V6
fk524(V6 v)
{
v = m6v6(M, v);
/* restore e-terms */
#ifdef ETERMS
{
double m; /* modulus of position vector */
V3 s0;
V3 s1, s1dot;
V3 r0, r0dot;
V3 r1, r1dot;
/* cache the modulus */
m = v6mod(v);
/* convert the state vector back to a unit vector */
v6GetPos(v) = v3scale(v6GetPos(v), 1/m);
v6GetVel(v) = v3scale(v6GetVel(v), CB/(m*as2r(1)));
/* now proceed with the standard treatment */
r1 = v6GetPos(v);
r1dot = v6GetVel(v);
s1 = v3unit(r1);
s0 = s1;
r0 = v3sum(s1, v3diff(A, v3scale(s0, v3dot(s0, A))));
#ifdef ETERMS_ITERATE
s0 = v3unit(r0);
r0 = v3sum(s1, v3diff(A, v3scale(s0, v3dot(s0, A))));
#endif
v6SetPos(v, r0);
#ifdef ETERMS_VEL
s1dot = v3scale(r1dot, 1/v3mod(r1));
r0dot = v3sum(s1dot, v3diff(Adot, v3scale(s0, v3dot(s0, Adot))));
v6SetVel(v, r0dot);
#endif
/* convert the unit vector back into a state vector */
v6GetPos(v) = v3scale(v6GetPos(v), m);
v6GetVel(v) = v3scale(v6GetVel(v), (m*as2r(1))/CB);
}
#endif
return(v);
}
V6
cat2v6r1(double r, double d, double rd, double dd, double px, double rv, double C)
{
V6 v6; /* the state vector */
double m; /* vector modulus */
/* get the vector the ES way, and scale it manually */
v6 = cat2v6u2(r, d, rd, dd, px, rv, C);
if (px > 0.001) {
m = 1 / as2r(px);
v6GetPos(v6) = v3scale(v6GetPos(v6), m);
v6GetVel(v6) = v3scale(v6GetVel(v6), m*as2r(1)/C);
} else {
m = 1e10;
v6GetPos(v6) = v3scale(v6GetPos(v6), m);
v6GetVel(v6) = v3scale(v6GetVel(v6), m*as2r(1)/C);
}
return(v6);
}
V6
fk425(V6 v)
{
/* ensure cartesian vectors */
v = v6s2c(v);
#ifdef ETERMS
{
double m; /* modulus of position vector */
V3 u0, u0dot;
V3 u1, u1dot;
/* cache the modulus */
m = v6mod(v);
/* convert the state vector back to a unit vector */
v6GetPos(v) = v3scale(v6GetPos(v), 1/m);
v6GetVel(v) = v3scale(v6GetVel(v), CB/(m*as2r(1)));
/* now proceed with the standard treatment */
u0 = v6GetPos(v);
u1 = v3diff(u0, v3diff(A, v3scale(u0, v3dot(u0, A))));
v6SetPos(v, u1);
#ifdef ETERMS_VEL
u0dot = v6GetVel(v);
u1dot = v3diff(u0dot, v3diff(Adot, v3scale(u0, v3dot(u0, Adot))));
v6SetVel(v, u1dot);
#endif
/* convert the unit vector back into a state vector */
v6GetPos(v) = v3scale(v6GetPos(v), m);
v6GetVel(v) = v3scale(v6GetVel(v), (m*as2r(1))/CB);
}
#endif
v = m6v6(M, v);
return(v);
}
void
nutations(double tdt, double *delta_phi, double *delta_eps)
{
double D;
double F;
double T; /* elapsed julian centuries */
double deps; /* nutation in obliquity */
double dphi; /* nutation in longitude */
double lm;
double ls;
double omega;
int i;
#ifdef PLANETARY_TERMS
double V; /* venus */
double S; /* saturn */
double Q; /* mercury */
double M; /* moon */
double J; /* jupiter */
double E; /* earth */
#endif
T = (tdt - J2000) / 36525;
/* in arcseconds */
omega = 450160.280 + (T * (-482890.539 + (T * (7.455 + (T * 0.008)))));
/* convert to radians */
omega = as2r(omega);
/* add in whole revs */
omega -= 5.0 * 2 * M_PI * T;
/* in arcseconds */
lm = 485866.733 + (T * (715922.633 + (T * (31.310 + (T * 0.064)))));
/* convert to radians */
lm = as2r(lm);
/* add in whole revs */
lm += 1325.0 * 2 * M_PI * T;
/* in arcseconds */
ls = 1287099.804 + (T * (1292581.244 + (T * (-0.577 + (T * -0.012)))));
/* convert to radians */
ls = as2r(ls);
/* add in whole revs */
ls += 99.0 * 2 * M_PI * T;
/* in arcseconds */
F = 335778.877 + (T * (295263.137 + (T * (-13.257 + (T * 0.011)))));
/* convert to radians */
F = as2r(F);
/* add in whole revs */
F += 1342.0 * 2 * M_PI * T;
/* in arcseconds */
D = 1072261.307 + (T * (1105601.328 + (T * (-6.891 + (T * 0.019)))));
/* convert to radians */
D = as2r(D);
/* add in whole revs */
D += 1236.0 * 2 * M_PI * T;
/**************************/
/* initialize the outputs */
/**************************/
