/* * Unit SGP_Obs * Author: Dr TS Kelso * Original Version: 1992 Jun 02 * Current Revision: 1992 Sep 28 * Version: 1.40 * Copyright: 1992, All Rights Reserved * * Ported to C by: Neoklis Kyriazis April 9 2001 */ #include "sgp4sdp4.h" /* Procedure Calculate_User_PosVel passes the user's geodetic position */ /* and the time of interest and returns the ECI position and velocity */ /* of the observer. The velocity calculation assumes the geodetic */ /* position is stationary relative to the earth's surface. */ void Calculate_User_PosVel(double _time, geodetic_t *geodetic, vector_t *obs_pos, vector_t *obs_vel) { /* Reference: The 1992 Astronomical Almanac, page K11. */ double c,sq,achcp; geodetic->theta = FMod2p(ThetaG_JD(_time) + geodetic->lon);/*LMST*/ c = 1/sqrt(1 + __f*(__f - 2)*Sqr(sin(geodetic->lat))); sq = Sqr(1 - __f)*c; achcp = (xkmper*c + geodetic->alt)*cos(geodetic->lat); obs_pos->x = achcp*cos(geodetic->theta);/*kilometers*/ obs_pos->y = achcp*sin(geodetic->theta); obs_pos->z = (xkmper*sq + geodetic->alt)*sin(geodetic->lat); obs_vel->x = -mfactor*obs_pos->y;/*kilometers/second*/ obs_vel->y = mfactor*obs_pos->x; obs_vel->z = 0; SgpMagnitude(obs_pos); SgpMagnitude(obs_vel); } /*Procedure Calculate_User_PosVel*/ /*------------------------------------------------------------------*/ /* Procedure Calculate_LatLonAlt will calculate the geodetic */ /* position of an object given its ECI position pos and time. */ /* It is intended to be used to determine the ground track of */ /* a satellite. The calculations assume the earth to be an */ /* oblate spheroid as defined in WGS '72. */ void Calculate_LatLonAlt(double _time, vector_t *pos, geodetic_t *geodetic) { /* Reference: The 1992 Astronomical Almanac, page K12. */ double r,e2,phi,c; geodetic->theta = AcTan(pos->y,pos->x);/*radians*/ geodetic->lon = FMod2p(geodetic->theta - ThetaG_JD(_time));/*radians*/ r = sqrt(Sqr(pos->x) + Sqr(pos->y)); e2 = __f*(2 - __f); geodetic->lat = AcTan(pos->z,r);/*radians*/ do { phi = geodetic->lat; c = 1/sqrt(1 - e2*Sqr(sin(phi))); geodetic->lat = AcTan(pos->z + xkmper*c*e2*sin(phi),r); } while(fabs(geodetic->lat - phi) >= 1E-10); geodetic->alt = r/cos(geodetic->lat) - xkmper*c;/*kilometers*/ if( geodetic->lat > pio2 ) geodetic->lat -= twopi; } /*Procedure Calculate_LatLonAlt*/ /*------------------------------------------------------------------*/ /* The procedures Calculate_Obs and Calculate_RADec calculate */ /* the *topocentric* coordinates of the object with ECI position, */ /* {pos}, and velocity, {vel}, from location {geodetic} at {time}. */ /* The {obs_set} returned for Calculate_Obs consists of azimuth, */ /* elevation, range, and range rate (in that order) with units of */ /* radians, radians, kilometers, and kilometers/second, respectively. */ /* The WGS '72 geoid is used and the effect of atmospheric refraction */ /* (under standard temperature and pressure) is incorporated into the */ /* elevation calculation; the effect of atmospheric refraction on */ /* range and range rate has not yet been quantified. */ /* The {obs_set} for Calculate_RADec consists of right ascension and */ /* declination (in that order) in radians. Again, calculations are */ /* based on *topocentric* position using the WGS '72 geoid and */ /* incorporating atmospheric refraction. */ void Calculate_Obs(double _time, vector_t *pos, vector_t *vel, geodetic_t *geodetic, vector_t *obs_set) { double sin_lat,cos_lat, sin_theta,cos_theta, el,azim, top_s,top_e,top_z; vector_t obs_pos,obs_vel,range,rgvel; Calculate_User_PosVel(_time, geodetic, &obs_pos, &obs_vel); range.x = pos->x - obs_pos.x; range.y = pos->y - obs_pos.y; range.z = pos->z - obs_pos.z; rgvel.x = vel->x - obs_vel.x; rgvel.y = vel->y - obs_vel.y; rgvel.z = vel->z - obs_vel.z; SgpMagnitude(&range); sin_lat = sin(geodetic->lat); cos_lat = cos(geodetic->lat); sin_theta = sin(geodetic->theta); cos_theta = cos(geodetic->theta); top_s = sin_lat*cos_theta*range.x + sin_lat*sin_theta*range.y - cos_lat*range.z; top_e = -sin_theta*range.x + cos_theta*range.y; top_z = cos_lat*cos_theta*range.x + cos_lat*sin_theta*range.y + sin_lat*range.z; azim = atan(-top_e/top_s); /*Azimuth*/ if( top_s > 0 ) azim = azim + pi; if( azim < 0 ) azim = azim + twopi; el = ArcSin(top_z/range.w); obs_set->x = azim; /* Azimuth (radians) */ obs_set->y = el; /* Elevation (radians)*/ obs_set->z = range.w; /* Range (kilometers) */ /*Range Rate (kilometers/second)*/ obs_set->w = Dot(&range, &rgvel)/range.w; /* Corrections for atmospheric refraction */ /* Reference: Astronomical Algorithms by Jean Meeus, pp. 101-104 */ /* Correction is meaningless when apparent elevation is below horizon */ obs_set->y = obs_set->y + Radians((1.02/tan(Radians(Degrees(el)+ 10.3/(Degrees(el)+5.11))))/60); if( obs_set->y >= 0 ) SetFlag(VISIBLE_FLAG); else { obs_set->y = el; /*Reset to true elevation*/ ClearFlag(VISIBLE_FLAG); } /*else*/ } /*Procedure Calculate_Obs*/ /*------------------------------------------------------------------*/ void Calculate_RADec( double _time, vector_t *pos, vector_t *vel, geodetic_t *geodetic, vector_t *obs_set) { /* Reference: Methods of Orbit Determination by */ /* Pedro Ramon Escobal, pp. 401-402 */ double phi,theta,sin_theta,cos_theta,sin_phi,cos_phi, az,el,Lxh,Lyh,Lzh,Sx,Ex,Zx,Sy,Ey,Zy,Sz,Ez,Zz, Lx,Ly,Lz,cos_delta,sin_alpha,cos_alpha; Calculate_Obs(_time,pos,vel,geodetic,obs_set); /* if( isFlagSet(VISIBLE_FLAG) ) {*/ az = obs_set->x; el = obs_set->y; phi = geodetic->lat; theta = FMod2p(ThetaG_JD(_time) + geodetic->lon); sin_theta = sin(theta); cos_theta = cos(theta); sin_phi = sin(phi); cos_phi = cos(phi); Lxh = -cos(az)*cos(el); Lyh = sin(az)*cos(el); Lzh = sin(el); Sx = sin_phi*cos_theta; Ex = -sin_theta; Zx = cos_theta*cos_phi; Sy = sin_phi*sin_theta; Ey = cos_theta; Zy = sin_theta*cos_phi; Sz = -cos_phi; Ez = 0; Zz = sin_phi; Lx = Sx*Lxh + Ex*Lyh + Zx*Lzh; Ly = Sy*Lxh + Ey*Lyh + Zy*Lzh; Lz = Sz*Lxh + Ez*Lyh + Zz*Lzh; obs_set->y = ArcSin(Lz); /*Declination (radians)*/ cos_delta = sqrt(1 - Sqr(Lz)); sin_alpha = Ly/cos_delta; cos_alpha = Lx/cos_delta; obs_set->x = AcTan(sin_alpha,cos_alpha); /*Right Ascension (radians)*/ obs_set->x = FMod2p(obs_set->x); /*}*/ /*if*/ } /* Procedure Calculate_RADec */ /*------------------------------------------------------------------*/