/// <summary>
/// Calculate satellite ECI position/velocity for a given time.
/// </summary>
/// <param name="tsince">Target time, in minutes-past-epoch format.</param>
/// <returns>AU-based position/velocity ECI coordinates.</returns>
/// <remarks>
/// 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.
/// The algorithm uses NORAD's Simplified General Perturbation 4 deep space
/// orbit model.
/// </remarks>
public override EciTime GetPosition(double tsince)
{
// Update for secular gravity and atmospheric drag
double xmdf = Orbit.MeanAnomaly + m_xmdot * tsince;
double omgadf = Orbit.ArgPerigee + m_omgdot * tsince;
double xnoddf = Orbit.RAAN + m_xnodot * tsince;
double tsq = tsince * tsince;
double xnode = xnoddf + m_xnodcf * tsq;
double tempa = 1.0 - m_c1 * tsince;
double tempe = Orbit.BStar * m_c4 * tsince;
double templ = m_t2cof * tsq;
double xn = m_xnodp;
double em = 0.0;
double xinc = 0.0;
DeepSecular(ref xmdf, ref omgadf, ref xnode, ref em, ref xinc, ref xn, ref tsince);
double a = Math.Pow(Globals.Xke / xn, 2.0 / 3.0) * Globals.Sqr(tempa);
double e = em - tempe;
double xmam = xmdf + m_xnodp * templ;
DeepPeriodics(ref e, ref xinc, ref omgadf, ref xnode, ref xmam, tsince);
double xl = xmam + omgadf + xnode;
xn = Globals.Xke / Math.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, "deep space" orbit
// model.
//
// tsince - Time in minutes since the TLE epoch (GMT).
// pECI - pointer to location to store the ECI data.
// To convert the returned ECI position vector to km,
// multiply each component by:
// (XKMMPER / Globals.AE).
// To convert the returned ECI velocity vector to km/sec,
// multiply each component by:
// (XKMPER / Globals.AE) * (MIN_PER_DAY / 86400).
public override Eci getPosition(double tsince)
{
DeepInit(ref m_eosq, ref m_sinio, ref m_cosio, ref m_betao, ref m_aodp, ref m_theta2,
ref m_sing, ref m_cosg, ref m_betao2, ref m_xmdot, ref m_omgdot, ref m_xnodot);
// Update for secular gravity and atmospheric drag
double xmdf = m_Orbit.mnAnomaly() + 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_xnodp;
double em = 0.0;
double xinc = 0.0;
DeepSecular(ref xmdf, ref omgadf, ref xnode, ref em, ref xinc, ref xn, ref tsince);
double a = Math.Pow(Globals.XKE / xn, Globals.TWOTHRD) * Globals.Sqr(tempa);
double e = em - tempe;
double xmam = xmdf + m_xnodp * templ;
DeepPeriodics(ref e, ref xinc, ref omgadf, ref xnode, ref xmam);
double xl = xmam + omgadf + xnode;
xn = Globals.XKE / Math.Pow(a, 1.5);
return(FinalPosition(xinc, omgadf, e, a, xl, xnode, xn, tsince));
}
// ///////////////////////////////////////////////////////////////////
// Calculate the ECI coordinates of the location "geo" at time "date".
// Assumes geo coordinates are km-based.
// Assumes the earth is an oblate spheroid as defined in WGS '72.
