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sgp8.cpp
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sgp8.cpp
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/* Copyright (C) 2018, Project Pluto. See LICENSE. */
#include <math.h>
#include <string.h>
#include "norad.h"
#include "norad_in.h"
#define tthmun params[0]
#define sini2 params[1]
#define cosi2 params[2]
#define unm5th params[3]
#define unmth2 params[4]
#define xmdt1 params[5]
#define xgdt1 params[6]
#define xhdt1 params[7]
#define xndt params[8]
#define edot params[9]
#define ed params[10]
#define gamma params[11]
#define omgdt params[12]
#define ovgpp params[13]
#define pp params[14]
#define qq params[15]
#define sini params[16]
#define cosi params[17]
#define cosio_2 params[18]
#define xlldot params[19]
#define xnd params[20]
#define xnodot_ params[21]
#define xnodp_ params[22]
#define simple_flag *((int *)( params + 23))
void sxpall_common_init( const tle_t *tle, deep_arg_t *deep_arg);
void sxp8_common_init( double *params, const tle_t *tle, deep_arg_t *deep_arg)
{
const double half_inclination = tle->xincl*.5;
const double cosio4 = deep_arg->cosio2 * deep_arg->cosio2;
double po, pom2, pardt1, pardt2, pardt4;
deep_arg->sing = sin( tle->omegao);
deep_arg->cosg = cos( tle->omegao);
sini2 = sin( half_inclination);
cosi2 = cos( half_inclination);
tthmun = deep_arg->cosio2 * 3. - 1.;
unm5th = 1.-deep_arg->cosio2 * 5.;
unmth2 = 1.-deep_arg->cosio2;
po = deep_arg->aodp * deep_arg->betao2;
pom2 = 1./(po*po);
pardt1 = 3. * ck2 * pom2 * deep_arg->xnodp;
pardt2 = pardt1 * ck2 * pom2;
pardt4 = ck4 * 1.25 * pom2 * pom2 * deep_arg->xnodp;
xmdt1 = .5 * pardt1 * deep_arg->betao * tthmun;
xgdt1 = -.5 * pardt1 * unm5th;
xhdt1 = -pardt1 * deep_arg->cosio;
deep_arg->xmdot = deep_arg->xnodp+xmdt1+pardt2*.0625*deep_arg->betao*
(13.-deep_arg->cosio2*78.+cosio4*137.);
deep_arg->omgdot = xgdt1+pardt2*.0625*(7.-deep_arg->cosio2*
114.+cosio4*395.)+pardt4*(3.-deep_arg->cosio2*
36.+cosio4*49.);
deep_arg->xnodot = xhdt1+(pardt2*.5*(4.-deep_arg->cosio2*19.)+pardt4*
2.*(3.-deep_arg->cosio2*7.))*deep_arg->cosio;
}
void DLL_FUNC SGP8_init( double *params, const tle_t *tle)
{
const double rho = .15696615;
const double b = tle->bstar*2./rho;
double
alpha2, b1, b2, b3, c0,
c1, c4, c5, cos2g, d1, d2, d3, d4,
d5, eeta, eta, eta2, eddot, etdt,
po, psim2, r1, tsi, xndtn;
deep_arg_t deep_arg;
sxpall_common_init( tle, &deep_arg);
sxp8_common_init( params, tle, &deep_arg);
sini = sin( tle->xincl);
cosi = deep_arg.cosio;
cosio_2 = deep_arg.cosio2;
/* Initialization */
xnodp_ = deep_arg.xnodp;
xlldot = deep_arg.xmdot;
omgdt = deep_arg.omgdot;
xnodot_ = deep_arg.xnodot;
po = deep_arg.aodp * deep_arg.betao2;
tsi = 1./(po-s_const);
eta = tle->eo*s_const*tsi;
eta2 = eta * eta;
psim2 = (r1 = 1./(1.-eta2), fabs(r1));
alpha2 = deep_arg.eosq+1.;
eeta = tle->eo*eta;
cos2g = deep_arg.cosg * deep_arg.cosg * 2. - 1.;
d5 = tsi*psim2;
d1 = d5/po;
d2 = eta2*(eta2*4.5+36.)+12.;
d3 = eta2*(eta2*2.5+15.);
d4 = eta*(eta2*3.75+5.);
b1 = ck2*tthmun;
b2 = -ck2*unmth2;
b3 = a3ovk2*sini;
r1 = tsi, r1 *= r1;
c0 = b*.5*rho*qoms2t*xnodp_*deep_arg.aodp*(r1*r1)*
pow(psim2, 3.5)/sqrt(alpha2);
r1 = alpha2;
c1 = xnodp_*1.5*(r1*r1)*c0;
c4 = d1*d3*b2;
c5 = d5*d4*b3;
xndt = c1*(eta2*(deep_arg.eosq*34.+3.)+2.+eeta*5.*(eta2+4.)
