/* * Unit SGP4SDP4 * Author: Dr TS Kelso * Original Version: 1991 Oct 30 * Current Revision: 1992 Sep 03 * Version: 1.50 * Copyright: 1991-1992, All Rights Reserved * * Ported to C by: Neoklis Kyriazis April 10 2001 */ #include "sgp4sdp4.h" /* SGP4 */ /* This function is used to calculate the position and velocity */ /* of near-earth (period < 225 minutes) satellites. tsince is */ /* time since epoch in minutes, tle is a pointer to a tle_t */ /* structure with Keplerian orbital elements and pos and vel */ /* are vector_t structures returning ECI satellite position and */ /* velocity. Use Convert_Sat_State() to convert to km and km/s.*/ void SGP4(double tsince, tle_t *tle, vector_t *pos, vector_t *vel, double* phase) { static double aodp,aycof,c1,c4,c5,cosio,d2,d3,d4,delmo,omgcof, eta,omgdot,sinio,xnodp,sinmo,t2cof,t3cof,t4cof,t5cof, x1mth2,x3thm1,x7thm1,xmcof,xmdot,xnodcf,xnodot,xlcof; double cosuk,sinuk,rfdotk,vx,vy,vz,ux,uy,uz,xmy,xmx, cosnok,sinnok,cosik,sinik,rdotk,xinck,xnodek,uk, rk,cos2u,sin2u,u,sinu,cosu,betal,rfdot,rdot,r,pl, elsq,esine,ecose,epw,cosepw,x1m5th,xhdot1,tfour, sinepw,capu,ayn,xlt,aynl,xll,axn,xn,beta,xl,e,a, tcube,delm,delomg,templ,tempe,tempa,xnode,tsq,xmp, omega,xnoddf,omgadf,xmdf,a1,a3ovk2,ao,betao,betao2, c1sq,c2,c3,coef,coef1,del1,delo,eeta,eosq,etasq, perige,pinvsq,psisq,qoms24,s4,temp,temp1,temp2, temp3,temp4,temp5,temp6,theta2,theta4,tsi; int i; /* Initialization */ if (isFlagClear(SGP4_INITIALIZED_FLAG)) { SetFlag(SGP4_INITIALIZED_FLAG); /* Recover original mean motion (xnodp) and */ /* semimajor axis (aodp) from input elements. */ a1 = pow(xke/tle->xno,tothrd); cosio = cos(tle->xincl); theta2 = cosio*cosio; x3thm1 = 3*theta2-1.0; eosq = tle->eo*tle->eo; betao2 = 1-eosq; betao = sqrt(betao2); del1 = 1.5*ck2*x3thm1/(a1*a1*betao*betao2); ao = a1*(1-del1*(0.5*tothrd+del1*(1+134/81*del1))); delo = 1.5*ck2*x3thm1/(ao*ao*betao*betao2); xnodp = tle->xno/(1+delo); aodp = ao/(1-delo); /* For perigee less than 220 kilometers, the "simple" flag is set */ /* and the equations are truncated to linear variation in sqrt a */ /* and quadratic variation in mean anomaly. Also, the c3 term, */ /* the delta omega term, and the delta m term are dropped. */ if((aodp*(1-tle->eo)/ae) < (220/xkmper+ae)) SetFlag(SIMPLE_FLAG); else ClearFlag(SIMPLE_FLAG); /* For perigee below 156 km, the */ /* values of s and qoms2t are altered. */ s4 = __s__; qoms24 = qoms2t; perige = (aodp*(1-tle->eo)-ae)*xkmper; if(perige < 156) { if(perige <= 98) s4 = 20; else s4 = perige-78; qoms24 = pow((120-s4)*ae/xkmper,4); s4 = s4/xkmper+ae; }; /* End of if(perige <= 98) */ pinvsq = 1/(aodp*aodp*betao2*betao2); tsi = 1/(aodp-s4); eta = aodp*tle->eo*tsi; etasq = eta*eta; eeta = tle->eo*eta; psisq = fabs(1-etasq); coef = qoms24*pow(tsi,4); coef1 = coef/pow(psisq,3.5); c2 = coef1*xnodp*(aodp*(1+1.5*etasq+eeta*(4+etasq))+ 0.75*ck2*tsi/psisq*x3thm1*(8+3*etasq*(8+etasq))); c1 = tle->bstar*c2; sinio = sin(tle->xincl); a3ovk2 = -xj3/ck2*pow(ae,3); c3 = coef*tsi*a3ovk2*xnodp*ae*sinio/tle->eo; x1mth2 = 1-theta2; c4 = 2*xnodp*coef1*aodp*betao2*(eta*(2+0.5*etasq)+ tle->eo*(0.5+2*etasq)-2*ck2*tsi/(aodp*psisq)* (-3*x3thm1*(1-2*eeta+etasq*(1.5-0.5*eeta))+0.75* x1mth2*(2*etasq-eeta*(1+etasq))*cos(2*tle->omegao))); c5 = 2*coef1*aodp*betao2*(1+2.75*(etasq+eeta)+eeta*etasq); theta4 = theta2*theta2; temp1 = 3*ck2*pinvsq*xnodp; temp2 = temp1*ck2*pinvsq; temp3 = 1.25*ck4*pinvsq*pinvsq*xnodp; xmdot = xnodp+0.5*temp1*betao*x3thm1+ 