// Reference: The 1992 Astronomical Almanac, page K11
// Reference: www.celestrak.com (Dr. TS Kelso)
public Eci(CoordGeo geo, Julian date)
{
m_VectorUnits = VectorUnits.Km;
double mfactor = Globals.TWOPI * (Globals.OMEGA_E / Globals.SEC_PER_DAY);
double lat = geo.Latitude;
double lon = geo.Longitude;
double alt = geo.Altitude;
// Calculate Local Mean Sidereal Time (theta)
double theta = date.toLMST(lon);
double c = 1.0 / Math.Sqrt(1.0 + Globals.F * (Globals.F - 2.0) * Globals.Sqr(Math.Sin(lat)));
double s = Globals.Sqr(1.0 - Globals.F) * c;
double achcp = (Globals.XKMPER * c + alt) * Math.Cos(lat);
m_Date = date;
m_Position = new Vector();
m_Position.X = achcp * Math.Cos(theta); // km
m_Position.Y = achcp * Math.Sin(theta); // km
m_Position.Z = (Globals.XKMPER * s + alt) * Math.Sin(lat); // km
m_Position.W = Math.Sqrt(Globals.Sqr(m_Position.X) +
Globals.Sqr(m_Position.Y) +
Globals.Sqr(m_Position.Z)); // range, km
m_Velocity = new Vector();
m_Velocity.X = -mfactor * m_Position.Y; // km / sec
m_Velocity.Y = mfactor * m_Position.X;
m_Velocity.Z = 0.0;
m_Velocity.W = Math.Sqrt(Globals.Sqr(m_Velocity.X) + // range rate km/sec^2
Globals.Sqr(m_Velocity.Y));
}
// ///////////////////////////////////////////////////////////////////////////
// Return the corresponding geodetic position (based on the current ECI
// coordinates/Julian date).
// Assumes the earth is an oblate spheroid as defined in WGS '72.
// Side effects: Converts the position and velocity vectors to km-based units.
// Reference: The 1992 Astronomical Almanac, page K12.
// Reference: www.celestrak.com (Dr. TS Kelso)
public CoordGeo toGeo()
{
ae2km(); // Vectors must be in kilometer-based units
double theta = Globals.AcTan(m_Position.Y, m_Position.X);
double lon = (theta - m_Date.toGMST()) % Globals.TWOPI;
if (lon < 0.0)
{
lon += Globals.TWOPI; // "wrap" negative modulo
}
double r = Math.Sqrt(Globals.Sqr(m_Position.X) + Globals.Sqr(m_Position.Y));
double e2 = Globals.F * (2.0 - Globals.F);
double lat = Globals.AcTan(m_Position.Z, r);
const double DELTA = 1.0e-07;
double phi;
double c;
do
{
phi = lat;
c = 1.0 / Math.Sqrt(1.0 - e2 * Globals.Sqr(Math.Sin(phi)));
lat = Globals.AcTan(m_Position.Z + Globals.XKMPER * c * e2 * Math.Sin(phi), r);
}while (Math.Abs(lat - phi) > DELTA);
double alt = r / Math.Cos(lat) - Globals.XKMPER * c;
return(new CoordGeo(lat, lon, alt)); // radians, radians, kilometers
}
/// <summary>
/// Creates a instance of the class from geodetic coordinates.
/// </summary>
/// <param name="geo">The geocentric coordinates.</param>
/// <param name="date">The Julian date.</param>
/// <remarks>
/// Assumes the Earth is an oblate spheroid.
/// Reference: The 1992 Astronomical Almanac, page K11
/// Reference: www.celestrak.com (Dr. T.S. Kelso)
/// </remarks>
public Eci(Geo geo, Julian date)
{
double lat = geo.LatitudeRad;
double lon = geo.LongitudeRad;
double alt = geo.Altitude;
// Calculate Local Mean Sidereal Time (theta)
double theta = date.ToLmst(lon);
double c = 1.0 / Math.Sqrt(1.0 + Globals.F * (Globals.F - 2.0) *
Globals.Sqr(Math.Sin(lat)));
double s = Globals.Sqr(1.0 - Globals.F) * c;
double achcp = (Globals.Xkmper * c + alt) * Math.Cos(lat);
Position = new Vector();
Position.X = achcp * Math.Cos(theta); // km
Position.Y = achcp * Math.Sin(theta); // km
Position.Z = (Globals.Xkmper * s + alt) * Math.Sin(lat); // km
Position.W = Math.Sqrt(Globals.Sqr(Position.X) +
Globals.Sqr(Position.Y) +
Globals.Sqr(Position.Z)); // range, km
Velocity = new Vector();
double mfactor = Globals.TwoPi * (Globals.OmegaE / Globals.SecPerDay);
Velocity.X = -mfactor * Position.Y; // km / sec
Velocity.Y = mfactor * Position.X; // km / sec
Velocity.Z = 0.0; // km / sec
Velocity.W = Math.Sqrt(Globals.Sqr(Velocity.X) + // range rate km/sec^2
Globals.Sqr(Velocity.Y));
}
/// <summary>
/// Creates a new instance of the class given XYZ coordinates.
