#include <cmath>
#include "bnctides.h"
#include "bncutils.h"
using namespace std;
// Auxiliary Functions
///////////////////////////////////////////////////////////////////////////
namespace {
static const double RHO_DEG = 180.0 / M_PI;
static const double RHO_SEC = 3600.0 * RHO_DEG;
static const double MJD_J2000 = 51544.5;
double Frac (double x) { return x-floor(x); };
double Modulo (double x, double y) { return y*Frac(x/y); }
Matrix rotX(double Angle) {
const double C = cos(Angle);
const double S = sin(Angle);
Matrix UU(3,3);
UU[0][0] = 1.0; UU[0][1] = 0.0; UU[0][2] = 0.0;
UU[1][0] = 0.0; UU[1][1] = +C; UU[1][2] = +S;
UU[2][0] = 0.0; UU[2][1] = -S; UU[2][2] = +C;
return UU;
}
Matrix rotY(double Angle) {
const double C = cos(Angle);
const double S = sin(Angle);
Matrix UU(3,3);
UU[0][0] = +C; UU[0][1] = 0.0; UU[0][2] = -S;
UU[1][0] = 0.0; UU[1][1] = 1.0; UU[1][2] = 0.0;
UU[2][0] = +S; UU[2][1] = 0.0; UU[2][2] = +C;
return UU;
}
Matrix rotZ(double Angle) {
const double C = cos(Angle);
const double S = sin(Angle);
Matrix UU(3,3);
UU[0][0] = +C; UU[0][1] = +S; UU[0][2] = 0.0;
UU[1][0] = -S; UU[1][1] = +C; UU[1][2] = 0.0;
UU[2][0] = 0.0; UU[2][1] = 0.0; UU[2][2] = 1.0;
return UU;
}
}
// Greenwich Mean Sidereal Time
///////////////////////////////////////////////////////////////////////////
double GMST(double Mjd_UT1) {
const double Secs = 86400.0;
double Mjd_0 = floor(Mjd_UT1);
double UT1 = Secs*(Mjd_UT1-Mjd_0);
double T_0 = (Mjd_0 -MJD_J2000)/36525.0;
double T = (Mjd_UT1-MJD_J2000)/36525.0;
double gmst = 24110.54841 + 8640184.812866*T_0 + 1.002737909350795*UT1
+ (0.093104-6.2e-6*T)*T*T;
return 2.0*M_PI*Frac(gmst/Secs);
}
// Nutation Matrix
///////////////////////////////////////////////////////////////////////////
Matrix NutMatrix(double Mjd_TT) {
const double T = (Mjd_TT-MJD_J2000)/36525.0;
double ls = 2.0*M_PI*Frac(0.993133+ 99.997306*T);
double D = 2.0*M_PI*Frac(0.827362+1236.853087*T);
double F = 2.0*M_PI*Frac(0.259089+1342.227826*T);
double N = 2.0*M_PI*Frac(0.347346- 5.372447*T);
double dpsi = ( -17.200*sin(N) - 1.319*sin(2*(F-D+N)) - 0.227*sin(2*(F+N))
+ 0.206*sin(2*N) + 0.143*sin(ls) ) / RHO_SEC;
double deps = ( + 9.203*cos(N) + 0.574*cos(2*(F-D+N)) + 0.098*cos(2*(F+N))
- 0.090*cos(2*N) ) / RHO_SEC;
double eps = 0.4090928-2.2696E-4*T;
return rotX(-eps-deps)*rotZ(-dpsi)*rotX(+eps);
}
// Precession Matrix
///////////////////////////////////////////////////////////////////////////
Matrix PrecMatrix (double Mjd_1, double Mjd_2) {
const double T = (Mjd_1-MJD_J2000)/36525.0;
const double dT = (Mjd_2-Mjd_1)/36525.0;
double zeta = ( (2306.2181+(1.39656-0.000139*T)*T)+
((0.30188-0.000344*T)+0.017998*dT)*dT )*dT/RHO_SEC;
double z = zeta + ( (0.79280+0.000411*T)+0.000205*dT)*dT*dT/RHO_SEC;
double theta = ( (2004.3109-(0.85330+0.000217*T)*T)-
((0.42665+0.000217*T)+0.041833*dT)*dT )*dT/RHO_SEC;
return rotZ(-z) * rotY(theta) * rotZ(-zeta);
}
// Sun's position
///////////////////////////////////////////////////////////////////////////
ColumnVector Sun(double Mjd_TT) {
const double eps = 23.43929111/RHO_DEG;
const double T = (Mjd_TT-MJD_J2000)/36525.0;
double M = 2.0*M_PI * Frac ( 0.9931267 + 99.9973583*T);