0.0625*temp2*betao*(13-78*theta2+137*theta4); x1m5th = 1-5*theta2; omgdot = -0.5*temp1*x1m5th+0.0625*temp2*(7-114*theta2+ 395*theta4)+temp3*(3-36*theta2+49*theta4); xhdot1 = -temp1*cosio; xnodot = xhdot1+(0.5*temp2*(4-19*theta2)+ 2*temp3*(3-7*theta2))*cosio; omgcof = tle->bstar*c3*cos(tle->omegao); xmcof = -tothrd*coef*tle->bstar*ae/eeta; xnodcf = 3.5*betao2*xhdot1*c1; t2cof = 1.5*c1; xlcof = 0.125*a3ovk2*sinio*(3+5*cosio)/(1+cosio); aycof = 0.25*a3ovk2*sinio; delmo = pow(1+eta*cos(tle->xmo),3); sinmo = sin(tle->xmo); x7thm1 = 7*theta2-1; if (isFlagClear(SIMPLE_FLAG)) { c1sq = c1*c1; d2 = 4*aodp*tsi*c1sq; temp = d2*tsi*c1/3; d3 = (17*aodp+s4)*temp; d4 = 0.5*temp*aodp*tsi*(221*aodp+31*s4)*c1; t3cof = d2+2*c1sq; t4cof = 0.25*(3*d3+c1*(12*d2+10*c1sq)); t5cof = 0.2*(3*d4+12*c1*d3+6*d2*d2+15*c1sq*(2*d2+c1sq)); }; /* End of if (isFlagClear(SIMPLE_FLAG)) */ }; /* End of SGP4() initialization */ /* Update for secular gravity and atmospheric drag. */ xmdf = tle->xmo+xmdot*tsince; omgadf = tle->omegao+omgdot*tsince; xnoddf = tle->xnodeo+xnodot*tsince; omega = omgadf; xmp = xmdf; tsq = tsince*tsince; xnode = xnoddf+xnodcf*tsq; tempa = 1-c1*tsince; tempe = tle->bstar*c4*tsince; templ = t2cof*tsq; if (isFlagClear(SIMPLE_FLAG)) { delomg = omgcof*tsince; delm = xmcof*(pow(1+eta*cos(xmdf),3)-delmo); temp = delomg+delm; xmp = xmdf+temp; omega = omgadf-temp; tcube = tsq*tsince; tfour = tsince*tcube; tempa = tempa-d2*tsq-d3*tcube-d4*tfour; tempe = tempe+tle->bstar*c5*(sin(xmp)-sinmo); templ = templ+t3cof*tcube+tfour*(t4cof+tsince*t5cof); }; /* End of if (isFlagClear(SIMPLE_FLAG)) */ a = aodp*pow(tempa,2); e = tle->eo-tempe; xl = xmp+omega+xnode+xnodp*templ; beta = sqrt(1-e*e); xn = xke/pow(a,1.5); /* Long period periodics */ axn = e*cos(omega); temp = 1/(a*beta*beta); xll = temp*xlcof*axn; aynl = temp*aycof; xlt = xl+xll; ayn = e*sin(omega)+aynl; /* Solve Kepler's' Equation */ capu = FMod2p(xlt-xnode); temp2 = capu; i = 0; do { sinepw = sin(temp2); cosepw = cos(temp2); temp3 = axn*sinepw; temp4 = ayn*cosepw; temp5 = axn*cosepw; temp6 = ayn*sinepw; epw = (capu-temp4+temp3-temp2)/(1-temp5-temp6)+temp2; if(fabs(epw-temp2) <= e6a) break; temp2 = epw; } while( i++ < 10 ); /* Short period preliminary quantities */ ecose = temp5+temp6; esine = temp3-temp4; elsq = axn*axn+ayn*ayn; temp = 1-elsq; pl = a*temp; r = a*(1-ecose); temp1 = 1/r; rdot = xke*sqrt(a)*esine*temp1; rfdot = xke*sqrt(pl)*temp1; temp2 = a*temp1; betal = sqrt(temp); temp3 = 1/(1+betal); cosu = temp2*(cosepw-axn+ayn*esine*temp3); sinu = temp2*(sinepw-ayn-axn*esine*temp3); u = AcTan(sinu, cosu); sin2u = 2*sinu*cosu; cos2u = 2*cosu*cosu-1; temp = 1/pl; temp1 = ck2*temp; temp2 = temp1*temp; /* Update for short periodics */ rk = r*(1-1.5*temp2*betal*x3thm1)+0.5*temp1*x1mth2*cos2u; uk = u-0.25*temp2*x7thm1*sin2u; xnodek = xnode+1.5*temp2*cosio*sin2u; xinck = tle->xincl+1.5*temp2*cosio*sinio*cos2u; rdotk = rdot-xn*temp1*x1mth2*sin2u; rfdotk = rfdot+xn*temp1*(x1mth2*cos2u+1.5*x3thm1); /* Orientation vectors */ sinuk = sin(uk); cosuk = cos(uk); sinik = sin(xinck); cosik = cos(xinck); sinnok = sin(xnodek); cosnok = cos(xnodek); xmx = -sinnok*cosik; xmy = cosnok*cosik; ux = xmx*sinuk+cosnok*cosuk; uy = xmy*sinuk+sinnok*cosuk; uz = sinik*sinuk; vx = xmx*cosuk-cosnok*sinuk; vy = xmy*cosuk-sinnok*sinuk; vz = sinik*cosuk; /* Position and velocity */ pos->x = rk*ux; pos->y = rk*uy; pos->z = rk*uz; vel->x = rdotk*ux+rfdotk*vx; vel->y = rdotk*uy+rfdotk*vy; vel->z = rdotk*uz+rfdotk*vz; *phase = xlt-xnode-omgadf+twopi; if(*phase < 0) *phase += twopi; *phase = FMod2p(*phase); tle->omegao1=omega; tle->xincl1=xinck; tle->xnodeo1=xnodek; } /*SGP4*/ /*------------------------------------------------------------------*/ /* SDP4 */ /* This function is used to calculate the position and velocity */ /* of deep-space (period > 225 minutes) satellites. tsince is */ /* time since epoch in minutes, tle is a pointer to a tle_t */ /* structure with Keplerian orbital elements and pos and vel */ /* are vector_t structures returning ECI satellite position and */ /* velocity. Use Convert_Sat_State() to convert to km and km/s. */ void SDP4(double tsince, tle_t *tle, vector_t *pos, vector_t *vel, double* phase) { int i; static double x3thm1,c1,x1mth2,c4,xnodcf,t2cof,xlcof,aycof,x7thm1; double a,axn,ayn,aynl,beta,betal,capu,cos2u,cosepw,cosik, cosnok,cosu,cosuk,ecose,elsq,epw,esine,pl,theta4, rdot,rdotk,rfdot,rfdotk,rk,sin2u,sinepw,sinik, sinnok,sinu,sinuk,tempe,templ,tsq,u,uk,ux,uy,uz, vx,vy,vz,xinck,xl,xlt,xmam,xmdf,xmx,xmy,xnoddf, xnodek,xll,a1,a3ovk2,ao,c2,coef,coef1,x1m5th, xhdot1,del1,r,delo,eeta,eta,etasq,perige, psisq,tsi,qoms24,s4,pinvsq,temp,tempa,temp1, temp2,temp3,temp4,temp5,temp6; static deep_arg_t deep_arg; /* Initialization */ if (isFlagClear(SDP4_INITIALIZED_FLAG)) { SetFlag(SDP4_INITIALIZED_FLAG); /* Recover original mean motion (xnodp) and */ /* semimajor axis (aodp) from input elements. */ a1 = pow(xke/tle->xno,tothrd); deep_arg.cosio = cos(tle->xincl); deep_arg.theta2 = deep_arg.cosio*deep_arg.cosio; x3thm1 = 3*deep_arg.theta2-1; deep_arg.eosq = tle->eo*tle->eo; deep_arg.betao2 = 1-deep_arg.eosq; deep_arg.betao = sqrt(deep_arg.betao2); del1 = 1.5*ck2*x3thm1/(a1*a1*deep_arg.betao*deep_arg.betao2); ao = a1*(1-del1*(0.5*tothrd+del1*(1+134/81*del1))); delo = 1.5*ck2*x3thm1/(ao*ao*deep_arg.betao*deep_arg.betao2); deep_arg.xnodp = tle->xno/(1+delo); deep_arg.aodp = ao/(1-delo); /* For perigee below 156 km, the values */ /* of s and qoms2t are altered. */ s4 = __s__; qoms24 = qoms2t; perige = (deep_arg.aodp*(1-tle->eo)-ae)*xkmper; if(perige < 156) { if(perige <= 98) s4 = 20; else s4 = perige-78; qoms24 = pow((120-s4)*ae/xkmper,4); s4 = s4/xkmper+ae; } pinvsq = 1/(deep_arg.aodp*deep_arg.aodp* deep_arg.betao2*deep_arg.betao2); deep_arg.sing = sin(tle->omegao); deep_arg.cosg = cos(tle->omegao); tsi = 1/(deep_arg.aodp-s4); eta = deep_arg.aodp*tle->eo*tsi; etasq = eta*eta; eeta = tle->eo*eta; psisq = fabs(1-etasq); coef = qoms24*pow(tsi,4); coef1 = coef/pow(psisq,3.5); c2 = coef1*deep_arg.xnodp*(deep_arg.aodp*(1+1.5*etasq+eeta* (4+etasq))+0.75*ck2*tsi/psisq*x3thm1*(8+3*etasq*(8+etasq))); c1 = tle->bstar*c2; deep_arg.sinio = sin(tle->xincl); a3ovk2 = -xj3/ck2*pow(ae,3); x1mth2 = 1-deep_arg.theta2; c4 = 2*deep_arg.xnodp*coef1*deep_arg.aodp*deep_arg.betao2* (eta*(2+0.5*etasq)+tle->eo*(0.5+2*etasq)-2*ck2*tsi/ (deep_arg.aodp*psisq)*(-3*x3thm1*(1-2*eeta+etasq* (1.5-0.5*eeta))+0.75*x1mth2*(2*etasq-eeta*(1+etasq))* cos(2*tle->omegao))); theta4 = deep_arg.theta2*deep_arg.theta2; temp1 = 3*ck2*pinvsq*deep_arg.xnodp; temp2 = temp1*ck2*pinvsq; temp3 = 1.25*ck4*pinvsq*pinvsq*deep_arg.xnodp; deep_arg.xmdot = deep_arg.xnodp+0.5*temp1*deep_arg.betao* x3thm1+0.0625*temp2*deep_arg.betao* (13-78*deep_arg.theta2+137*theta4); x1m5th = 1-5*deep_arg.theta2; deep_arg.omgdot = -0.5*temp1*x1m5th+0.0625*temp2* (7-114*deep_arg.theta2+395*theta4)+ temp3*(3-36*deep_arg.theta2+49*theta4); xhdot1 = -temp1*deep_arg.cosio; deep_arg.xnodot = xhdot1+(0.5*temp2*(4-19*deep_arg.theta2)+ 2*temp3*(3-7*deep_arg.theta2))*deep_arg.cosio; xnodcf = 3.5*deep_arg.betao2*xhdot1*c1; t2cof = 1.5*c1; xlcof = 0.125*a3ovk2*deep_arg.sinio*(3+5*deep_arg.cosio)/ (1+deep_arg.cosio); aycof = 0.25*a3ovk2*deep_arg.sinio; x7thm1 = 7*deep_arg.theta2-1; /* initialize Deep() */ Deep(dpinit, tle, &deep_arg); }; /*End of SDP4() initialization */ /* Update for secular gravity and atmospheric drag */ xmdf = tle->xmo+deep_arg.xmdot*tsince; deep_arg.omgadf = tle->omegao+deep_arg.omgdot*tsince; xnoddf = tle->xnodeo+deep_arg.xnodot*tsince; tsq = tsince*tsince; deep_arg.xnode = xnoddf+xnodcf*tsq; tempa = 1-c1*tsince; tempe = tle->bstar*c4*tsince; templ = t2cof*tsq; deep_arg.xn = deep_arg.xnodp; /* Update for deep-space secular effects */ deep_arg.xll = xmdf; deep_arg.t = tsince; Deep(dpsec, tle, &deep_arg); xmdf = deep_arg.xll; a = pow(xke/deep_arg.xn,tothrd)*tempa*tempa; deep_arg.em = deep_arg.em-tempe; xmam = xmdf+deep_arg.xnodp*templ; /* Update for deep-space periodic effects */ deep_arg.xll = xmam; Deep(dpper, tle, &deep_arg); xmam = deep_arg.xll; xl = xmam+deep_arg.omgadf+deep_arg.xnode; beta = sqrt(1-deep_arg.em*deep_arg.em); deep_arg.xn = xke/pow(a,1.5); /* Long period periodics */ axn = deep_arg.em*cos(deep_arg.omgadf); temp = 1/(a*beta*beta); xll = temp*xlcof*axn; aynl = temp*aycof; xlt = xl+xll; ayn = deep_arg.em*sin(deep_arg.omgadf)+aynl; /* Solve Kepler's Equation */ capu = FMod2p(xlt-deep_arg.xnode); temp2 = capu; i = 0; do { sinepw = sin(temp2); cosepw = cos(temp2); temp3 = axn*sinepw; temp4 = ayn*cosepw; temp5 = axn*cosepw; temp6 = ayn*sinepw; epw = (capu-temp4+temp3-temp2)/(1-temp5-temp6)+temp2; if(fabs(epw-temp2) <= e6a) break; temp2 = epw; } while( i++ < 10 ); /* Short period preliminary quantities */ ecose = temp5+temp6; esine = temp3-temp4; elsq = axn*axn+ayn*ayn; temp = 1-elsq; pl = a*temp; r = a*(1-ecose); temp1 = 1/r; rdot = xke*sqrt(a)*esine*temp1; rfdot = xke*sqrt(pl)*temp1; temp2 = a*temp1; betal = sqrt(temp); temp3 = 1/(1+betal); cosu = temp2*(cosepw-axn+ayn*esine*temp3); sinu = temp2*(sinepw-ayn-axn*esine*temp3); u = AcTan(sinu,cosu); sin2u = 2*sinu*cosu; cos2u = 2*cosu*cosu-1; temp = 1/pl; temp1 = ck2*temp; temp2 = temp1*temp; /* Update for short periodics */ rk = r*(1-1.5*temp2*betal*x3thm1)+0.5*temp1*x1mth2*cos2u; uk = u-0.25*temp2*x7thm1*sin2u; xnodek = deep_arg.xnode+1.5*temp2*deep_arg.cosio*sin2u; xinck = deep_arg.xinc+1.5*temp2*deep_arg.cosio*deep_arg.sinio*cos2u; rdotk = rdot-deep_arg.xn*temp1*x1mth2*sin2u; rfdotk = rfdot+deep_arg.xn*temp1*(x1mth2*cos2u+1.5*x3thm1); /* Orientation vectors */ sinuk = sin(uk); cosuk = cos(uk); sinik = sin(xinck); cosik = cos(xinck); sinnok = sin(xnodek); cosnok = cos(xnodek); xmx = -sinnok*cosik; xmy = cosnok*cosik; ux = xmx*sinuk+cosnok*cosuk; uy = xmy*sinuk+sinnok*cosuk; uz = sinik*sinuk; vx = xmx*cosuk-cosnok*sinuk; vy = xmy*cosuk-sinnok*sinuk; vz = sinik*cosuk; /* Position and velocity */ pos->x = rk*ux; pos->y = rk*uy; pos->z = rk*uz; vel->x = rdotk*ux+rfdotk*vx; vel->y = rdotk*uy+rfdotk*vy; vel->z = rdotk*uz+rfdotk*vz; /* Phase in rads */ *phase = xlt-deep_arg.xnode-deep_arg.omgadf+twopi; if(*phase < 0) *phase += twopi; *phase = FMod2p(*phase); tle->omegao1=deep_arg.omgadf; tle->xincl1=deep_arg.xinc; tle->xnodeo1=deep_arg.xnode; } /* SDP4 */ /*------------------------------------------------------------------*/ /* DEEP */ /* This function is used by SDP4 to add lunar and solar */ /* perturbation effects to deep-space orbit