/// </summary>
private Geo(Vector pos, double theta)
{
theta = theta % Globals.TwoPi;
if (theta < 0.0)
{
// "wrap" negative modulo
theta += Globals.TwoPi;
}
double r = Math.Sqrt(Globals.Sqr(pos.X) + Globals.Sqr(pos.Y));
double e2 = Globals.F * (2.0 - Globals.F);
double lat = Globals.AcTan(pos.Z, r);
const double DELTA = 1.0e-07;
double phi;
double c;
do
{
phi = lat;
c = 1.0 / Math.Sqrt(1.0 - e2 * Globals.Sqr(Math.Sin(phi)));
lat = Globals.AcTan(pos.Z + Globals.Xkmper * c * e2 * Math.Sin(phi), r);
}while(Math.Abs(lat - phi) > DELTA);
LatitudeRad = lat;
LongitudeRad = theta;
Altitude = (r / Math.Cos(lat)) - Globals.Xkmper * c;
}
/// <summary>
/// Standard constructor.
/// </summary>
/// <param name="tle">Two-line element orbital parameters.</param>
public Orbit(Tle tle)
{
Tle = tle;
Epoch = Tle.EpochJulian;
m_Inclination = GetRad(Tle.Field.Inclination);
m_Eccentricity = Tle.GetField(Tle.Field.Eccentricity);
m_RAAN = GetRad(Tle.Field.Raan);
m_ArgPerigee = GetRad(Tle.Field.ArgPerigee);
m_BStar = Tle.GetField(Tle.Field.BStarDrag);
m_Drag = Tle.GetField(Tle.Field.MeanMotionDt);
m_MeanAnomaly = GetRad(Tle.Field.MeanAnomaly);
m_TleMeanMotion = Tle.GetField(Tle.Field.MeanMotion);
// Recover the original mean motion and semimajor axis from the
// input elements.
double mm = TleMeanMotion;
double rpmin = mm * Globals.TwoPi / Globals.MinPerDay; // rads per minute
double a1 = Math.Pow(Globals.Xke / rpmin, 2.0 / 3.0);
double e = Eccentricity;
double i = Inclination;
double temp = (1.5 * Globals.Ck2 * (3.0 * Globals.Sqr(Math.Cos(i)) - 1.0) /
Math.Pow(1.0 - e * e, 1.5));
double delta1 = temp / (a1 * a1);
double a0 = a1 *
(1.0 - delta1 *
((1.0 / 3.0) + delta1 *
(1.0 + 134.0 / 81.0 * delta1)));
double delta0 = temp / (a0 * a0);
m_rmMeanMotionRec = rpmin / (1.0 + delta0);
m_aeAxisSemiMajorRec = a0 / (1.0 - delta0);
m_aeAxisSemiMinorRec = m_aeAxisSemiMajorRec * Math.Sqrt(1.0 - (e * e));
m_kmPerigeeRec = Globals.Xkmper * (m_aeAxisSemiMajorRec * (1.0 - e) - Globals.Ae);
m_kmApogeeRec = Globals.Xkmper * (m_aeAxisSemiMajorRec * (1.0 + e) - Globals.Ae);
if (Period.TotalMinutes >= 225.0)
{
// SDP4 - period >= 225 minutes.
