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deep.c
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deep.c
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/***************************************************************************\
* PREDICT: A satellite tracking/orbital prediction program *
* Project started 26-May-1991 by John A. Magliacane, KD2BD *
* Last update: 04-May-2018 *
*****************************************************************************
* *
* This program is free software; you can redistribute it and/or modify it *
* under the terms of the GNU General Public License as published by the *
* Free Software Foundation; either version 2 of the License or any later *
* version. *
* *
* This program is distributed in the hope that it will be useful, *
* but WITHOUT ANY WARRANTY; without even the implied warranty of *
* MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU *
* General Public License for more details. *
* *
*****************************************************************************
* See the "CREDITS" file for the names of those who have *
* generously contributed their time, talent, and effort to this project. *
\***************************************************************************/
#include "deep.h"
#include "constants.h"
#include <math.h>
/* Functions for testing and setting/clearing flags used in SGP4/SDP4 code */
static int isFlagSet(int flag)
{
extern int Flags;
return (Flags&flag);
}
static int isFlagClear(int flag)
{
extern int Flags;
return (~Flags&flag);
}
static void SetFlag(int flag)
{
extern int Flags;
Flags|=flag;
}
static void ClearFlag(int flag)
{
extern int Flags;
Flags&=~flag;
}
extern double AcTan(double sinx, double cosx);
extern double FMod2p(double x);
extern double Modulus(double arg1, double arg2);
extern double Julian_Date_of_Year(double year);
static double ThetaG(double epoch, deep_arg_t *deep_arg)
{
/* The function ThetaG calculates the Greenwich Mean Sidereal Time */
/* for an epoch specified in the format used in the NORAD two-line */
/* element sets. It has now been adapted for dates beyond the year */
/* 1999, as described above. The function ThetaG_JD provides the */
/* same calculation except that it is based on an input in the */
/* form of a Julian Date. */
/* Reference: The 1992 Astronomical Almanac, page B6. */
/* Modification to support Y2K */
/* Valid 1957 through 2056 */
double year;
double day=modf(epoch*1E-3,&year)*1E3;
if (year<57)
year+=2000;
else
year+=1900;
const double UT=modf(day,&day);
const double jd=Julian_Date_of_Year(year)+day;
const double TU=(jd-2451545.0)/36525;
double GMST=24110.54841+TU*(8640184.812866+TU*(0.093104-TU*6.2E-6));
GMST=Modulus(GMST+secday*omega_E*UT,secday);
deep_arg->ds50=jd-2433281.5+UT;
return FMod2p(6.3003880987*deep_arg->ds50+1.72944494);
}
void Deep_init(struct deep_state_st *state, const tle_t * tle, deep_arg_t * deep_arg)
{
state->thgr=ThetaG(tle->epoch,deep_arg);
const double eq=tle->eo;
state->xnq=deep_arg->xnodp;
const double aqnv=1/deep_arg->aodp;
state->xqncl=tle->xincl;
const double xmao=tle->xmo;
const double xpidot=deep_arg->omgdot+deep_arg->xnodot;