objects. */ void Deep(int ientry, tle_t *tle, deep_arg_t *deep_arg) { static double thgr,xnq,xqncl,omegaq,zmol,zmos,savtsn,ee2,e3,xi2, xl2,xl3,xl4,xgh2,xgh3,xgh4,xh2,xh3,sse,ssi,ssg,xi3, se2,si2,sl2,sgh2,sh2,se3,si3,sl3,sgh3,sh3,sl4,sgh4, ssl,ssh,d3210,d3222,d4410,d4422,d5220,d5232,d5421, d5433,del1,del2,del3,fasx2,fasx4,fasx6,xlamo,xfact, xni,atime,stepp,stepn,step2,preep,pl,sghs,xli, d2201,d2211,sghl,sh1,pinc,pe,shs,zsingl,zcosgl, zsinhl,zcoshl,zsinil,zcosil; double a1,a2,a3,a4,a5,a6,a7,a8,a9,a10,ainv2,alfdp,aqnv, sgh,sini2,sinis,sinok,sh,si,sil,day,betdp,dalf, bfact,c,cc,cosis,cosok,cosq,ctem,f322,zx,zy, dbet,dls,eoc,eq,f2,f220,f221,f3,f311,f321,xnoh, f330,f441,f442,f522,f523,f542,f543,g200,g201, g211,pgh,ph,s1,s2,s3,s4,s5,s6,s7,se,sel,ses,xls, g300,g310,g322,g410,g422,g520,g521,g532,g533,gam, sinq,sinzf,sis,sl,sll,sls,stem,temp,temp1,x1,x2, x2li,x2omi,x3,x4,x5,x6,x7,x8,xl,xldot,xmao,xnddt, xndot,xno2,xnodce,xnoi,xomi,xpidot,z1,z11,z12,z13, z2,z21,z22,z23,z3,z31,z32,z33,ze,zf,zm,zmo,zn, zsing,zsinh,zsini,zcosg,zcosh,zcosi,delt=0,ft=0; switch(ientry) { case dpinit : /* Entrance for deep space initialization */ thgr = ThetaG(tle->epoch, deep_arg); eq = tle->eo; xnq = deep_arg->xnodp; aqnv = 1/deep_arg->aodp; xqncl = tle->xincl; xmao = tle->xmo; xpidot = deep_arg->omgdot+deep_arg->xnodot; sinq = sin(tle->xnodeo); cosq = cos(tle->xnodeo); omegaq = tle->omegao; /* Initialize lunar solar terms */ day = deep_arg->ds50+18261.5; /*Days since 1900 Jan 0.5*/ if (day != preep) { preep = day; xnodce = 4.5236020-9.2422029E-4*day; stem = sin(xnodce); ctem = cos(xnodce); zcosil = 0.91375164-0.03568096*ctem; zsinil = sqrt(1-zcosil*zcosil); zsinhl = 0.089683511*stem/zsinil; zcoshl = sqrt(1-zsinhl*zsinhl); c = 4.7199672+0.22997150*day; gam = 5.8351514+0.0019443680*day; zmol = FMod2p(c-gam); zx = 0.39785416*stem/zsinil; zy = zcoshl*ctem+0.91744867*zsinhl*stem; zx = AcTan(zx,zy); zx = gam+zx-xnodce; zcosgl = cos(zx); zsingl = sin(zx); zmos = 6.2565837+0.017201977*day; zmos = FMod2p(zmos); } /* End if(day != preep) */ /* Do solar terms */ savtsn = 1E20; zcosg = zcosgs; zsing = zsings; zcosi = zcosis; zsini = zsinis; zcosh = cosq; zsinh = sinq; cc = c1ss; zn = zns; ze = zes; zmo = zmos; xnoi = 1/xnq; /* Loop breaks when Solar terms are done a second */ /* time, after Lunar terms are initialized */ for(;;) { /* Solar terms done again after Lunar terms are done */ a1 = zcosg*zcosh+zsing*zcosi*zsinh; a3 = -zsing*zcosh+zcosg*zcosi*zsinh; a7 = -zcosg*zsinh+zsing*zcosi*zcosh; a8 = zsing*zsini; a9 = zsing*zsinh+zcosg*zcosi*zcosh; a10 = zcosg*zsini; a2 = deep_arg->cosio*a7+ deep_arg->sinio*a8; a4 = deep_arg->cosio*a9+ deep_arg->sinio*a10; a5 = -deep_arg->sinio*a7+ deep_arg->cosio*a8; a6 = -deep_arg->sinio*a9+ deep_arg->cosio*a10; x1 = a1*deep_arg->cosg+a2*deep_arg->sing; x2 = a3*deep_arg->cosg+a4*deep_arg->sing; x3 = -a1*deep_arg->sing+a2*deep_arg->cosg; x4 = -a3*deep_arg->sing+a4*deep_arg->cosg; x5 = a5*deep_arg->sing; x6 = a6*deep_arg->sing; x7 = a5*deep_arg->cosg; x8 = a6*deep_arg->cosg; z31 = 12*x1*x1-3*x3*x3; z32 = 24*x1*x2-6*x3*x4; z33 = 12*x2*x2-3*x4*x4; z1 = 3*(a1*a1+a2*a2)+z31*deep_arg->eosq; z2 = 6*(a1*a3+a2*a4)+z32*deep_arg->eosq; z3 = 3*(a3*a3+a4*a4)+z33*deep_arg->eosq; z11 = -6*a1*a5+deep_arg->eosq*(-24*x1*x7-6*x3*x5); z12 = -6*(a1*a6+a3*a5)+ deep_arg->eosq* (-24*(x2*x7+x1*x8)-6*(x3*x6+x4*x5)); z13 = -6*a3*a6+deep_arg->eosq*(-24*x2*x8-6*x4*x6); z21 = 6*a2*a5+deep_arg->eosq*(24*x1*x5-6*x3*x7); z22 = 6*(a4*a5+a2*a6)+ deep_arg->eosq* (24*(x2*x5+x1*x6)-6*(x4*x7+x3*x8)); z23 = 6*a4*a6+deep_arg->eosq*(24*x2*x6-6*x4*x8); z1 = z1+z1+deep_arg->betao2*z31; z2 = z2+z2+deep_arg->betao2*z32; z3 = z3+z3+deep_arg->betao2*z33; s3 = cc*xnoi; s2 = -0.5*s3/deep_arg->betao; s4 = s3*deep_arg->betao; s1 = -15*eq*s4; s5 = x1*x3+x2*x4; s6 = x2*x3+x1*x4; s7 = x2*x4-x1*x3; se = s1*zn*s5; si = s2*zn*(z11+z13); sl = -zn*s3*(z1+z3-14-6*deep_arg->eosq); sgh = s4*zn*(z31+z33-6); sh = -zn*s2*(z21+z23); if (xqncl < 5.2359877E-2) sh = 0; ee2 = 2*s1*s6; e3 = 2*s1*s7; xi2 = 2*s2*z12; xi3 = 2*s2*(z13-z11); xl2 = -2*s3*z2; xl3 = -2*s3*(z3-z1); xl4 = -2*s3*(-21-9*deep_arg->eosq)*ze; xgh2 = 2*s4*z32; xgh3 = 2*s4*(z33-z31); xgh4 = -18*s4*ze; xh2 = -2*s2*z22; xh3 = -2*s2*(z23-z21); if(isFlagSet(LUNAR_TERMS_DONE_FLAG)) break; /* Do lunar terms */ sse = se; ssi = si; ssl = sl; ssh = sh/deep_arg->sinio; ssg = sgh-deep_arg->cosio*ssh; se2 = ee2; si2 = xi2; sl2 = xl2; sgh2 = xgh2; sh2 = xh2; se3 = e3; si3 = xi3; sl3 = xl3; sgh3 = xgh3; sh3 = xh3; sl4 = xl4; sgh4 = xgh4; zcosg = zcosgl; zsing = zsingl; zcosi = zcosil; zsini = zsinil; zcosh = zcoshl*cosq+zsinhl*sinq; zsinh = sinq*zcoshl-cosq*zsinhl; zn = znl; cc = c1l; ze = zel; zmo = zmol; SetFlag(LUNAR_TERMS_DONE_FLAG); } /* End of for(;;) */ sse = sse+se; ssi = ssi+si; ssl = ssl+sl; ssg = ssg+sgh-deep_arg->cosio/deep_arg->sinio*sh; ssh = ssh+sh/deep_arg->sinio; /* Geopotential resonance initialization for 12 hour orbits */ ClearFlag(RESONANCE_FLAG); ClearFlag(SYNCHRONOUS_FLAG); if( !((xnq < 0.0052359877) && (xnq > 0.0034906585)) ) { if( (xnq < 0.00826) || (xnq > 0.00924) ) return; if (eq < 0.5) return; SetFlag(RESONANCE_FLAG); eoc = eq*deep_arg->eosq; g201 = -0.306-(eq-0.64)*0.440; if (eq <= 0.65) { g211 = 3.616-13.247*eq+16.290*deep_arg->eosq; g310 = -19.302+117.390*eq-228.419* deep_arg->eosq+156.591*eoc; g322 = -18.9068+109.7927*eq-214.6334* deep_arg->eosq+146.5816*eoc; g410 = -41.122+242.694*eq-471.094* deep_arg->eosq+313.953*eoc; g422 = -146.407+841.880*eq-1629.014* deep_arg->eosq+1083.435*eoc; g520 = -532.114+3017.977*eq-5740* deep_arg->eosq+3708.276*eoc; } else { g211 = -72.099+331.819*eq-508.738* deep_arg->eosq+266.724*eoc; g310 = -346.844+1582.851*eq-2415.925* deep_arg->eosq+1246.113*eoc; g322 = -342.585+1554.908*eq-2366.899* deep_arg->eosq+1215.972*eoc; g410 = -1052.797+4758.686*eq-7193.992* deep_arg->eosq+3651.957*eoc; g422 = -3581.69+16178.11*eq-24462.77* deep_arg->eosq+ 12422.52*eoc; if (eq <= 0.715) g520 = 1464.74-4664.75*eq+3763.64*deep_arg->eosq; else g520 = -5149.66+29936.92*eq-54087.36* deep_arg->eosq+31324.56*eoc; } /* End if (eq <= 0.65) */ if (eq < 0.7) { g533 = -919.2277+4988.61*eq-9064.77* deep_arg->eosq+5542.21*eoc; g521 = -822.71072+4568.6173*eq-8491.4146* deep_arg->eosq+5337.524*eoc; g532 = -853.666+4690.25*eq-8624.77* deep_arg->eosq+ 5341.4*eoc; } else { g533 = -37995.78+161616.52*eq-229838.2* deep_arg->eosq+109377.94*eoc; g521 = -51752.104+218913.95*eq-309468.16* deep_arg->eosq+146349.42*eoc; g532 = -40023.88+170470.89*eq-242699.48* deep_arg->eosq+115605.82*eoc; } /* End if (eq <= 0.7) */ sini2 = deep_arg->sinio*deep_arg->sinio; f220 = 0.75*(1+2*deep_arg->cosio+deep_arg->theta2); f221 = 1.5*sini2; f321 = 1.875*deep_arg->sinio*(1-2*\ deep_arg->cosio-3*deep_arg->theta2); f322 = -1.875*deep_arg->sinio*(1+2* deep_arg->cosio-3*deep_arg->theta2); f441 = 35*sini2*f220; f442 = 39.3750*sini2*sini2; f522 = 9.84375*deep_arg->sinio*(sini2*(1-2*deep_arg->cosio-5* deep_arg->theta2)+0.33333333*(-2+4*deep_arg->cosio+ 