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#include <stddef.h>
#include <math.h>
#include "norad.h"
#include "norad_in.h"
#include <stdio.h>
/* For high satellites, we do a numerical integration that uses a */
/* rather drastic set of simplifications. We include the earth, */
/* moon, and sun, but with low-precision approximations for the */
/* positions of those last two. References are to Meeus' _Astronomical */
/* Algorithms_, 2nd edition. Results are in meters from the center */
/* of the earth. */
static void lunar_solar_position( const double jd, double *lunar_xyzr, double *solar_xyzr)
{
const double j2000 = 2451545; /* 1.5 Jan 2000 = JD 2451545 */
const double t_cen = (jd - j2000) / 36525.;
/* Mean lunar longitude, (47.1) */
const double l_prime = 218.3164477 * pi / 180.
+ (481267.88123421 * pi / 180.) * t_cen;
/* Lunar mean anomaly, (47.4) */
const double m_prime = 134.9633964 * pi / 180.
+ (477198.8675055 * pi / 180.) * t_cen;
/* Solar mean longitude, (25.2) */
const double l_solar = 280.46646 * pi / 180.
+ (36000.76983 * pi / 180.) * t_cen;
/* Solar mean anomaly, (47.3) */
const double m_solar = 357.5291092 * pi / 180.
+ (35999.0502909 * pi / 180.) * t_cen;
/* Lunar mean argument of latitude (47.5) */
const double f = 93.2720950 * pi / 180.
+ (483202.0175233 * pi / 180.) * t_cen;
const double lunar_mean_elong = (297.8501921 * pi / 180.)
+ (445267.1114034 * pi / 180.) * t_cen;
const double term2 = 2. * lunar_mean_elong - m_prime;
const double lunar_lon = l_prime /* See table 47.A */
+ (6.288774 * pi / 180.) * sin( m_prime)
+ (1.274027 * pi / 180.) * sin( term2)
+ (0.658314 * pi / 180.) * sin( 2. * lunar_mean_elong)
+ (0.213618 * pi / 180.) * sin( 2. * m_prime)
- (0.185166 * pi / 180.) * sin( m_solar)
- (0.114332 * pi / 180.) * sin( 2. * f);
const double lunar_lat = (5.128122 * pi / 180.) * sin( f)
+ (0.280602 * pi / 180.) * sin( m_prime + f)
+ (0.277693 * pi / 180.) * sin( m_prime - f)
+ (0.173237 * pi / 180.) * sin( 2. * lunar_mean_elong - f);
const double lunar_r = 385000560. /* in meters */
- 20905355. * cos( m_prime)
- 3699111. * cos( term2)
- 2955968 * cos( 2. * lunar_mean_elong)
- 569925 * cos( 2. * m_solar);
const double solar_ecc = 0.016708634; /* (25.4) */
const double solar_lon = l_solar /* (above (25.5)) */
+ (1.914602 * pi / 180.) * sin( m_solar);
const double au_in_meters = 1.495978707e+11;
const double solar_r = au_in_meters * (1. - solar_ecc * cos( m_solar));
double tval;
tval = lunar_r * cos( lunar_lat);
*lunar_xyzr++ = tval * cos( lunar_lon);
*lunar_xyzr++ = tval * sin( lunar_lon);
*lunar_xyzr++ = lunar_r * sin( lunar_lat);
*lunar_xyzr++ = lunar_r;
*solar_xyzr++ = solar_r * cos( solar_lon);
*solar_xyzr++ = solar_r * sin( solar_lon);
*solar_xyzr++ = 0.;
*solar_xyzr++ = solar_r;
}
static void cached_lunar_solar_position( const double jd,
double *lunar_xyzr, double *solar_xyzr)
{
static double curr_jd = 0., lunar[4], solar[4];
size_t i;
if( curr_jd != jd)
{
curr_jd = jd;
lunar_solar_position( jd, lunar, solar);
}
for( i = 0; i < 4; i++)
{
lunar_xyzr[i] = lunar[i];