const double sinq=sin(tle->xnodeo);
const double cosq=cos(tle->xnodeo);
state->omegaq=tle->omegao;
/* Initialize lunar solar terms */
const double day=deep_arg->ds50+18261.5; /* Days since 1900 Jan 0.5 */
if (day!=state->preep)
{
state->preep=day;
const double xnodce=4.5236020-9.2422029E-4*day;
const double stem=sin(xnodce);
const double ctem=cos(xnodce);
state->zcosil=0.91375164-0.03568096*ctem;
state->zsinil=sqrt(1-state->zcosil*state->zcosil);
state->zsinhl=0.089683511*stem/state->zsinil;
state->zcoshl=sqrt(1-state->zsinhl*state->zsinhl);
const double c=4.7199672+0.22997150*day;
const double gam=5.8351514+0.0019443680*day;
state->zmol=FMod2p(c-gam);
double zx=0.39785416*stem/state->zsinil;
const double zy=state->zcoshl*ctem+0.91744867*state->zsinhl*stem;
zx=AcTan(zx,zy);
zx=gam+zx-xnodce;
state->zcosgl=cos(zx);
state->zsingl=sin(zx);
state->zmos=6.2565837+0.017201977*day;
state->zmos=FMod2p(state->zmos);
}
/* Do solar terms */
state->savtsn=1E20;
double zcosg=zcosgs;
double zsing=zsings;
double zcosi=zcosis;
double zsini=zsinis;
double zcosh=cosq;
double zsinh= sinq;
double cc=c1ss;
double zn=zns;
double ze=zes;
const double xnoi=1/state->xnq;
/* Loop breaks when Solar terms are done a second */
/* time, after Lunar terms are initialized */
double se,si,sl,sgh,sh;
for (;;)
{
/* Solar terms done again after Lunar terms are done */
const double a1=zcosg*zcosh+zsing*zcosi*zsinh;
const double a3=-zsing*zcosh+zcosg*zcosi*zsinh;
const double a7=-zcosg*zsinh+zsing*zcosi*zcosh;
const double a8=zsing*zsini;
const double a9=zsing*zsinh+zcosg*zcosi*zcosh;
const double a10=zcosg*zsini;
const double a2=deep_arg->cosio*a7+deep_arg->sinio*a8;
const double a4=deep_arg->cosio*a9+deep_arg->sinio*a10;
const double a5=-deep_arg->sinio*a7+deep_arg->cosio*a8;
const double a6=-deep_arg->sinio*a9+deep_arg->cosio*a10;
const double x1=a1*deep_arg->cosg+a2*deep_arg->sing;
const double x2=a3*deep_arg->cosg+a4*deep_arg->sing;
const double x3=-a1*deep_arg->sing+a2*deep_arg->cosg;
const double x4=-a3*deep_arg->sing+a4*deep_arg->cosg;
const double x5=a5*deep_arg->sing;
const double x6=a6*deep_arg->sing;
const double x7=a5*deep_arg->cosg;
const double x8=a6*deep_arg->cosg;
const double z31=12*x1*x1-3*x3*x3;
const double z32=24*x1*x2-6*x3*x4;
const double z33=12*x2*x2-3*x4*x4;
double z1=3*(a1*a1+a2*a2)+z31*deep_arg->eosq;
double z2=6*(a1*a3+a2*a4)+z32*deep_arg->eosq;
double z3=3*(a3*a3+a4*a4)+z33*deep_arg->eosq;
const double z11=-6*a1*a5+deep_arg->eosq*(-24*x1*x7-6*x3*x5);
const double z12=-6*(a1*a6+a3*a5)+deep_arg->eosq*(-24*(x2*x7+x1*x8)-6*(x3*x6+x4*x5));
const double z13=-6*a3*a6+deep_arg->eosq*(-24*x2*x8-6*x4*x6);
const double z21=6*a2*a5+deep_arg->eosq*(24*x1*x5-6*x3*x7);
const double z22=6*(a4*a5+a2*a6)+deep_arg->eosq*(24*(x2*x5+x1*x6)-6*(x4*x7+x3*x8));
const double 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;
const double s3=cc*xnoi;
const double s2=-0.5*s3/deep_arg->betao;
const double s4=s3*deep_arg->betao;
const double s1=-15*eq*s4;
const double s5=x1*x3+x2*x4;
const double s6=x2*x3+x1*x4;
const double 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 (state->xqncl<5.2359877E-2)
sh=0;
state->ee2=2*s1*s6;