6*deep_arg->theta2)); f523 = deep_arg->sinio*(4.92187512*sini2*(-2-4* deep_arg->cosio+10*deep_arg->theta2)+6.56250012 *(1+2*deep_arg->cosio-3*deep_arg->theta2)); f542 = 29.53125*deep_arg->sinio*(2-8* deep_arg->cosio+deep_arg->theta2* (-12+8*deep_arg->cosio+10*deep_arg->theta2)); f543 = 29.53125*deep_arg->sinio*(-2-8*deep_arg->cosio+ deep_arg->theta2*(12+8*deep_arg->cosio-10* deep_arg->theta2)); xno2 = xnq*xnq; ainv2 = aqnv*aqnv; temp1 = 3*xno2*ainv2; temp = temp1*root22; d2201 = temp*f220*g201; d2211 = temp*f221*g211; temp1 = temp1*aqnv; temp = temp1*root32; d3210 = temp*f321*g310; d3222 = temp*f322*g322; temp1 = temp1*aqnv; temp = 2*temp1*root44; d4410 = temp*f441*g410; d4422 = temp*f442*g422; temp1 = temp1*aqnv; temp = temp1*root52; d5220 = temp*f522*g520; d5232 = temp*f523*g532; temp = 2*temp1*root54; d5421 = temp*f542*g521; d5433 = temp*f543*g533; xlamo = xmao+tle->xnodeo+tle->xnodeo-thgr-thgr; bfact = deep_arg->xmdot+deep_arg->xnodot+ deep_arg->xnodot-thdt-thdt; bfact = bfact+ssl+ssh+ssh; } /* if( !(xnq < 0.0052359877) && (xnq > 0.0034906585) ) */ else { SetFlag(RESONANCE_FLAG); SetFlag(SYNCHRONOUS_FLAG); /* Synchronous resonance terms initialization */ g200 = 1+deep_arg->eosq*(-2.5+0.8125*deep_arg->eosq); g310 = 1+2*deep_arg->eosq; g300 = 1+deep_arg->eosq*(-6+6.60937*deep_arg->eosq); f220 = 0.75*(1+deep_arg->cosio)*(1+deep_arg->cosio); f311 = 0.9375*deep_arg->sinio*deep_arg->sinio* (1+3*deep_arg->cosio)-0.75*(1+deep_arg->cosio); f330 = 1+deep_arg->cosio; f330 = 1.875*f330*f330*f330; del1 = 3*xnq*xnq*aqnv*aqnv; del2 = 2*del1*f220*g200*q22; del3 = 3*del1*f330*g300*q33*aqnv; del1 = del1*f311*g310*q31*aqnv; fasx2 = 0.13130908; fasx4 = 2.8843198; fasx6 = 0.37448087; xlamo = xmao+tle->xnodeo+tle->omegao-thgr; bfact = deep_arg->xmdot+xpidot-thdt; bfact = bfact+ssl+ssg+ssh; } /* End if( !(xnq < 0.0052359877) && (xnq > 0.0034906585) ) */ xfact = bfact-xnq; /* Initialize integrator */ xli = xlamo; xni = xnq; atime = 0; stepp = 720; stepn = -720; step2 = 259200; /* End case dpinit: */ return; case dpsec: /* Entrance for deep space secular effects */ deep_arg->xll = deep_arg->xll+ssl*deep_arg->t; deep_arg->omgadf = deep_arg->omgadf+ssg*deep_arg->t; deep_arg->xnode = deep_arg->xnode+ssh*deep_arg->t; deep_arg->em = tle->eo+sse*deep_arg->t; deep_arg->xinc = tle->xincl+ssi*deep_arg->t; if (deep_arg->xinc < 0) { deep_arg->xinc = -deep_arg->xinc; deep_arg->xnode = deep_arg->xnode + pi; deep_arg->omgadf = deep_arg->omgadf-pi; } if( isFlagClear(RESONANCE_FLAG) ) return; do { if( (atime == 0) || ((deep_arg->t >= 0) && (atime < 0)) || ((deep_arg->t < 0) && (atime >= 0)) ) { /* Epoch restart */ if( deep_arg->t >= 0 ) delt = stepp; else delt = stepn; atime = 0; xni = xnq; xli = xlamo; } else { if( fabs(deep_arg->t) >= fabs(atime) ) { if ( deep_arg->t > 0 ) delt = stepp; else delt = stepn; } } do { if ( fabs(deep_arg->t-atime) >= stepp ) { SetFlag(DO_LOOP_FLAG); ClearFlag(EPOCH_RESTART_FLAG); } else { ft = deep_arg->t-atime; ClearFlag(DO_LOOP_FLAG); } if( fabs(deep_arg->t) < fabs(atime) ) { if (deep_arg->t >= 0) delt = stepn; else delt = stepp; SetFlag(DO_LOOP_FLAG | EPOCH_RESTART_FLAG); } /* Dot terms calculated */ if( isFlagSet(SYNCHRONOUS_FLAG) ) { xndot = del1*sin(xli-fasx2)+del2*sin(2*(xli-fasx4)) +del3*sin(3*(xli-fasx6)); xnddt = del1*cos(xli-fasx2)+2*del2*cos(2*(xli-fasx4)) +3*del3*cos(3*(xli-fasx6)); } else { xomi = omegaq+deep_arg->omgdot*atime; x2omi = xomi+xomi; x2li = xli+xli; xndot = d2201*sin(x2omi+xli-g22) +d2211*sin(xli-g22) +d3210*sin(xomi+xli-g32) +d3222*sin(-xomi+xli-g32) +d4410*sin(x2omi+x2li-g44) +d4422*sin(x2li-g44) +d5220*sin(xomi+xli-g52) +d5232*sin(-xomi+xli-g52) +d5421*sin(xomi+x2li-g54) +d5433*sin(-xomi+x2li-g54); xnddt = d2201*cos(x2omi+xli-g22) +d2211*cos(xli-g22) +d3210*cos(xomi+xli-g32) +d3222*cos(-xomi+xli-g32) +d5220*cos(xomi+xli-g52) +d5232*cos(-xomi+xli-g52) +2*(d4410*cos(x2omi+x2li-g44) +d4422*cos(x2li-g44) +d5421*cos(xomi+x2li-g54) +d5433*cos(-xomi+x2li-g54)); } /* End of if (isFlagSet(SYNCHRONOUS_FLAG)) */ xldot = xni+xfact; xnddt = xnddt*xldot; if(isFlagSet(DO_LOOP_FLAG)) { xli = xli+xldot*delt+xndot*step2; xni = xni+xndot*delt+xnddt*step2; atime = atime+delt; } } while(isFlagSet(DO_LOOP_FLAG) && isFlagClear(EPOCH_RESTART_FLAG)); } while(isFlagSet(DO_LOOP_FLAG) && isFlagSet(EPOCH_RESTART_FLAG)); deep_arg->xn = xni+xndot*ft+xnddt*ft*ft*0.5; xl = xli+xldot*ft+xndot*ft*ft*0.5; temp = -deep_arg->xnode+thgr+deep_arg->t*thdt; if (isFlagClear(SYNCHRONOUS_FLAG)) deep_arg->xll = xl+temp+temp; else deep_arg->xll = xl-deep_arg->omgadf+temp; return; /*End case dpsec: */ case dpper: /* Entrance for lunar-solar periodics */ sinis = sin(deep_arg->xinc); cosis = cos(deep_arg->xinc); if (fabs(savtsn-deep_arg->t) >= 30) { savtsn = deep_arg->t; zm = zmos+zns*deep_arg->t; zf = zm+2*zes*sin(zm); sinzf = sin(zf); f2 = 0.5*sinzf*sinzf-0.25; f3 = -0.5*sinzf*cos(zf); ses = se2*f2+se3*f3; sis = si2*f2+si3*f3; sls = sl2*f2+sl3*f3+sl4*sinzf; sghs = sgh2*f2+sgh3*f3+sgh4*sinzf; shs = sh2*f2+sh3*f3; zm = zmol+znl*deep_arg->t; zf = zm+2*zel*sin(zm); sinzf = sin(zf); f2 = 0.5*sinzf*sinzf-0.25; f3 = -0.5*sinzf*cos(zf); sel = ee2*f2+e3*f3; sil = xi2*f2+xi3*f3; sll = xl2*f2+xl3*f3+xl4*sinzf; sghl = xgh2*f2+xgh3*f3+xgh4*sinzf; sh1 = xh2*f2+xh3*f3; pe = ses+sel; pinc = sis+sil; pl = sls+sll; } pgh = sghs+sghl; ph = shs+sh1; deep_arg->xinc = deep_arg->xinc+pinc; deep_arg->em = deep_arg->em+pe; if (xqncl >= 0.2) { /* Apply periodics directly */ ph = ph/deep_arg->sinio; pgh = pgh-deep_arg->cosio*ph; deep_arg->omgadf = deep_arg->omgadf+pgh; deep_arg->xnode = deep_arg->xnode+ph; deep_arg->xll = deep_arg->xll+pl; } else { /* Apply periodics with Lyddane modification */ sinok = sin(deep_arg->xnode); cosok = cos(deep_arg->xnode); alfdp = sinis*sinok; betdp = sinis*cosok; dalf = ph*cosok+pinc*cosis*sinok; dbet = -ph*sinok+pinc*cosis*cosok; alfdp = alfdp+dalf; betdp = betdp+dbet; deep_arg->xnode = FMod2p(deep_arg->xnode); xls = deep_arg->xll+deep_arg->omgadf+cosis*deep_arg->xnode; dls = pl+pgh-pinc*deep_arg->xnode*sinis; xls = xls+dls; xnoh = deep_arg->xnode; deep_arg->xnode = AcTan(alfdp,betdp); /* This is a patch to Lyddane modification */ /* suggested by Rob Matson. */ if(fabs(xnoh-deep_arg->xnode) > pi) { if(deep_arg->xnode < xnoh) deep_arg->xnode +=twopi; else deep_arg->xnode -=twopi; } deep_arg->xll = deep_arg->xll+pl; deep_arg->omgadf = xls-deep_arg->xll-cos(deep_arg->xinc)* deep_arg->xnode; } /* End case dpper: */ return; } /* End switch(ientry) */ } /* End of Deep() */ /*------------------------------------------------------------------*/ /* Functions for testing and setting/clearing flags */ /* An int variable holding the single-bit flags */ static int Flags = 0; int isFlagSet(int flag) { return (Flags & flag); } int isFlagClear(int flag) { return (~Flags & flag); } void SetFlag(int flag) { Flags |= flag; } void ClearFlag(int flag) { Flags &= ~flag; } /*------------------------------------------------------------------*/