cNoradSDP4::cNoradSDP4(const cOrbit &orbit) :
cNoradBase(orbit)
{
double sinarg = sin(m_Orbit.ArgPerigee());
double cosarg = cos(m_Orbit.ArgPerigee());
double eqsq = sqr(m_Orbit.Eccentricity());
// Deep space initialization
cJulian jd = m_Orbit.Epoch();
dp_thgr = jd.ToGmst();
double eq = m_Orbit.Eccentricity();
double aqnv = 1.0 / m_Orbit.SemiMajor();
double xmao = m_Orbit.MeanAnomaly();
double xpidot = m_omgdot + m_xnodot;
double sinq = sin(m_Orbit.RAAN());
double cosq = cos(m_Orbit.RAAN());
// Initialize lunar solar terms
double day = jd.FromJan1_12h_1900();
double dpi_xnodce = 4.5236020 - 9.2422029E-4 * day;
double dpi_stem = sin(dpi_xnodce);
double dpi_ctem = cos(dpi_xnodce);
double dpi_zcosil = 0.91375164 - 0.03568096 * dpi_ctem;
double dpi_zsinil = sqrt(1.0 - dpi_zcosil * dpi_zcosil);
double dpi_zsinhl = 0.089683511 *dpi_stem / dpi_zsinil;
double dpi_zcoshl = sqrt(1.0 - dpi_zsinhl * dpi_zsinhl);
double dpi_c = 4.7199672 + 0.22997150 * day;
double dpi_gam = 5.8351514 + 0.0019443680 * day;
dp_zmol = Fmod2p(dpi_c - dpi_gam);
double dpi_zx = 0.39785416 * dpi_stem / dpi_zsinil;
double dpi_zy = dpi_zcoshl * dpi_ctem + 0.91744867 * dpi_zsinhl * dpi_stem;
dpi_zx = AcTan(dpi_zx,dpi_zy) + dpi_gam - dpi_xnodce;
double dpi_zcosgl = cos(dpi_zx);
double dpi_zsingl = sin(dpi_zx);
dp_zmos = 6.2565837 + 0.017201977 * day;
dp_zmos = Fmod2p(dp_zmos);
const double zcosis = 0.91744867;
const double zsinis = 0.39785416;
const double c1ss = 2.9864797e-06;
const double zsings = -0.98088458;
const double zcosgs = 0.1945905;
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;
double zmo = dp_zmos;
double xnoi = 1.0 / m_Orbit.MeanMotion();
double se = 0.0; double si = 0.0; double sl = 0.0;
double sgh = 0.0; double sh = 0.0;
// Apply the solar and lunar terms on the first pass, then re-apply the
// solar terms again on the second pass.
for (int pass = 1; pass <= 2; pass++)
{
// Do solar terms
double a1 = zcosg * zcosh + zsing * zcosi * zsinh;
double a3 = -zsing * zcosh + zcosg * zcosi * zsinh;
double a7 = -zcosg * zsinh + zsing * zcosi * zcosh;
double a8 = zsing * zsini;
double a9 = zsing * zsinh + zcosg * zcosi * zcosh;
double a10 = zcosg * zsini;
double a2 = m_cosio * a7 + m_sinio * a8;
double a4 = m_cosio * a9 + m_sinio * a10;
double a5 = -m_sinio * a7 + m_cosio * a8;
double a6 = -m_sinio * a9 + m_cosio * a10;
double x1 = a1 * cosarg + a2 * sinarg;
double x2 = a3 * cosarg + a4 * sinarg;
double x3 = -a1 * sinarg + a2 * cosarg;
double x4 = -a3 * sinarg + a4 * cosarg;
double x5 = a5 * sinarg;
double x6 = a6 * sinarg;
double x7 = a5 * cosarg;
