//////////////////////////////////////////////////////////////////////////////
// GetPosition()
// This procedure returns the ECI position and velocity for the satellite
// in the orbit at the given number of minutes since the TLE epoch time
// using the NORAD Simplified General Perturbation 4, "deep space" orbit
// model.
//
// tsince - Time in minutes since the TLE epoch (GMT).
//
// To convert the returned ECI position vector to km, multiply each
// component by:
// (Xkmper() / AE).
// To convert the returned ECI velocity vector to km/sec, multiply each
// component by:
// (Xkmper() / AE) * (MIN_PER_DAY / 86400).
cEci cNoradSDP4::GetPosition(double tsince)
{
// Update for secular gravity and atmospheric drag
double xmdf = m_Orbit.MeanAnomaly() + m_xmdot * tsince;
double omgadf = m_Orbit.ArgPerigee() + m_omgdot * tsince;
double xnoddf = m_Orbit.RAAN() + m_xnodot * tsince;
double tsq = tsince * tsince;
double xnode = xnoddf + m_xnodcf * tsq;
double tempa = 1.0 - m_c1 * tsince;
double tempe = m_Orbit.BStar() * m_c4 * tsince;
double templ = m_t2cof * tsq;
double xn = m_Orbit.MeanMotion();
double em;
double xinc;
DeepSecular(&xmdf, &omgadf, &xnode, &em, &xinc, &xn, tsince);
double a = pow(XKE / xn, TWOTHRD) * sqr(tempa);
double e = em - tempe;
double xmam = xmdf + m_Orbit.MeanMotion() * templ;
DeepPeriodics(&e, &xinc, &omgadf, &xnode, &xmam, tsince);
double xl = xmam + omgadf + xnode;
xn = XKE / pow(a, 1.5);
return FinalPosition(xinc, omgadf, e, a, xl, xnode, xn, tsince);
}
//////////////////////////////////////////////////////////////////////////////
// GetPosition()
// This procedure returns the ECI position and velocity for the satellite
// in the orbit at the given number of minutes since the TLE epoch time
// using the NORAD Simplified General Perturbation 4, near earth orbit
// model.
//
// tsince - Time in minutes since the TLE epoch (GMT).
cEciTime cNoradSGP4::GetPosition(double tsince)
{
// For m_perigee less than 220 kilometers, the isimp flag is set and
// the equations are truncated to linear variation in sqrt a and
// quadratic variation in mean anomaly. Also, the m_c3 term, the
// delta omega term, and the delta m term are dropped.
bool isimp = false;
if ((m_Orbit.SemiMajor() * (1.0 - m_Orbit.Eccentricity()) / AE) < (220.0 / XKMPER_WGS72 + AE))
{
isimp = true;
}
double d2 = 0.0;
double d3 = 0.0;
double d4 = 0.0;
double t3cof = 0.0;
double t4cof = 0.0;
double t5cof = 0.0;
if (!isimp)
{
double c1sq = m_c1 * m_c1;
d2 = 4.0 * m_Orbit.SemiMajor() * m_tsi * c1sq;
double temp = d2 * m_tsi * m_c1 / 3.0;
d3 = (17.0 * m_Orbit.SemiMajor() + m_s4) * temp;
d4 = 0.5 * temp * m_Orbit.SemiMajor() * m_tsi *
(221.0 * m_Orbit.SemiMajor() + 31.0 * m_s4) * m_c1;
t3cof = d2 + 2.0 * c1sq;
t4cof = 0.25 * (3.0 * d3 + m_c1 * (12.0 * d2 + 10.0 * c1sq));
t5cof = 0.2 * (3.0 * d4 + 12.0 * m_c1 * d3 + 6.0 *
d2 * d2 + 15.0 * c1sq * (2.0 * d2 + c1sq));
}
// Update for secular gravity and atmospheric drag.
double xmdf = m_Orbit.MeanAnomaly() + m_xmdot * tsince;
double omgadf = m_Orbit.ArgPerigee() + m_omgdot * tsince;
double xnoddf = m_Orbit.RAAN() + m_xnodot * tsince;
double omega = omgadf;
double xmp = xmdf;
double tsq = tsince * tsince;
double xnode = xnoddf + m_xnodcf * tsq;
double tempa = 1.0 - m_c1 * tsince;
double tempe = m_Orbit.BStar() * m_c4 * tsince;
double templ = m_t2cof * tsq;
if (!isimp)
{
double delomg = m_omgcof * tsince;
double delm = m_xmcof * (pow(1.0 + m_eta * cos(xmdf), 3.0) - m_delmo);
double temp = delomg + delm;
xmp = xmdf + temp;
omega = omgadf - temp;
double tcube = tsq * tsince;
double tfour = tsince * tcube;
tempa = tempa - d2 * tsq - d3 * tcube - d4 * tfour;
tempe = tempe + m_Orbit.BStar() * m_c5 * (sin(xmp) - m_sinmo);
templ = templ + t3cof * tcube + tfour * (t4cof + tsince * t5cof);
}
double a = m_Orbit.SemiMajor() * sqr(tempa);
double e = m_Orbit.Eccentricity() - tempe;
double xl = xmp + omega + xnode + m_Orbit.MeanMotion() * templ;
double xn = XKE / pow(a, 1.5);
return FinalPosition(m_Orbit.Inclination(), omgadf, e, a, xl, xnode, xn, tsince);
}
