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sgp4sdp4.c
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/*
* 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
*/
#define SGP4SDP4_CONSTANTS
#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)
{
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;
} /*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)
{
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;
} /* 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,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;
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;
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 == 0.0) ||
((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;