double x8 = a6 * cosarg;
double z31 = 12.0 * x1 * x1 - 3.0 * x3 * x3;
double z32 = 24.0 * x1 * x2 - 6.0 * x3 * x4;
double z33 = 12.0 * x2 * x2 - 3.0 * x4 * x4;
double z1 = 3.0 * (a1 * a1 + a2 * a2) + z31 * eqsq;
double z2 = 6.0 * (a1 * a3 + a2 * a4) + z32 * eqsq;
double z3 = 3.0 * (a3 * a3 + a4 * a4) + z33 * eqsq;
double z11 = -6.0 * a1 * a5 + eqsq*(-24.0 * x1 * x7 - 6.0 * x3 * x5);
double z12 = -6.0 * (a1 * a6 + a3 * a5) +
eqsq * (-24.0 * (x2 * x7 + x1 * x8) - 6.0 * (x3 * x6 + x4 * x5));
double z13 = -6.0 * a3 * a6 + eqsq * (-24.0 * x2 * x8 - 6.0 * x4 * x6);
double z21 = 6.0 * a2 * a5 + eqsq * (24.0 * x1 * x5 - 6.0 * x3 * x7);
double z22 = 6.0*(a4 * a5 + a2 * a6) +
eqsq * (24.0 * (x2 * x5 + x1 * x6) - 6.0 * (x4 * x7 + x3 * x8));
double z23 = 6.0 * a4 * a6 + eqsq*(24.0 * x2 * x6 - 6.0 * x4 * x8);
z1 = z1 + z1 + m_betao2 * z31;
z2 = z2 + z2 + m_betao2 * z32;
z3 = z3 + z3 + m_betao2 * z33;
double s3 = cc * xnoi;
double s2 = -0.5 * s3 / m_betao;
double s4 = s3 * m_betao;
double s1 = -15.0 * eq * s4;
double s5 = x1 * x3 + x2 * x4;
double s6 = x2 * x3 + x1 * x4;
double s7 = x2 * x4 - x1 * x3;
se = s1 * zn * s5;
si = s2 * zn * (z11 + z13);
sl = -zn * s3 * (z1 + z3 - 14.0 - 6.0 * eqsq);
sgh = s4 * zn * (z31 + z33 - 6.0);
sh = -zn * s2 * (z21 + z23);
if (m_Orbit.Inclination() < 5.2359877E-2)
{
sh = 0.0;
}
dp_ee2 = 2.0 * s1 * s6;
dp_e3 = 2.0 * s1 * s7;
dp_xi2 = 2.0 * s2 * z12;
dp_xi3 = 2.0 * s2 * (z13 - z11);
dp_xl2 = -2.0 * s3 * z2;
dp_xl3 = -2.0 * s3 * (z3 - z1);
dp_xl4 = -2.0 * s3 * (-21.0 - 9.0 * eqsq) * ze;
dp_xgh2 = 2.0 * s4 * z32;
dp_xgh3 = 2.0 * s4 * (z33 - z31);
dp_xgh4 = -18.0 * s4 * ze;
dp_xh2 = -2.0 * s2 * z22;
dp_xh3 = -2.0 * s2 * (z23 - z21);
if (pass == 1)
{
// Do lunar terms
dp_sse = se;
dp_ssi = si;
dp_ssl = sl;
dp_ssh = sh / m_sinio;
dp_ssg = sgh - m_cosio * dp_ssh;
dp_se2 = dp_ee2;
dp_si2 = dp_xi2;
dp_sl2 = dp_xl2;
dp_sgh2 = dp_xgh2;
dp_sh2 = dp_xh2;
dp_se3 = dp_e3;
dp_si3 = dp_xi3;
dp_sl3 = dp_xl3;
dp_sgh3 = dp_xgh3;
dp_sh3 = dp_xh3;
dp_sl4 = dp_xl4;
dp_sgh4 = dp_xgh4;
zcosg = dpi_zcosgl;
zsing = dpi_zsingl;
zcosi = dpi_zcosil;
zsini = dpi_zsinil;
zcosh = dpi_zcoshl * cosq + dpi_zsinhl * sinq;
zsinh = sinq * dpi_zcoshl - cosq * dpi_zsinhl;
zn = znl;
const double c1l = 4.7968065e-07;
cc = c1l;
ze = zel;
zmo = dp_zmol;
}
}
dp_sse = dp_sse + se;
dp_ssi = dp_ssi + si;
dp_ssl = dp_ssl + sl;
dp_ssg = dp_ssg + sgh - m_cosio / m_sinio * sh;
dp_ssh = dp_ssh + sh / m_sinio;
// Geopotential resonance initialization
gp_reso = false;
gp_sync = false;
double g310;
double f220;
double bfact = 0.0;
// Determine if orbit is 24- or 12-hour resonant.