state->e3=2*s1*s7;
state->xi2=2*s2*z12;
state->xi3=2*s2*(z13-z11);
state->xl2=-2*s3*z2;
state->xl3=-2*s3*(z3-z1);
state->xl4=-2*s3*(-21-9*deep_arg->eosq)*ze;
state->xgh2=2*s4*z32;
state->xgh3=2*s4*(z33-z31);
state->xgh4=-18*s4*ze;
state->xh2=-2*s2*z22;
state->xh3=-2*s2*(z23-z21);
if (isFlagSet(LUNAR_TERMS_DONE_FLAG))
break;
/* Do lunar terms */
state->sse=se;
state->ssi=si;
state->ssl=sl;
state->ssh=sh/deep_arg->sinio;
state->ssg=sgh-deep_arg->cosio* state->ssh;
state->se2=state->ee2;
state->si2=state->xi2;
state->sl2=state->xl2;
state->sgh2=state->xgh2;
state->sh2=state->xh2;
state->se3=state->e3;
state->si3=state->xi3;
state->sl3=state->xl3;
state->sgh3=state->xgh3;
state->sh3=state->xh3;
state->sl4=state->xl4;
state->sgh4=state->xgh4;
zcosg=state->zcosgl;
zsing=state->zsingl;
zcosi=state->zcosil;
zsini=state->zsinil;
zcosh=state->zcoshl*cosq+state->zsinhl*sinq;
zsinh=sinq*state->zcoshl-cosq*state->zsinhl;
zn=znl;
cc=c1l;
ze=zel;
SetFlag(LUNAR_TERMS_DONE_FLAG);
}
state->sse=state->sse+se;
state->ssi=state->ssi+si;
state->ssl=state->ssl+sl;
state->ssg=state->ssg+sgh-deep_arg->cosio/deep_arg->sinio*sh;
state->ssh= state->ssh+sh/deep_arg->sinio;
/* Geopotential resonance initialization for 12 hour orbits */
ClearFlag(RESONANCE_FLAG);
ClearFlag(SYNCHRONOUS_FLAG);
double bfact;
if (!((state->xnq<0.0052359877) && (state->xnq>0.0034906585)))
{
if ((state->xnq<0.00826) || (state->xnq>0.00924))
return;
if (eq<0.5)
return;
SetFlag(RESONANCE_FLAG);
const double eoc=eq*deep_arg->eosq;
const double g201=-0.306-(eq-0.64)*0.440;
double g211, g310, g322, g410, g422, g520;
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;
}
double g533, g521, g532;
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;
}
const double sini2=deep_arg->sinio*deep_arg->sinio;
const double f220=0.75*(1+2*deep_arg->cosio+deep_arg->theta2);
const double f221=1.5*sini2;
const double f321=1.875*deep_arg->sinio*(1-2*deep_arg->cosio-3*deep_arg->theta2);
const double f322=-1.875*deep_arg->sinio*(1+2*deep_arg->cosio-3*deep_arg->theta2);
const double f441=35*sini2*f220;
const double f442=39.3750*sini2*sini2;
const double 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));
const double 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));
const double f542=29.53125*deep_arg->sinio*(2-8*deep_arg->cosio+deep_arg->theta2*(-12+8*deep_arg->cosio+10*deep_arg->theta2));
const double f543=29.53125*deep_arg->sinio*(-2-8*deep_arg->cosio+deep_arg->theta2*(12+8*deep_arg->cosio-10*deep_arg->theta2));
const double xno2=state->xnq*state->xnq;
const double ainv2=aqnv*aqnv;
double temp1=3*xno2*ainv2;
double temp=temp1*root22;
state->d2201=temp*f220*g201;
state->d2211=temp*f221*g211;
temp1=temp1*aqnv;
temp=temp1*root32;
state->d3210=temp*f321*g310;
state->d3222=temp*f322*g322;
temp1=temp1*aqnv;
temp=2*temp1*root44;
state->d4410=temp*f441*g410;
state->d4422=temp*f442*g422;
temp1=temp1*aqnv;
temp=temp1*root52;
state->d5220=temp*f522*g520;
state->d5232=temp*f523*g532;
temp=2*temp1*root54;
state->d5421=temp*f542*g521;
state->d5433=temp*f543*g533;
state->xlamo=xmao+tle->xnodeo+tle->xnodeo-state->thgr-state->thgr;
bfact=deep_arg->xmdot+deep_arg->xnodot+deep_arg->xnodot-thdt-thdt;