NoradModel = new NoradSDP4(this);
}
else
{
// SGP4 - period < 225 minutes
NoradModel = new NoradSGP4(this);
}
}
// ///////////////////////////////////////////////////////////////////
public Orbit(Tle tle)
{
m_tle = tle;
m_jdEpoch = m_tle.EpochJulian;
// Recover the original mean motion and semimajor axis from the
// input elements.
double mm = mnMotion;
double rpmin = mm * Globals.TWOPI / Globals.MIN_PER_DAY; // rads per minute
double a1 = Math.Pow(Globals.XKE / rpmin, Globals.TWOTHRD);
double e = Eccentricity;
double i = Inclination;
double temp = (1.5 * Globals.CK2 * (3.0 * Globals.Sqr(Math.Cos(i)) - 1.0) /
Math.Pow(1.0 - e * e, 1.5));
double delta1 = temp / (a1 * a1);
double a0 = a1 *
(1.0 - delta1 *
((1.0 / 3.0) + delta1 *
(1.0 + 134.0 / 81.0 * delta1)));
double delta0 = temp / (a0 * a0);
m_rmMeanMotionRec = rpmin / (1.0 + delta0);
m_aeAxisSemiMajorRec = a0 / (1.0 - delta0);
m_aeAxisSemiMinorRec = m_aeAxisSemiMajorRec * Math.Sqrt(1.0 - (e * e));
m_kmPerigeeRec = Globals.XKMPER * (m_aeAxisSemiMajorRec * (1.0 - e) - Globals.AE);
m_kmApogeeRec = Globals.XKMPER * (m_aeAxisSemiMajorRec * (1.0 + e) - Globals.AE);
if (Period.TotalMinutes >= 225.0)
{
// SDP4 - period >= 225 minutes.
m_NoradModel = new NoradSDP4(this);
}
else
{
// SGP4 - period < 225 minutes
m_NoradModel = new NoradSGP4(this);
}
}
bool gp_sync; // geopotential synchronous
// ///////////////////////////////////////////////////////////////////////////
public NoradSDP4(Orbit orbit) :
base(orbit)
{
double sinarg = Math.Sin(Orbit.ArgPerigee);
double cosarg = Math.Cos(Orbit.ArgPerigee);
// Deep space initialization
Julian jd = Orbit.Epoch;
dp_thgr = jd.ToGmst();
double eq = Orbit.Eccentricity;
double aqnv = 1.0 / Orbit.SemiMajor;
dp_xqncl = Orbit.Inclination;
double xmao = Orbit.MeanAnomaly;
double xpidot = m_omgdot + m_xnodot;
double sinq = Math.Sin(Orbit.RAAN);
double cosq = Math.Cos(Orbit.RAAN);
dp_omegaq = Orbit.ArgPerigee;
#region Lunar / Solar terms
// Initialize lunar solar terms
double day = jd.FromJan0_12h_1900();
double dpi_xnodce = 4.5236020 - 9.2422029E-4 * day;
double dpi_stem = Math.Sin(dpi_xnodce);
double dpi_ctem = Math.Cos(dpi_xnodce);
double dpi_zcosil = 0.91375164 - 0.03568096 * dpi_ctem;
double dpi_zsinil = Math.Sqrt(1.0 - dpi_zcosil * dpi_zcosil);
double dpi_zsinhl = 0.089683511 * dpi_stem / dpi_zsinil;
double dpi_zcoshl = Math.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 = Globals.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 = Globals.AcTan(dpi_zx, dpi_zy) + dpi_gam - dpi_xnodce;
double dpi_zcosgl = Math.Cos(dpi_zx);
double dpi_zsingl = Math.Sin(dpi_zx);
dp_zmos = 6.2565837 + 0.017201977 * day;
dp_zmos = Globals.Fmod2p(dp_zmos);
const double zcosis = 0.91744867;
const double zsinis = 0.39785416;
const double zsings = -0.98088458;
