am]nncoM~a a acxoJ1-

    Horo reo~ean~ect

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