*delta_phi = 0.0;
*delta_eps = 0.0;
/*********************/
/* do the IAU theory */
/*********************/
dphi = 0.0;
deps = 0.0;
for (i = 0; i < N_IAU; i++) {
double angle;
angle = 0.0;
angle += iau[i].lm * lm;
angle += iau[i].ls * ls;
angle += iau[i].F * F;
angle += iau[i].D * D;
angle += iau[i].omega * omega;
dphi += (iau[i].S0 + (T * iau[i].S1)) * sin(angle);
deps += (iau[i].C0 + (T * iau[i].C1)) * cos(angle);
}
/* convert to arcseconds */
dphi *= 1e-4;
deps *= 1e-4;
/* convert to radians */
dphi = as2r(dphi);
deps = as2r(deps);
/* add this contribution */
*delta_phi += dphi;
*delta_eps += deps;
#ifdef IAU_CORRECTIONS
/**************************/
/* do the IAU corrections */
/**************************/
dphi = 0.0;
deps = 0.0;
for (i = 0; i < N_BIH; i++) {
double angle;
angle = 0.0;
angle += bih[i].lm * lm;
angle += bih[i].ls * ls;
angle += bih[i].F * F;
angle += bih[i].D * D;
angle += bih[i].omega * omega;
dphi += bih[i].LS * sin(angle) + bih[i].LC * cos(angle);
deps += bih[i].OC * cos(angle) + bih[i].OS * sin(angle);
}
/* convert to arcseconds */
dphi *= 1e-5;
deps *= 1e-5;
/* convert to radians */
dphi = as2r(dphi);
deps = as2r(deps);
/* add this contribution */
*delta_phi += dphi;
*delta_eps += deps;
#endif
#ifdef PLANETARY_TERMS
/**************************/
/* do the planetary terms */
/**************************/
Q = d2r(252.3 + T * 149472.7);
V = d2r(179.9 + T * 58517.8);
E = d2r(98.4 + T * 35999.4);
M = d2r(353.3 + T * 19140.3);
J = d2r(32.3 + T * 3034.9);
S = d2r(48.0 + T * 1222.1);
dphi = 0.0;
deps = 0.0;
for (i = 0; i < N_PLAN; i++) {
double angle;
angle = 0.0;
angle += plan[i].lm * lm;
angle += plan[i].F * F;
angle += plan[i].D * D;
angle += plan[i].omega * omega;
angle += plan[i].Q * Q;
angle += plan[i].V * V;
angle += plan[i].E * E;
angle += plan[i].M * M;
angle += plan[i].J * J;
angle += plan[i].S * S;
dphi = plan[i].LS * sin(angle) + plan[i].LC * cos(angle);
deps = plan[i].OC * cos(angle) + plan[i].OS * sin(angle);
}
/* convert to arcseconds */
dphi *= 1e-5;
deps *= 1e-5;
/* convert to radians */
dphi = as2r(dphi);
deps = as2r(deps);
/* add this contribution */
*delta_phi += dphi;
*delta_eps += deps;
#endif
return;
}
double
zetadot(double j1, double j2, int pflag)
{
double T;
double f = CB; /* conversion factor from centuries to days */
double t;
double zetadot;
switch (pflag) {
case PRECESS_NEWCOMB:
T = (j1 - BYEAR2JD(1850)) / CB;
t = (j2 - j1) / CB;
zetadot = 3 * (0.018);
zetadot *= t;
zetadot += 2 * (0.302);
zetadot *= t;
zetadot += (2304.250 + ((T-0.5) * (1.396)));
break;
case PRECESS_ANDOYER:
T = (j1 - BYEAR2JD(1850)) / CB;
t = (j2 - j1) / CB;
zetadot = 3 * (0.017995);
zetadot *= t;
zetadot += 2 * (0.30240 + (T * (-0.000270)));
zetadot *= t;
zetadot += (2303.5545 + (T * (1.39720 + (T * (0.000060)))));
break;
case PRECESS_KINOSHITA:
T = (j1 - BYEAR2JD(1850)) / CB;
t = (j2 - j1) / CB;
zetadot = 3* (0.017996);
zetadot *= t;
zetadot += 2 * (0.30242 + (T * (-0.000269)));
zetadot *= t;
zetadot += (2303.5548 + (T * (1.39720 + (T * (0.000059)))));
break;
case PRECESS_LIESKE:
T = (j1 - BYEAR2JD(1850)) / CB;
t = (j2 - j1) / CB;
zetadot = 3 * (0.0180);
zetadot *= t;
zetadot += 2 * (0.3023 + ((T-0.5) * (-0.000211)));
zetadot *= t;
zetadot += (2304.253 + ((T-0.5) * (1.3972 + ((T-0.5) * (0.000125)))));
break;
case PRECESS_FK5:
default:
T = (j1 - J2000) / CJ;
t = (j2 - j1) / CJ;
f = CJ;
zetadot = 3 * (0.017998);
zetadot *= t;
zetadot += 2 * (0.30188 + (T * (-0.000344)));
zetadot *= t;
zetadot += (2306.2181 + (T * (1.39656 + (T * (-0.000139)))));
break;
}
#ifdef DEBUG
(void)fprintf(stdout, "zetadot(%d): %.15e\n", pflag, zetadot);
#endif
/* convert to radians per day */
zetadot = as2r(zetadot)/f;
return(zetadot);
}