+deep_arg.eosq*8.5+d1*d2*b1+c4*cos2g+c5*deep_arg.sing);
xndtn = xndt/xnodp_;
/* If drag is very small, the isimp flag is set and the */
/* equations are truncated to linear variation in mean */
/* motion and quadratic variation in mean anomaly */
r1 = xndtn * minutes_per_day;
if( fabs(r1) > .00216)
{
const double d6 = eta*(eta2*22.5+30.);
const double d7 = eta*(eta2*12.5+5.);
const double d8 = eta2*(eta2+6.75)+1.;
const double d9 = eta*(deep_arg.eosq*68.+6.)+tle->eo*(eta2*15.+20.);
const double d10 = eta*5.*(eta2+4.)+tle->eo*(eta2*68.+17.);
const double d11 = eta*(eta2*18.+72.);
const double d12 = eta*(eta2*10.+30.);
const double d13 = eta2*11.25+5.;
const double d20 = two_thirds*.5*xndtn;
const double c8 = d1*d7*b2;
const double c9 = d5*d8*b3;
const double sin2g = deep_arg.sing*2.*deep_arg.cosg;
double d1dt, d2dt, d3dt, d4dt, d5dt, temp;
double d14, d15, d16, d17, d18, d19, d23, d25, aldtal, psdtps;
double c4dt, c5dt, c0dtc0, c1dtc1, rr2;
double d1ddt, etddt, tmnddt, tsdtts, tsddts, xnddt, xntrdt;
simple_flag = 0;
edot = -c0*(eta*(eta2+4.+deep_arg.eosq*(eta2*7.+15.5))+tle->eo*
(eta2*15.+5.)+d1*d6*b1+c8*cos2g+c9*deep_arg.sing);
tsdtts = deep_arg.aodp*2.*tsi*(d20*deep_arg.betao2+tle->eo*edot);
aldtal = tle->eo*edot/alpha2;
etdt = (edot+tle->eo*tsdtts)*tsi*s_const;
psdtps = -eta*etdt*psim2;
c0dtc0 = d20+tsdtts*4.-aldtal-psdtps*7.;
c1dtc1 = xndtn+aldtal*4.+c0dtc0;
d14 = tsdtts-psdtps*2.;
d15 = (d20+tle->eo*edot/deep_arg.betao2)*2.;
d1dt = d1*(d14+d15);
d2dt = etdt*d11;
d3dt = etdt*d12;
d4dt = etdt*d13;
d5dt = d5*d14;
c4dt = b2*(d1dt*d3+d1*d3dt);
c5dt = b3*(d5dt*d4+d5*d4dt);
d16 = d9*etdt+d10*edot+b1*(d1dt*d2+d1*d2dt)+c4dt*
cos2g+c5dt*deep_arg.sing+xgdt1*(c5*deep_arg.cosg-c4*2.*sin2g);
xnddt = c1dtc1*xndt+c1*d16;
eddot = c0dtc0*edot-c0*((eta2*3.+4.+eeta*30.+deep_arg.eosq*
(eta2*21.+15.5))*etdt+(eta2*15.+5.+eeta*
(eta2*14.+31.))*edot+b1*(d1dt*d6+d1*etdt*
(eta2*67.5+30.))+b2*(d1dt*d7+d1*etdt*
(eta2*37.5+5.))*cos2g+b3*(d5dt*d8+d5*etdt*eta*
(eta2*4.+13.5))*deep_arg.sing+xgdt1*(c9*deep_arg.cosg-c8*2.*sin2g));
r1 = edot;
d25 = r1*r1;
r1 = xndtn;
d17 = xnddt/xnodp_-r1*r1;
tsddts = tsdtts*2.*(tsdtts-d20)+deep_arg.aodp*tsi*
(two_thirds*deep_arg.betao2*d17-d20*4.*tle->eo*edot+