const double zcosgs = 0.1945905;
const double c1ss = 2.9864797E-6;
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 xnoi = 1.0 / Orbit.MeanMotion;
double a1; double a3; double a7; double a8; double a9; double a10;
double a2; double a4; double a5; double a6; double x1; double x2;
double x3; double x4; double x5; double x6; double x7; double x8;
double z31; double z32; double z33; double z1; double z2; double z3;
double z11; double z12; double z13; double z21; double z22; double z23;
double s3; double s2; double s4; double s1; double s5; double s6;
double s7;
double se = 0.0;
double si = 0.0;
double sl = 0.0;
double sgh = 0.0;
double sh = 0.0;
double eosq = Globals.Sqr(Orbit.Eccentricity);
// 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
a1 = zcosg * zcosh + zsing * zcosi * zsinh;
a3 = -zsing * zcosh + zcosg * zcosi * zsinh;
a7 = -zcosg * zsinh + zsing * zcosi * zcosh;
a8 = zsing * zsini;
a9 = zsing * zsinh + zcosg * zcosi * zcosh;
a10 = zcosg * zsini;
a2 = m_cosio * a7 + m_sinio * a8;
a4 = m_cosio * a9 + m_sinio * a10;
a5 = -m_sinio * a7 + m_cosio * a8;
a6 = -m_sinio * a9 + m_cosio * a10;
x1 = a1 * cosarg + a2 * sinarg;
x2 = a3 * cosarg + a4 * sinarg;
x3 = -a1 * sinarg + a2 * cosarg;
x4 = -a3 * sinarg + a4 * cosarg;
x5 = a5 * sinarg;
x6 = a6 * sinarg;
x7 = a5 * cosarg;
x8 = a6 * cosarg;
z31 = 12.0 * x1 * x1 - 3.0 * x3 * x3;
z32 = 24.0 * x1 * x2 - 6.0 * x3 * x4;
z33 = 12.0 * x2 * x2 - 3.0 * x4 * x4;
z1 = 3.0 * (a1 * a1 + a2 * a2) + z31 * eosq;
z2 = 6.0 * (a1 * a3 + a2 * a4) + z32 * eosq;
z3 = 3.0 * (a3 * a3 + a4 * a4) + z33 * eosq;
z11 = -6.0 * a1 * a5 + eosq * (-24.0 * x1 * x7 - 6.0 * x3 * x5);
z12 = -6.0 * (a1 * a6 + a3 * a5) +
eosq * (-24.0 * (x2 * x7 + x1 * x8) - 6.0 * (x3 * x6 + x4 * x5));
z13 = -6.0 * a3 * a6 + eosq * (-24.0 * x2 * x8 - 6.0 * x4 * x6);
z21 = 6.0 * a2 * a5 + eosq * (24.0 * x1 * x5 - 6.0 * x3 * x7);
z22 = 6.0 * (a4 * a5 + a2 * a6) +
eosq * (24.0 * (x2 * x5 + x1 * x6) - 6.0 * (x4 * x7 + x3 * x8));
z23 = 6.0 * a4 * a6 + eosq * (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;
s3 = cc * xnoi;
s2 = -0.5 * s3 / m_betao;
s4 = s3 * m_betao;
s1 = -15.0 * eq * s4;
s5 = x1 * x3 + x2 * x4;
s6 = x2 * x3 + x1 * x4;
s7 = x2 * x4 - x1 * x3;
se = s1 * zn * s5;
si = s2 * zn * (z11 + z13);
sl = -zn * s3 * (z1 + z3 - 14.0 - 6.0 * eosq);
sgh = s4 * zn * (z31 + z33 - 6.0);
if (Orbit.Inclination < 5.2359877E-2)
{
sh = 0.0;
}
else
{
sh = -zn * s2 * (z21 + z23);
}
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 * eosq) * 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-7;
cc = c1l;
ze = zel;
}
}
#endregion
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 for 12 hour orbits
gp_reso = false;
gp_sync = false;
double g310;
double f220;
double bfact = 0.0;
// Determine if orbit is 12- or 24-hour resonant.