double L = 2.0*M_PI * Frac ( 0.7859444 + M/2.0/M_PI +
(6892.0*sin(M)+72.0*sin(2.0*M)) / 1296.0e3);
double r = 149.619e9 - 2.499e9*cos(M) - 0.021e9*cos(2*M);
ColumnVector r_Sun(3);
r_Sun << r*cos(L) << r*sin(L) << 0.0; r_Sun = rotX(-eps) * r_Sun;
return rotZ(GMST(Mjd_TT))
* NutMatrix(Mjd_TT)
* PrecMatrix(MJD_J2000, Mjd_TT)
* r_Sun;
}
// Moon's position
///////////////////////////////////////////////////////////////////////////
ColumnVector Moon(double Mjd_TT) {
const double eps = 23.43929111/RHO_DEG;
const double T = (Mjd_TT-MJD_J2000)/36525.0;
double L_0 = Frac ( 0.606433 + 1336.851344*T );
double l = 2.0*M_PI*Frac ( 0.374897 + 1325.552410*T );
double lp = 2.0*M_PI*Frac ( 0.993133 + 99.997361*T );
double D = 2.0*M_PI*Frac ( 0.827361 + 1236.853086*T );
double F = 2.0*M_PI*Frac ( 0.259086 + 1342.227825*T );
double dL = +22640*sin(l) - 4586*sin(l-2*D) + 2370*sin(2*D) + 769*sin(2*l)
-668*sin(lp) - 412*sin(2*F) - 212*sin(2*l-2*D)- 206*sin(l+lp-2*D)
+192*sin(l+2*D) - 165*sin(lp-2*D) - 125*sin(D) - 110*sin(l+lp)
+148*sin(l-lp) - 55*sin(2*F-2*D);
double L = 2.0*M_PI * Frac( L_0 + dL/1296.0e3 );
double S = F + (dL+412*sin(2*F)+541*sin(lp)) / RHO_SEC;
double h = F-2*D;
double N = -526*sin(h) + 44*sin(l+h) - 31*sin(-l+h) - 23*sin(lp+h)
+11*sin(-lp+h) - 25*sin(-2*l+F) + 21*sin(-l+F);
double B = ( 18520.0*sin(S) + N ) / RHO_SEC;
double cosB = cos(B);
double R = 385000e3 - 20905e3*cos(l) - 3699e3*cos(2*D-l) - 2956e3*cos(2*D)
-570e3*cos(2*l) + 246e3*cos(2*l-2*D) - 205e3*cos(lp-2*D)
-171e3*cos(l+2*D) - 152e3*cos(l+lp-2*D);
ColumnVector r_Moon(3);
r_Moon << R*cos(L)*cosB << R*sin(L)*cosB << R*sin(B);
r_Moon = rotX(-eps) * r_Moon;
return rotZ(GMST(Mjd_TT))
* NutMatrix(Mjd_TT)
* PrecMatrix(MJD_J2000, Mjd_TT)
* r_Moon;
}
// Tidal Correction
////////////////////////////////////////////////////////////////////////////
void tides(const bncTime& time, ColumnVector& xyz) {
static double lastMjd = 0.0;
static ColumnVector xSun;
static ColumnVector xMoon;
static double rSun;
static double rMoon;
double Mjd = time.mjd() + time.daysec() / 86400.0;
if (Mjd != lastMjd) {
lastMjd = Mjd;
xSun = Sun(Mjd);
rSun = sqrt(DotProduct(xSun,xSun));
xSun /= rSun;
xMoon = Moon(Mjd);
rMoon = sqrt(DotProduct(xMoon,xMoon));
xMoon /= rMoon;
}
double rRec = sqrt(DotProduct(xyz, xyz));
ColumnVector xyzUnit = xyz / rRec;
// Love's Numbers
// --------------
const double H2 = 0.6078;
const double L2 = 0.0847;
// Tidal Displacement
// ------------------
double scSun = DotProduct(xyzUnit, xSun);
double scMoon = DotProduct(xyzUnit, xMoon);
double p2Sun = 3.0 * (H2/2.0-L2) * scSun * scSun - H2/2.0;
double p2Moon = 3.0 * (H2/2.0-L2) * scMoon * scMoon - H2/2.0;
double x2Sun = 3.0 * L2 * scSun;
double x2Moon = 3.0 * L2 * scMoon;
const double gmWGS = 398.6005e12;
const double gms = 1.3271250e20;
const double gmm = 4.9027890e12;
double facSun = gms / gmWGS *
(rRec * rRec * rRec * rRec) / (rSun * rSun * rSun);
double facMoon = gmm / gmWGS *
(rRec * rRec * rRec * rRec) / (rMoon * rMoon * rMoon);
ColumnVector dX = facSun * (x2Sun * xSun + p2Sun * xyzUnit) +
facMoon * (x2Moon * xMoon + p2Moon * xyzUnit);
xyz += dX;
}