(d25+tle->eo*eddot)*2.);
etddt = (eddot+edot*2.*tsdtts)*tsi*s_const+tsddts*eta;
r1 = tsdtts;
d18 = tsddts-r1*r1;
r1 = psdtps;
rr2 = psdtps;
d19 = -(r1*r1)/eta2-eta*etddt*psim2-rr2*rr2;
d23 = etdt*etdt;
d1ddt = d1dt*(d14+d15)+d1*(d18-d19*2.+two_thirds*d17+
(alpha2*d25/deep_arg.betao2+tle->eo*eddot)*2./deep_arg.betao2);
r1 = aldtal;
xntrdt = xndt*(two_thirds*2.*d17+(d25+tle->eo*eddot)*3./
alpha2-r1*r1*6.+d18*4.-d19*7.)+
c1dtc1*xnddt+c1*(c1dtc1*d16+d9*etddt+d10*
eddot+d23*(eeta*30.+6.+deep_arg.eosq*68.)+etdt*edot*
(eta2*30.+40.+eeta*272.)+d25*(eta2*68.+17.)+
b1*(d1ddt*d2+d1dt*2.*d2dt+d1*(etddt*d11+d23*
(eta2*54.+72.)))+b2*(d1ddt*d3+d1dt*2.*d3dt+d1
*(etddt*d12+d23*(eta2*30.+30.)))*cos2g+b3*
((d5dt*d14+d5*(d18-d19*2.))*d4+d4dt*2.*d5dt+
d5*(etddt*d13+eta*22.5*d23))*deep_arg.sing+xgdt1*((d20*
7.+tle->eo*4.*edot/deep_arg.betao2)*(c5*deep_arg.cosg-c4*2.*
sin2g)+(c5dt*2.*deep_arg.cosg-c4dt*4.*sin2g-xgdt1*
(c5*deep_arg.sing+c4*4.*cos2g))));
tmnddt = xnddt*1e9;
r1 = tmnddt;
temp = r1*r1-xndt*1e18*xntrdt;
r1 = tmnddt;
pp = (temp+r1*r1)/temp;
gamma = -xntrdt/(xnddt*(pp-2.));
xnd = xndt/(pp*gamma);
qq = 1.-eddot/(edot*gamma);
ed = edot/(qq*gamma);
ovgpp = 1./(gamma*(pp+1.));
}
else
{
simple_flag = 1;
edot = -two_thirds*xndtn*(1.-tle->eo);
} /* End of if (fabs(r1) > .00216) */
} /* End of SGP8() initialization */
int DLL_FUNC SGP8( const double tsince, const tle_t *tle, const double *params,
double *pos, double *vel)
{
int i;
double
am, aovr, axnm, aynm, beta, beta2m,
cose, cosos, cs2f2g, csf, csfg,
cslamb, di, diwc, dr, ecosf, em, fm,
g1, g10, g13, g14, g2, g3, g4, g5,
omgasm, pm, r1, rdot, rm, rr, rvdot,
sine, sinos, sn2f2g, snf, snfg,
sni2du, snlamb, temp, ux, uy,
uz, vx, vy, vz, xlamb, xmam, xn,
xnodes, y4, y5, z1, z7, zc2, zc5;
/* Update for secular gravity and atmospheric drag */
r1 = tle->xmo+xlldot*tsince;
xmam = FMod2p(r1);
omgasm = tle->omegao+omgdt*tsince;
xnodes = tle->xnodeo+xnodot_*tsince;
if( !simple_flag)
{
double temp1;
temp = 1.-gamma*tsince;
temp1 = pow(temp, pp);
xn = xnodp_+xnd*(1.-temp1);
em = tle->eo+ed*(1.-pow(temp, qq));
z1 = xnd*(tsince+ovgpp*(temp*temp1-1.));
}
else
{
xn = xnodp_+xndt*tsince;
em = tle->eo+edot*tsince;
z1 = xndt*.5*tsince*tsince;