// Mean motion is given in radians per minute.
if ((Orbit.MeanMotion > 0.0034906585) && (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;
#region 24-hour resonant
double g200 = 1.0 + eosq * (-2.5 + 0.8125 * eosq);
g310 = 1.0 + 2.0 * eosq;
double g300 = 1.0 + eosq * (-6.0 + 6.60937 * eosq);
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;
f330 = 1.875 * f330 * f330 * f330;
const double q22 = 1.7891679e-06;
const double q33 = 2.2123015e-07;
const double q31 = 2.1460748e-06;
dp_del1 = 3.0 * m_xnodp * m_xnodp * 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 + Orbit.RAAN + Orbit.ArgPerigee - dp_thgr;
bfact = m_xmdot + xpidot - thdt;
bfact = bfact + dp_ssl + dp_ssg + dp_ssh;
#endregion
}
else if (((Orbit.MeanMotion >= 8.26E-3) && (Orbit.MeanMotion <= 9.24E-3)) && (eq >= 0.5))
{
// Period is 12-hour resonant
gp_reso = true;
#region 12-hour resonant
double eoc = eq * eosq;
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 * eosq;
g310 = -19.302 + 117.390 * eq - 228.419 * eosq + 156.591 * eoc;
g322 = -18.9068 + 109.7927 * eq - 214.6334 * eosq + 146.5816 * eoc;
g410 = -41.122 + 242.694 * eq - 471.094 * eosq + 313.953 * eoc;
g422 = -146.407 + 841.880 * eq - 1629.014 * eosq + 1083.435 * eoc;
g520 = -532.114 + 3017.977 * eq - 5740.0 * eosq + 3708.276 * eoc;
}
else
{
g211 = -72.099 + 331.819 * eq - 508.738 * eosq + 266.724 * eoc;
g310 = -346.844 + 1582.851 * eq - 2415.925 * eosq + 1246.113 * eoc;
g322 = -342.585 + 1554.908 * eq - 2366.899 * eosq + 1215.972 * eoc;
g410 = -1052.797 + 4758.686 * eq - 7193.992 * eosq + 3651.957 * eoc;
g422 = -3581.69 + 16178.11 * eq - 24462.77 * eosq + 12422.52 * eoc;
if (eq <= 0.715)
{
g520 = 1464.74 - 4664.75 * eq + 3763.64 * eosq;
}
else
{
g520 = -5149.66 + 29936.92 * eq - 54087.36 * eosq + 31324.56 * eoc;
}
}
double g533;
double g521;
double g532;
if (eq < 0.7)
{
g533 = -919.2277 + 4988.61 * eq - 9064.77 * eosq + 5542.21 * eoc;
g521 = -822.71072 + 4568.6173 * eq - 8491.4146 * eosq + 5337.524 * eoc;
g532 = -853.666 + 4690.25 * eq - 8624.77 * eosq + 5341.4 * eoc;
}
else
{
g533 = -37995.78 + 161616.52 * eq - 229838.2 * eosq + 109377.94 * eoc;
g521 = -51752.104 + 218913.95 * eq - 309468.16 * eosq + 146349.42 * eoc;
g532 = -40023.88 + 170470.89 * eq - 242699.48 * eosq + 115605.82 * eoc;
}
double sini2 = m_sinio * m_sinio;
double cosi2 = m_cosio * m_cosio;
f220 = 0.75 * (1.0 + 2.0 * m_cosio + cosi2);
double f221 = 1.5 * sini2;
double f321 = 1.875 * m_sinio * (1.0 - 2.0 * m_cosio - 3.0 * cosi2);
double f322 = -1.875 * m_sinio * (1.0 + 2.0 * m_cosio - 3.0 * cosi2);
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 * cosi2) +
0.33333333 * (-2.0 + 4.0 * m_cosio + 6.0 * cosi2));
double f523 = m_sinio * (4.92187512 * sini2 * (-2.0 - 4.0 * m_cosio + 10.0 * cosi2) +
6.56250012 * (1.0 + 2.0 * m_cosio - 3.0 * cosi2));
double f542 = 29.53125 * m_sinio * (2.0 - 8.0 * m_cosio + cosi2 * (-12.0 + 8.0 * m_cosio + 10.0 * cosi2));
double f543 = 29.53125 * m_sinio * (-2.0 - 8.0 * m_cosio + cosi2 * (12.0 + 8.0 * m_cosio - 10.0 * cosi2));
double xno2 = m_xnodp * m_xnodp;
double ainv2 = aqnv * aqnv;
double temp1 = 3.0 * xno2 * ainv2;
const double root22 = 1.7891679E-6;
const double root32 = 3.7393792E-7;
const double root44 = 7.3636953E-9;
const double root52 = 1.1428639E-7;
const double root54 = 2.1765803E-9;
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 + Orbit.RAAN + Orbit.RAAN - dp_thgr - dp_thgr;
bfact = m_xmdot + m_xnodot + m_xnodot - thdt - thdt;
bfact = bfact + dp_ssl + dp_ssh + dp_ssh;
#endregion
}
if (gp_reso || gp_sync)
{
dp_xfact = bfact - m_xnodp;
// Initialize integrator
dp_xli = dp_xlamo;
dp_xni = m_xnodp;
// dp_atime = 0.0; // performed by runtime
dp_stepp = 720.0;
dp_stepn = -720.0;
dp_step2 = 259200.0;
}
}
/// <summary>
/// Returns the topo-centric (azimuth, elevation, etc.) coordinates for
/// a target object described by the given ECI coordinates.