// Mean motion is given in radians per minute.
if ((m_Orbit.MeanMotion() > 0.0034906585) && (m_Orbit.MeanMotion() < 0.0052359877))
{
// Orbit is within the Clarke Belt (period is 24-hour resonant).
// Synchronous resonance terms initialization
gp_reso = true;
gp_sync = true;
double g200 = 1.0 + eqsq * (-2.5 + 0.8125 * eqsq);
g310 = 1.0 + 2.0 * eqsq;
double g300 = 1.0 + eqsq * (-6.0 + 6.60937 * eqsq);
f220 = 0.75 * (1.0 + m_cosio) * (1.0 + m_cosio);
double f311 = 0.9375 * m_sinio * m_sinio * (1.0 + 3 * m_cosio) - 0.75 * (1.0 + m_cosio);
double f330 = 1.0 + m_cosio;
const double q22 = 1.7891679e-06;
const double q31 = 2.1460748e-06;
const double q33 = 2.2123015e-07;
f330 = 1.875 * f330 * f330 * f330;
dp_del1 = 3.0 * m_Orbit.MeanMotion() * m_Orbit.MeanMotion() * aqnv * aqnv;
dp_del2 = 2.0 * dp_del1 * f220 * g200 * q22;
dp_del3 = 3.0 * dp_del1 * f330 * g300 * q33 * aqnv;
dp_del1 = dp_del1 * f311 * g310 * q31 * aqnv;
dp_xlamo = xmao + m_Orbit.RAAN() + m_Orbit.ArgPerigee() - dp_thgr;
bfact = m_xmdot + xpidot - thdt;
bfact = bfact + dp_ssl + dp_ssg + dp_ssh;
}
else if (((m_Orbit.MeanMotion() >= 8.26E-03) && (m_Orbit.MeanMotion() <= 9.24E-03)) && (eq >= 0.5))
{
// Period is 12-hour resonant
gp_reso = true;
double eoc = eq * eqsq;
double g201 = -0.306 - (eq - 0.64) * 0.440;
double g211; double g322;
double g410; double g422;
double g520;
if (eq <= 0.65)
{
g211 = 3.616 - 13.247 * eq + 16.290 * eqsq;
g310 = -19.302 + 117.390 * eq - 228.419 * eqsq + 156.591 * eoc;
g322 = -18.9068 + 109.7927 * eq - 214.6334 * eqsq + 146.5816 * eoc;
g410 = -41.122 + 242.694 * eq - 471.094 * eqsq + 313.953 * eoc;
g422 = -146.407 + 841.880 * eq - 1629.014 * eqsq + 1083.435 * eoc;
g520 = -532.114 + 3017.977 * eq - 5740.0 * eqsq + 3708.276 * eoc;
}
else
{
g211 = -72.099 + 331.819 * eq - 508.738 * eqsq + 266.724 * eoc;
g310 = -346.844 + 1582.851 * eq - 2415.925 * eqsq + 1246.113 * eoc;
g322 = -342.585 + 1554.908 * eq - 2366.899 * eqsq + 1215.972 * eoc;
g410 = -1052.797 + 4758.686 * eq - 7193.992 * eqsq + 3651.957 * eoc;
g422 = -3581.69 + 16178.11 * eq - 24462.77 * eqsq + 12422.52 * eoc;
if (eq <= 0.715)
{
g520 = 1464.74 - 4664.75 * eq + 3763.64 * eqsq;
}
else
{
g520 = -5149.66 + 29936.92 * eq - 54087.36 * eqsq + 31324.56 * eoc;
}
}
double g533;
double g521;
double g532;
if (eq < 0.7)
{
g533 = -919.2277 + 4988.61 * eq - 9064.77 * eqsq + 5542.21 * eoc;
g521 = -822.71072 + 4568.6173 * eq - 8491.4146 * eqsq + 5337.524 * eoc;
g532 = -853.666 + 4690.25 * eq - 8624.77 * eqsq + 5341.4 * eoc;
}
else
{
g533 = -37995.78 + 161616.52 * eq - 229838.2 * eqsq + 109377.94 * eoc;
g521 = -51752.104 + 218913.95 * eq - 309468.16 * eqsq + 146349.42 * eoc;