} /* if(isFlagClear(SIMPLE_FLAG)) */
z7 = two_thirds*3.5*z1/xnodp_;
r1 = xmam+z1+z7*xmdt1;
xmam = FMod2p(r1);
omgasm += z7*xgdt1;
xnodes += z7*xhdt1;
/* Solve Kepler's equation */
zc2 = xmam+em*sin(xmam)*(em*cos(xmam)+1.);
i = 0;
do
{
double cape;
sine = sin(zc2);
cose = cos(zc2);
zc5 = 1./(1.-em*cose);
cape = (xmam+em*sine-zc2)*zc5+zc2;
r1 = cape-zc2;
if(fabs(r1) <= e6a) break;
zc2 = cape;
}
while(i++ < 10 );
/* Short period preliminary quantities */
am = pow( xke / xn, two_thirds);
beta2m = 1.-em*em;
sinos = sin(omgasm);
cosos = cos(omgasm);
axnm = em*cosos;
aynm = em*sinos;
pm = am*beta2m;
g1 = 1./pm;
g2 = ck2*.5*g1;
g3 = g2*g1;
beta = sqrt(beta2m);
g4 = a3ovk2 * .25 * sini;
g5 = a3ovk2 * .25 * g1;
snf = beta*sine*zc5;
csf = (cose-em)*zc5;
fm = atan2(snf, csf);
if( fm < 0.)
fm += pi + pi;
snfg = snf*cosos+csf*sinos;
csfg = csf*cosos-snf*sinos;
sn2f2g = snfg*2.*csfg;
r1 = csfg;
cs2f2g = r1*r1*2.-1.;
ecosf = em*csf;
g10 = fm-xmam+em*snf;
rm = pm/(ecosf+1.);
aovr = am/rm;
g13 = xn*aovr;
g14 = -g13*aovr;
dr = g2*(unmth2*cs2f2g-tthmun*3.)-g4*snfg;
diwc = g3*3.*sini*cs2f2g-g5*aynm;
di = diwc*cosi;
/* Update for short period periodics */
sni2du = sini2*(g3*((1.-cosio_2*7.)*.5*sn2f2g-unm5th*3.*g10)-
g5*sini*csfg*(ecosf+2.))-g5*.5f*cosio_2*axnm/cosi2;
xlamb = fm+omgasm+xnodes+g3*((cosi*6.+1.-cosio_2*7.)*
.5*sn2f2g-(unm5th+cosi*2.)*3.*g10)+g5*sini*
(cosi*axnm/(cosi+1.)-(ecosf+2.)*csfg);
y4 = sini2*snfg+csfg*sni2du+snfg*.5*cosi2*di;
y5 = sini2*csfg-snfg*sni2du+csfg*.5*cosi2*di;
rr = rm+dr;
rdot = xn*am*em*snf/beta+g14*(g2*2.*unmth2*sn2f2g+g4*csfg);
r1 = am;
rvdot = xn*(r1*r1)*beta/rm+g14 *
dr+am*g13*sini*diwc;
/* Orientation vectors */
snlamb = sin(xlamb);
cslamb = cos(xlamb);
temp = (y5*snlamb-y4*cslamb)*2.;
ux = y4*temp+cslamb;
vx = y5*temp-snlamb;
temp = (y5*cslamb+y4*snlamb)*2.;
uy = -y4*temp+snlamb;
vy = -y5*temp+cslamb;
temp = sqrt(1.-y4*y4-y5*y5)*2.;
uz = y4*temp;
vz = y5*temp;
/* Position and velocity */
pos[0] = rr*ux*earth_radius_in_km;
pos[1] = rr*uy*earth_radius_in_km;
pos[2] = rr*uz*earth_radius_in_km;
if( vel)
{
vel[0] = (rdot*ux+rvdot*vx)*earth_radius_in_km;
vel[1] = (rdot*uy+rvdot*vy)*earth_radius_in_km;
vel[2] = (rdot*uz+rvdot*vz)*earth_radius_in_km;
}
return( 0);
} /* SGP8 */