solar_xyzr[i] = solar[i];
}
}
static const double sin_obliq_2000 = 0.397777155931913701597179975942380896684;
static const double cos_obliq_2000 = 0.917482062069181825744000384639406458043;
static void equatorial_to_ecliptic( double *vect)
{
double temp;
temp = vect[2] * cos_obliq_2000 - vect[1] * sin_obliq_2000;
vect[1] = vect[1] * cos_obliq_2000 + vect[2] * sin_obliq_2000;
vect[2] = temp;
}
static void ecliptic_to_equatorial( double *vect)
{
double temp;
temp = vect[2] * cos_obliq_2000 + vect[1] * sin_obliq_2000;
vect[1] = vect[1] * cos_obliq_2000 - vect[2] * sin_obliq_2000;
vect[2] = temp;
}
static void init_high_ephemeris( double *params, const tle_t *tle)
{
const double *state_vect = &tle->xincl; /* position at epoch, in meters */
size_t i;
for( i = 0; i < 6; i++)
params[i] = state_vect[i];
equatorial_to_ecliptic( params);
equatorial_to_ecliptic( params + 3);
}
#define c1 params[2]
#define c4 params[3]
#define xnodcf params[4]
#define t2cof params[5]
#define deep_arg ((deep_arg_t *)( params + 10))
void DLL_FUNC SDP4_init( double *params, const tle_t *tle)
{
init_t init;
if( tle->ephemeris_type == 'H')
{
init_high_ephemeris( params, tle);
return;
}
sxpx_common_init( params, tle, &init, deep_arg);
deep_arg->sing = sin(tle->omegao);
deep_arg->cosg = cos(tle->omegao);
/* initialize Deep() */
Deep_dpinit( tle, deep_arg);
#ifdef RETAIN_PERTURBATION_VALUES_AT_EPOCH
/* initialize lunisolar perturbations: */
deep_arg->t = 0.; /* added 30 Dec 2003 */
deep_arg->solar_lunar_init_flag = 1;
Deep_dpper( tle, deep_arg);
deep_arg->solar_lunar_init_flag = 0;
#endif
} /*End of SDP4() initialization */
static inline double vector_len( const double *vect)
{
double len2 = vect[0] * vect[0] + vect[1] * vect[1] + vect[2] * vect[2];
return( sqrt( len2));
}
/* Input position is in meters, accel is in m/sec^2 */
static int calc_accel( const double jd, const double *pos, double *accel)
{
size_t i;
const double earth_gm = 3.9860044e+14; /* in m^3/s^2 */
const double solar_gm = 1.3271243994e+20; /* m^3/s^2 */
const double lunar_gm = 4.902798e+12; /* m^3/s^2 */
double r = vector_len( pos);
double accel_factor = -earth_gm / (r * r * r);
double lunar_xyzr[4], solar_xyzr[4];
unsigned obj_idx;
for( i = 0; i < 3; i++)
accel[i] = accel_factor * pos[i];
cached_lunar_solar_position( jd, lunar_xyzr, solar_xyzr);
for( obj_idx = 0; obj_idx < 2; obj_idx++)
{
double *opos = (obj_idx ? lunar_xyzr : solar_xyzr);
double delta[3], d;
const double gm = (obj_idx ? lunar_gm : solar_gm);
double accel_factor2;
accel_factor = gm / (opos[3] * opos[3] * opos[3]);
for( i = 0; i < 3; i++)
delta[i] = opos[i] - pos[i];
d = vector_len( delta);
accel_factor2 = gm / (d * d * d);
for( i = 0; i < 3; i++)
accel[i] -= accel_factor * opos[i] - accel_factor2 * delta[i];
}
return( 0);
}
static int calc_state_vector_deriv( const double jd,
const double state_vect[6], double deriv[6])
{
deriv[0] = state_vect[3];
deriv[1] = state_vect[4];
deriv[2] = state_vect[5];
return( calc_accel( jd, state_vect, deriv + 3));
}
/* NOTE: t_since is in minutes, posn is in km, vel is in km/minutes.
