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#include <math.h>
#include <assert.h>
#include "norad.h"
#include "norad_in.h"
/* params[1] and [6]-[9] were used in earlier implementations, but are
now unused */
#define c2 params[0]
#define c1 params[2]
#define c4 params[3]
#define xnodcf params[4]
#define t2cof params[5]
void sxpall_common_init( const tle_t *tle, deep_arg_t *deep_arg)
{
const double a1 = pow(xke / tle->xno, two_thirds); /* in Earth radii */
double del1, ao, delo, tval;
/* Recover original mean motion (xnodp) and */
/* semimajor axis (aodp) from input elements. */
deep_arg->cosio = cos( tle->xincl);
deep_arg->cosio2 = deep_arg->cosio * deep_arg->cosio;
deep_arg->eosq = tle->eo*tle->eo;
deep_arg->betao2 = 1-deep_arg->eosq;
deep_arg->betao = sqrt(deep_arg->betao2);
tval = 1.5 * ck2 * (3. * deep_arg->cosio2 - 1.) / (deep_arg->betao * deep_arg->betao2);
del1 = tval / (a1 * a1);
ao = a1 * (1. - del1 * (1. / 3. + del1 * ( 1. + 134./81. * del1)));
delo = tval / (ao * ao);
deep_arg->xnodp = tle->xno / (1+delo); /* in radians/minute */
deep_arg->aodp = ao / (1-delo);
}
void sxpx_common_init( double *params, const tle_t *tle,
init_t *init, deep_arg_t *deep_arg)
{
double
eeta, etasq, perige, pinv, pinvsq,
psisq, qoms24, temp1, temp2, temp3,
cosio4, tsi_squared, x3thm1, xhdot1;
sxpall_common_init( tle, deep_arg);
x3thm1 = 3. * deep_arg->cosio2 - 1.;
/* For perigee below 156 km, the values */
/* of s and qoms2t are altered. */
init->s4 = s_const;
qoms24 = qoms2t;
perige = (deep_arg->aodp * (1-tle->eo) - ae) * earth_radius_in_km;
if( perige < 156.)
{
double temp_val, temp_val_squared;
if(perige <= 98.)
init->s4 = 20;
else
init->s4 = perige-78.;
temp_val = (120. - init->s4) * ae / earth_radius_in_km;
temp_val_squared = temp_val * temp_val;
qoms24 = temp_val_squared * temp_val_squared;
init->s4 = init->s4 / earth_radius_in_km + ae;
} /* End of if(perige <= 156) */
pinv = 1. / (deep_arg->aodp * deep_arg->betao2);
pinvsq = pinv * pinv;
init->tsi = 1. / (deep_arg->aodp - init->s4);
init->eta = deep_arg->aodp*tle->eo*init->tsi;
etasq = init->eta*init->eta;
eeta = tle->eo*init->eta;
psisq = fabs(1-etasq);
tsi_squared = init->tsi * init->tsi;
init->coef = qoms24 * tsi_squared * tsi_squared;
init->coef1 = init->coef / pow(psisq,3.5);
c2 = init->coef1 * deep_arg->xnodp * (deep_arg->aodp*(1+1.5*etasq+eeta*
(4+etasq))+0.75*ck2*init->tsi/psisq*x3thm1*(8+3*etasq*(8+etasq)));
c1 = tle->bstar*c2;
deep_arg->sinio = sin(tle->xincl);
c4 = 2*deep_arg->xnodp*init->coef1*deep_arg->aodp*deep_arg->betao2*
(init->eta*(2+0.5*etasq)+tle->eo*(0.5+2*etasq)-2*ck2*init->tsi/
(deep_arg->aodp*psisq)*(-3*x3thm1*(1-2*eeta+etasq*
(1.5-0.5*eeta))+0.75*(1. - deep_arg->cosio2) *(2*etasq-eeta*(1+etasq))*
cos(2*tle->omegao)));
cosio4 = deep_arg->cosio2 * deep_arg->cosio2;
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
+ temp1 * deep_arg->betao* x3thm1 / 2.
+ temp2 * deep_arg->betao*
(13-78*deep_arg->cosio2+137*cosio4) / 16.;
deep_arg->omgdot = -temp1 * (1. - 5 * deep_arg->cosio2) / 2.
+ temp2 * (7-114*deep_arg->cosio2+395*cosio4) / 16.
+ temp3 * (3-36*deep_arg->cosio2+49*cosio4);
xhdot1 = -temp1*deep_arg->cosio;
deep_arg->xnodot = xhdot1+(temp2*(4-19*deep_arg->cosio2) / 2.