g532 = -40023.88 + 170470.89 * eq - 242699.48 * eqsq + 115605.82 * eoc;
}
double sini2 = sqr(m_sinio);
double theta2 = sqr(m_cosio);
f220 = 0.75 * (1.0 + 2.0 * m_cosio + theta2);
const double root22 = 1.7891679e-06;
const double root32 = 3.7393792e-07;
const double root44 = 7.3636953e-09;
const double root52 = 1.1428639e-07;
const double root54 = 2.1765803e-09;
double f221 = 1.5 * sini2;
double f321 = 1.875 * m_sinio * (1.0 - 2.0 * m_cosio - 3.0 * theta2);
double f322 = -1.875 * m_sinio * (1.0 + 2.0 * m_cosio - 3.0 * theta2);
double f441 = 35.0 * sini2 * f220;
double f442 = 39.3750 * sini2 * sini2;
double f522 = 9.84375 * m_sinio * (sini2 * (1.0 - 2.0 * m_cosio - 5.0 * theta2) +
0.33333333*(-2.0 + 4.0 * m_cosio + 6.0 * theta2));
double f523 = m_sinio * (4.92187512 * sini2 * (-2.0 - 4.0 * m_cosio + 10.0 * theta2) +
6.56250012 * (1.0 + 2.0 * m_cosio - 3.0 * theta2));
double f542 = 29.53125 * m_sinio * ( 2.0 - 8.0 * m_cosio + theta2 * (-12.0 + 8.0 * m_cosio + 10.0 * theta2));
double f543 = 29.53125 * m_sinio * (-2.0 - 8.0 * m_cosio + theta2 * ( 12.0 + 8.0 * m_cosio - 10.0 * theta2));
double xno2 = m_Orbit.MeanMotion() * m_Orbit.MeanMotion();
double ainv2 = aqnv * aqnv;
double temp1 = 3.0 * xno2 * ainv2;
double temp = temp1 * root22;
dp_d2201 = temp * f220 * g201;
dp_d2211 = temp * f221 * g211;
temp1 = temp1 * aqnv;
temp = temp1 * root32;
dp_d3210 = temp * f321 * g310;
dp_d3222 = temp * f322 * g322;
temp1 = temp1 * aqnv;
temp = 2.0 * temp1 * root44;
dp_d4410 = temp * f441 * g410;
dp_d4422 = temp * f442 * g422;
temp1 = temp1 * aqnv;
temp = temp1 * root52;
dp_d5220 = temp * f522 * g520;
dp_d5232 = temp * f523 * g532;
temp = 2.0 * temp1 * root54;
dp_d5421 = temp * f542 * g521;
dp_d5433 = temp * f543 * g533;
dp_xlamo = xmao + m_Orbit.RAAN() + m_Orbit.RAAN() - dp_thgr - dp_thgr;
bfact = m_xmdot + m_xnodot + m_xnodot - thdt - thdt;
bfact = bfact + dp_ssl + dp_ssh + dp_ssh;
}
if (gp_reso || gp_sync)
{
dp_xfact = bfact - m_Orbit.MeanMotion();
// Initialize integrator
dp_xli = dp_xlamo;
dp_xni = m_Orbit.MeanMotion();
dp_atime = 0.0;
dp_stepp = 720.0;
dp_stepn = -720.0;
dp_step2 = 259200.0;
}
else
{
dp_xfact = 0.0;
dp_xli = 0.0;
dp_xni = 0.0;
dp_atime = 0.0;
dp_stepp = 0.0;
dp_stepn = 0.0;
dp_step2 = 0.0;
}
}
bool cNoradBase::FinalPosition(double incl, double omega,
double e, double a,
double xl, double xnode,
double xn, double tsince,
cEci &eci)
{
if ((e * e) > 1.0)
{
// error in satellite data
return false;
}
double beta = sqrt(1.0 - e * e);
// Long period periodics
double axn = e * cos(omega);
double temp = 1.0 / (a * beta * beta);
double xll = temp * m_xlcof * axn;
double aynl = temp * m_aycof;
double xlt = xl + xll;