bfact=bfact+state->ssl+ state->ssh+ state->ssh;
}
else
{
SetFlag(RESONANCE_FLAG);
SetFlag(SYNCHRONOUS_FLAG);
/* Synchronous resonance terms initialization */
const double g200=1+deep_arg->eosq*(-2.5+0.8125*deep_arg->eosq);
const double g310=1+2*deep_arg->eosq;
const double g300=1+deep_arg->eosq*(-6+6.60937*deep_arg->eosq);
const double f220=0.75*(1+deep_arg->cosio)*(1+deep_arg->cosio);
const double f311=0.9375*deep_arg->sinio*deep_arg->sinio*(1+3*deep_arg->cosio)-0.75*(1+deep_arg->cosio);
double f330=1+deep_arg->cosio;
f330=1.875*f330*f330*f330;
state->del1=3*state->xnq*state->xnq*aqnv*aqnv;
state->del2=2*state->del1*f220*g200*q22;
state->del3=3*state->del1*f330*g300*q33*aqnv;
state->del1=state->del1*f311*g310*q31*aqnv;
state->fasx2=0.13130908;
state->fasx4=2.8843198;
state->fasx6=0.37448087;
state->xlamo=xmao+tle->xnodeo+tle->omegao-state->thgr;
bfact=deep_arg->xmdot+xpidot-thdt;
bfact=bfact+state->ssl+state->ssg+ state->ssh;
}
state->xfact=bfact-state->xnq;
/* Initialize integrator */
state->xli=state->xlamo;
state->xni=state->xnq;
state->atime=0;
state->stepp=720;
state->stepn=-720;
state->step2=259200;
return;
}
void Deep_sec(struct deep_state_st *state, const tle_t * tle, deep_arg_t * deep_arg) /* Entrance for deep space secular effects */
{
deep_arg->xll=deep_arg->xll+state->ssl*deep_arg->t;
deep_arg->omgadf=deep_arg->omgadf+state->ssg*deep_arg->t;
deep_arg->xnode=deep_arg->xnode+ state->ssh*deep_arg->t;
deep_arg->em=tle->eo+state->sse*deep_arg->t;
deep_arg->xinc=tle->xincl+state->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;
double delt, ft, xndot, xnddt, xldot;
do
{
if ((state->atime==0) || ((deep_arg->t>=0) && (state->atime<0)) || ((deep_arg->t<0) && (state->atime>=0)))
{
/* Epoch restart */
if (deep_arg->t>=0)
delt=state->stepp;
else
delt=state->stepn;
state->atime=0;
state->xni=state->xnq;
state->xli=state->xlamo;
}
else
{
if (fabs(deep_arg->t)>=fabs(state->atime))
{
if (deep_arg->t>0)
delt=state->stepp;
else
delt=state->stepn;
}
}
do
{
if (fabs(deep_arg->t-state->atime)>=state->stepp)
{
SetFlag(DO_LOOP_FLAG);
ClearFlag(EPOCH_RESTART_FLAG);
}
else
{
ft=deep_arg->t-state->atime;
ClearFlag(DO_LOOP_FLAG);
}
if (fabs(deep_arg->t)<fabs(state->atime))
{
if (deep_arg->t>=0)
delt=state->stepn;
else
delt=state->stepp;
SetFlag(DO_LOOP_FLAG | EPOCH_RESTART_FLAG);
}
/* Dot terms calculated */
if (isFlagSet(SYNCHRONOUS_FLAG))
{
xndot=state->del1*sin(state->xli-state->fasx2)+state->del2*sin(2*(state->xli-state->fasx4))+state->del3*sin(3*(state->xli-state->fasx6));
xnddt=state->del1*cos(state->xli-state->fasx2)+2*state->del2*cos(2*(state->xli-state->fasx4))+3*state->del3*cos(3*(state->xli-state->fasx6));
}
else
{
const double xomi=state->omegaq+deep_arg->omgdot*state->atime;
const double x2omi=xomi+xomi;
const double x2li=state->xli+state->xli;
xndot=state->d2201*sin(x2omi+state->xli-g22)+state->d2211*sin(state->xli-g22)+state->d3210*sin(xomi+state->xli-g32)+state->d3222*sin(-xomi+state->xli-g32)+state->d4410*sin(x2omi+x2li-g44)+state->d4422*sin(x2li-g44)+state->d5220*sin(xomi+state->xli-g52)+state->d5232*sin(-xomi+state->xli-g52)+state->d5421*sin(xomi+x2li-g54)+state->d5433*sin(-xomi+x2li-g54);