+ 2*temp3*(3-7*deep_arg->cosio2))*deep_arg->cosio;
xnodcf = 3.5*deep_arg->betao2*xhdot1*c1;
t2cof = 1.5*c1;
}
inline double centralize_angle( const double ival)
{
double rval = fmod( ival, twopi);
if( rval > pi)
rval -= twopi;
else if( rval < - pi)
rval += twopi;
return( rval);
}
#define MAX_KEPLER_ITER 10
int sxpx_posn_vel( const double xnode, const double a, const double ecc,
const double cosio, const double sinio,
const double xincl, const double omega,
const double xl, double *pos, double *vel)
{
/* Long period periodics */
const double axn = ecc*cos(omega);
double temp = 1/(a*(1.-ecc*ecc));
const double xlcof = .125 * a3ovk2 * sinio * (3+5*cosio)/ (1. + cosio);
const double aycof = 0.25 * a3ovk2 * sinio;
const double xll = temp*xlcof*axn;
const double aynl = temp*aycof;
const double xlt = xl+xll;
const double ayn = ecc*sin(omega)+aynl;
const double elsq = axn*axn+ayn*ayn;
const double capu = centralize_angle( xlt - xnode);
const double chicken_factor_on_eccentricity = 1.e-6;
double epw = capu;
double temp1, temp2;
double ecosE, esinE, pl, r;
double betal;
double u, sinu, cosu, sin2u, cos2u;
double rk, uk, xnodek, xinck;
double sinuk, cosuk, sinik, cosik, sinnok, cosnok, xmx, xmy;
double sinEPW, cosEPW;
double ux, uy, uz;
int i, rval = 0;
/* Dundee changes: items dependent on cosio get recomputed: */
const double cosio_squared = cosio * cosio;
const double x3thm1 = 3.0 * cosio_squared - 1.0;
const double sinio2 = 1.0 - cosio_squared;
const double x7thm1 = 7.0 * cosio_squared - 1.0;
/* Added 29 Mar 2003, modified 26 Sep 2006: extremely */
/* decayed satellites can end up "orbiting" within the */
/* earth. Eventually, the semimajor axis becomes zero, */
/* then negative. In that case, or if the orbit is near */
/* to parabolic, we zero the posn/vel and quit. If the */
/* object has a perigee or apogee indicating a crash, we */
/* just flag it. Revised 28 Oct 2006. */
if( a < 0.)
rval = SXPX_ERR_NEGATIVE_MAJOR_AXIS;
if( elsq > 1. - chicken_factor_on_eccentricity)
rval = SXPX_ERR_NEARLY_PARABOLIC;
for( i = 0; i < 3; i++)
{
pos[i] = 0.;
if( vel)
vel[i] = 0.;
}
if( rval)
return( rval);
if( a * (1. - ecc) < 1. && a * (1. + ecc) < 1.) /* entirely within earth */
rval = SXPX_WARN_ORBIT_WITHIN_EARTH; /* remember, e can be negative */
if( a * (1. - ecc) < 1. || a * (1. + ecc) < 1.) /* perigee within earth */
rval = SXPX_WARN_PERIGEE_WITHIN_EARTH;
/* Solve Kepler's' Equation */
for( i = 0; i < MAX_KEPLER_ITER; i++)
{
const double newton_raphson_epsilon = 1e-12;
double f, fdot, delta_epw;
int do_second_order_newton_raphson = 1;
sinEPW = sin( epw);
cosEPW = cos( epw);
ecosE = axn * cosEPW + ayn * sinEPW;
esinE = axn * sinEPW - ayn * cosEPW;
f = capu - epw + esinE;
if (fabs(f) < newton_raphson_epsilon) break;
fdot = 1. - ecosE;
delta_epw = f / fdot;
if( !i)
{
const double max_newton_raphson = 1.25 * fabs( ecc);
do_second_order_newton_raphson = 0;
if( delta_epw > max_newton_raphson)
delta_epw = max_newton_raphson;
else if( delta_epw < -max_newton_raphson)
delta_epw = -max_newton_raphson;
else
do_second_order_newton_raphson = 1;
}
if( do_second_order_newton_raphson)
delta_epw = f / (fdot + 0.5*esinE*delta_epw);
/* f/(fdot - 0.5*fdotdot * f / fdot) */
epw += delta_epw;
}
if( i == MAX_KEPLER_ITER)
return( SXPX_ERR_CONVERGENCE_FAIL);
/* Short period preliminary quantities */
temp = 1-elsq;
pl = a*temp;
r = a*(1-ecosE);
temp2 = a / r;
betal = sqrt(temp);
temp = esinE/(1+betal);
cosu = temp2 * (cosEPW - axn + ayn * temp);
sinu = temp2 * (sinEPW - ayn - axn * temp);
u = atan2( sinu, cosu);
sin2u = 2*sinu*cosu;
cos2u = 2*cosu*cosu-1;
temp1 = ck2 / pl;
temp2 = temp1 / pl;
/* Update for short periodics */
rk = r*(1-1.5*temp2*betal*x3thm1)+0.5*temp1*sinio2*cos2u;
uk = u-0.25*temp2*x7thm1*sin2u;
xnodek = xnode+1.5*temp2*cosio*sin2u;
xinck = xincl+1.5*temp2*cosio*sinio*cos2u;
/* 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;
/* Position and velocity */
pos[0] = rk * ux * earth_radius_in_km;
pos[1] = rk * uy * earth_radius_in_km;
pos[2] = rk * uz * earth_radius_in_km;
if( vel)
{
const double rdot = xke * sqrt(a) * esinE / r;
const double rfdot = xke * sqrt(pl) / r;
const double xn = xke / (a * sqrt(a));
const double rdotk = rdot - xn * temp1 * sinio2 * sin2u;
const double rfdotk = rfdot + xn * temp1 * (sinio2 * cos2u + 1.5 * x3thm1);
const double vx = xmx * cosuk - cosnok * sinuk;
const double vy = xmy * cosuk - sinnok * sinuk;
const double vz = sinik*cosuk;
vel[0] = (rdotk * ux + rfdotk * vx) * earth_radius_in_km;
vel[1] = (rdotk * uy + rfdotk * vy) * earth_radius_in_km;
vel[2] = (rdotk * uz + rfdotk * vz) * earth_radius_in_km;
}
return( rval);
} /*SGP4*/
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