State vector is in meters and m/s. Hence some conversions... */
static int high_ephemeris( double tsince, const tle_t *tle, const double *params,
double *pos, double *vel)
{
const double meters_per_km = 1000.;
const double seconds_per_minute = 60.;
const double seconds_per_day =
seconds_per_minute * minutes_per_day; /* a.k.a. 86400 */
size_t i, j;
double jd = tle->epoch, state_vect[6];
for( i = 0; i < 6; i++)
state_vect[i] = params[i];
tsince /= minutes_per_day; /* input was in minutes; days are */
while( tsince) /* more convenient hereforth */
{
double dt = tsince, dt_in_seconds;
const double max_step = 1.;
double kvects[4][6];
if( tsince > max_step)
dt = max_step;
else if( tsince < -max_step)
dt = -max_step;
dt_in_seconds = dt * seconds_per_day;
calc_state_vector_deriv( jd, state_vect, kvects[0]);
for( j = 1; j < 4; j++)
{
const double step = (j == 3 ? dt_in_seconds : dt_in_seconds * .5);
double tstate[6];
for( i = 0; i < 6; i++)
tstate[i] = state_vect[i] + step * kvects[j - 1][i];
calc_state_vector_deriv( jd + (j == 3 ? dt : dt / 2.),
tstate, kvects[j]);
}
for( i = 0; i < 6; i++)
state_vect[i] += (dt_in_seconds / 6.) *
(kvects[0][i] + 2. * (kvects[1][i] + kvects[2][i]) + kvects[3][i]);
jd += dt;
tsince -= dt;
}
for( i = 0; i < 3; i++)
{
pos[i] = state_vect[i];
vel[i] = state_vect[i + 3];
}
ecliptic_to_equatorial( vel);
ecliptic_to_equatorial( pos);
/* Now, cvt meters to km, meters/second to km/minute: */
for( i = 0; i < 3; i++)
{
pos[i] /= meters_per_km;
vel[i] *= seconds_per_minute / meters_per_km;
}
return( 0);
}
int DLL_FUNC SDP4( const double tsince, const tle_t *tle, const double *params,
double *pos, double *vel)
{
double
a, tempa, tsince_squared,
xl, xnoddf;
if( tle->ephemeris_type == 'H')
{
double unused_vel[3];
return( high_ephemeris( tsince, tle, params, pos, (vel ? vel : unused_vel)));
}
/* Update for secular gravity and atmospheric drag */
deep_arg->omgadf = tle->omegao + deep_arg->omgdot * tsince;
xnoddf = tle->xnodeo + deep_arg->xnodot * tsince;
tsince_squared = tsince*tsince;
deep_arg->xnode = xnoddf + xnodcf * tsince_squared;
deep_arg->xn = deep_arg->xnodp;
/* Update for deep-space secular effects */
deep_arg->xll = tle->xmo + deep_arg->xmdot * tsince;
deep_arg->t = tsince;
Deep_dpsec( tle, deep_arg);
tempa = 1-c1*tsince;
if( deep_arg->xn < 0.)
return( SXPX_ERR_NEGATIVE_XN);
a = pow(xke/deep_arg->xn,two_thirds)*tempa*tempa;
deep_arg->em -= tle->bstar*c4*tsince;
/* Update for deep-space periodic effects */
deep_arg->xll += deep_arg->xnodp * t2cof * tsince_squared;
Deep_dpper( tle, deep_arg);
/* Keeping xinc positive is not really necessary, unless */
/* you're displaying elements and dislike negative inclinations. */
#ifdef KEEP_INCLINATION_POSITIVE
if (deep_arg->xinc < 0.) /* Begin April 1983 errata correction: */
{
deep_arg->xinc = -deep_arg->xinc;
deep_arg->sinio = -deep_arg->sinio;
deep_arg->xnode += pi;
deep_arg->omgadf -= pi;
} /* End April 1983 errata correction. */
#endif
xl = deep_arg->xll + deep_arg->omgadf + deep_arg->xnode;
/* Dundee change: Reset cosio, sinio for new xinc: */
deep_arg->cosio = cos( deep_arg->xinc);
deep_arg->sinio = sin( deep_arg->xinc);
return( sxpx_posn_vel( deep_arg->xnode, a, deep_arg->em, deep_arg->cosio,
deep_arg->sinio, deep_arg->xinc, deep_arg->omgadf,
xl, pos, vel));
} /* SDP4 */
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