xnddt=state->d2201*cos(x2omi+state->xli-g22)+state->d2211*cos(state->xli-g22)+state->d3210*cos(xomi+state->xli-g32)+state->d3222*cos(-xomi+state->xli-g32)+state->d5220*cos(xomi+state->xli-g52)+state->d5232*cos(-xomi+state->xli-g52)+2*(state->d4410*cos(x2omi+x2li-g44)+state->d4422*cos(x2li-g44)+state->d5421*cos(xomi+x2li-g54)+state->d5433*cos(-xomi+x2li-g54));
}
xldot=state->xni+state->xfact;
xnddt=xnddt*xldot;
if (isFlagSet(DO_LOOP_FLAG))
{
state->xli=state->xli+xldot*delt+xndot*state->step2;
state->xni=state->xni+xndot*delt+xnddt*state->step2;
state->atime=state->atime+delt;
}
} while (isFlagSet(DO_LOOP_FLAG) && isFlagClear(EPOCH_RESTART_FLAG));
} while (isFlagSet(DO_LOOP_FLAG) && isFlagSet(EPOCH_RESTART_FLAG));
deep_arg->xn=state->xni+xndot*ft+xnddt*ft*ft*0.5;
const double xl=state->xli+xldot*ft+xndot*ft*ft*0.5;
double temp=-deep_arg->xnode+state->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;
}
void Deep_per(struct deep_state_st *state, const tle_t * tle, deep_arg_t * deep_arg)/* Entrance for lunar-solar periodics */
{
const double sinis=sin(deep_arg->xinc);
const double cosis=cos(deep_arg->xinc);
if (fabs(state->savtsn-deep_arg->t)>=30)
{
state->savtsn=deep_arg->t;
double zm=state->zmos+zns*deep_arg->t;
double zf=zm+2*zes*sin(zm);
double sinzf=sin(zf);
double f2=0.5*sinzf*sinzf-0.25;
double f3=-0.5*sinzf*cos(zf);
const double ses=state->se2*f2+state->se3*f3;
const double sis=state->si2*f2+state->si3*f3;
const double sls=state->sl2*f2+state->sl3*f3+state->sl4*sinzf;
state->sghs=state->sgh2*f2+state->sgh3*f3+state->sgh4*sinzf;
state->shs=state->sh2*f2+state->sh3*f3;
zm=state->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);
const double sel=state->ee2*f2+state->e3*f3;
const double sil=state->xi2*f2+state->xi3*f3;
const double sll=state->xl2*f2+state->xl3*f3+state->xl4*sinzf;
state->sghl=state->xgh2*f2+state->xgh3*f3+state->xgh4*sinzf;
state->sh1=state->xh2*f2+state->xh3*f3;
state->pe=ses+sel;
state->pinc=sis+sil;
state->pl=sls+sll;
}
double pgh=state->sghs+state->sghl;
double ph=state->shs+state->sh1;
deep_arg->xinc=deep_arg->xinc+state->pinc;
deep_arg->em=deep_arg->em+state->pe;
if (state->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+state->pl;
}
else
{
/* Apply periodics with Lyddane modification */
const double sinok=sin(deep_arg->xnode);
const double cosok=cos(deep_arg->xnode);
double alfdp=sinis*sinok;
double betdp=sinis*cosok;
const double dalf=ph*cosok+state->pinc*cosis*sinok;
const double dbet=-ph*sinok+state->pinc*cosis*cosok;
alfdp=alfdp+dalf;
betdp=betdp+dbet;
deep_arg->xnode=FMod2p(deep_arg->xnode);
double xls=deep_arg->xll+deep_arg->omgadf+cosis*deep_arg->xnode;
const double dls=state->pl+pgh-state->pinc*deep_arg->xnode*sinis;
xls=xls+dls;
const double xnoh=deep_arg->xnode;
deep_arg->xnode=AcTan(alfdp,betdp);
/* This is a patch to Lyddane modification */
/* suggested by Rob Matson. */
if (fabs(xnoh-deep_arg->xnode)>pi)
{
if (deep_arg->xnode<xnoh)
deep_arg->xnode+=twopi;
else
deep_arg->xnode-=twopi;
}
deep_arg->xll=deep_arg->xll+state->pl;
deep_arg->omgadf=xls-deep_arg->xll-cos(deep_arg->xinc)*deep_arg->xnode;
}
return;
}