double ayn = e * sin(omega) + aynl;
// Solve Kepler's Equation
double capu = Fmod2p(xlt - xnode);
double temp2 = capu;
double temp3 = 0.0;
double temp4 = 0.0;
double temp5 = 0.0;
double temp6 = 0.0;
double sinepw = 0.0;
double cosepw = 0.0;
bool fDone = false;
for (int i = 1; (i <= 10) && !fDone; i++)
{
sinepw = sin(temp2);
cosepw = cos(temp2);
temp3 = axn * sinepw;
temp4 = ayn * cosepw;
temp5 = axn * cosepw;
temp6 = ayn * sinepw;
double epw = (capu - temp4 + temp3 - temp2) /
(1.0 - temp5 - temp6) + temp2;
if (fabs(epw - temp2) <= E6A)
fDone = true;
else
temp2 = epw;
}
// Short period preliminary quantities
double ecose = temp5 + temp6;
double esine = temp3 - temp4;
double elsq = axn * axn + ayn * ayn;
temp = 1.0 - elsq;
double pl = a * temp;
double r = a * (1.0 - ecose);
double temp1 = 1.0 / r;
double rdot = XKE * sqrt(a) * esine * temp1;
double rfdot = XKE * sqrt(pl) * temp1;
temp2 = a * temp1;
double betal = sqrt(temp);
temp3 = 1.0 / (1.0 + betal);
double cosu = temp2 * (cosepw - axn + ayn * esine * temp3);
double sinu = temp2 * (sinepw - ayn - axn * esine * temp3);
double u = AcTan(sinu, cosu);
double sin2u = 2.0 * sinu * cosu;
double cos2u = 2.0 * cosu * cosu - 1.0;
temp = 1.0 / pl;
temp1 = CK2 * temp;
temp2 = temp1 * temp;
// Update for short periodics
double rk = r * (1.0 - 1.5 * temp2 * betal * m_x3thm1) +
0.5 * temp1 * m_x1mth2 * cos2u;
double uk = u - 0.25 * temp2 * m_x7thm1 * sin2u;
double xnodek = xnode + 1.5 * temp2 * m_cosio * sin2u;
double xinck = incl + 1.5 * temp2 * m_cosio * m_sinio * cos2u;
double rdotk = rdot - xn * temp1 * m_x1mth2 * sin2u;
double rfdotk = rfdot + xn * temp1 * (m_x1mth2 * cos2u + 1.5 * m_x3thm1);
// Orientation vectors
double sinuk = sin(uk);
double cosuk = cos(uk);
double sinik = sin(xinck);
double cosik = cos(xinck);
double sinnok = sin(xnodek);
double cosnok = cos(xnodek);
double xmx = -sinnok * cosik;
double xmy = cosnok * cosik;
double ux = xmx * sinuk + cosnok * cosuk;
double uy = xmy * sinuk + sinnok * cosuk;
double uz = sinik * sinuk;
double vx = xmx * cosuk - cosnok * sinuk;
double vy = xmy * cosuk - sinnok * sinuk;
double vz = sinik * cosuk;
// Position
double x = rk * ux;
double y = rk * uy;
double z = rk * uz;
cVector vecPos(x, y, z);
// Validate on altitude
double altKm = (vecPos.Magnitude() * (XKMPER_WGS72 / AE));
if ((altKm < XKMPER_WGS72) || (altKm > (2 * GEOSYNC_ALT)))
return false;
// Velocity
double xdot = rdotk * ux + rfdotk * vx;
double ydot = rdotk * uy + rfdotk * vy;
double zdot = rdotk * uz + rfdotk * vz;
cVector vecVel(xdot, ydot, zdot);
cJulian gmt = m_Orbit.Epoch();
gmt.addMin(tsince);
eci = cEci(vecPos, vecVel, gmt);
return true;
}