/// </summary>
/// <param name="eci">The ECI coordinates of the target object.</param>
/// <returns>The look angle to the target object.</returns>
public TopoTime GetLookAngle(EciTime eci)
{
// Calculate the ECI coordinates for this Site object at the time
// of interest.
Julian date = eci.Date;
EciTime eciSite = PositionEci(date);
Vector vecRgRate = new Vector(eci.Velocity.X - eciSite.Velocity.X,
eci.Velocity.Y - eciSite.Velocity.Y,
eci.Velocity.Z - eciSite.Velocity.Z);
double x = eci.Position.X - eciSite.Position.X;
double y = eci.Position.Y - eciSite.Position.Y;
double z = eci.Position.Z - eciSite.Position.Z;
double w = Math.Sqrt(Globals.Sqr(x) + Globals.Sqr(y) + Globals.Sqr(z));
Vector vecRange = new Vector(x, y, z, w);
// The site's Local Mean Sidereal Time at the time of interest.
double theta = date.ToLmst(LongitudeRad);
double sin_lat = Math.Sin(LatitudeRad);
double cos_lat = Math.Cos(LatitudeRad);
double sin_theta = Math.Sin(theta);
double cos_theta = Math.Cos(theta);
double top_s = sin_lat * cos_theta * vecRange.X +
sin_lat * sin_theta * vecRange.Y -
cos_lat * vecRange.Z;
double top_e = -sin_theta * vecRange.X +
cos_theta * vecRange.Y;
double top_z = cos_lat * cos_theta * vecRange.X +
cos_lat * sin_theta * vecRange.Y +
sin_lat * vecRange.Z;
double az = Math.Atan(-top_e / top_s);
if (top_s > 0.0)
{
az += Globals.Pi;
}
if (az < 0.0)
{
az += 2.0 * Globals.Pi;
}
double el = Math.Asin(top_z / vecRange.W);
double rate = (vecRange.X * vecRgRate.X +
vecRange.Y * vecRgRate.Y +
vecRange.Z * vecRgRate.Z) / vecRange.W;
TopoTime topo = new TopoTime(az, // azimuth, radians
el, // elevation, radians
vecRange.W, // range, km
rate, // rate, km / sec
eci.Date);
#if WANT_ATMOSPHERIC_CORRECTION
// Elevation correction for atmospheric refraction.
// Reference: Astronomical Algorithms by Jean Meeus, pp. 101-104
// Note: Correction is meaningless when apparent elevation is below horizon
topo.ElevationRad += Globals.ToRadians((1.02 /
Math.Tan(Globals.ToRadians(Globals.ToDegrees(el) + 10.3 /
(Globals.ToDegrees(el) + 5.11)))) / 60.0);
if (topo.ElevationRad < 0.0)
{
topo.ElevationRad = el; // Reset to true elevation
}
if (topo.ElevationRad > (Math.PI / 2.0))
{
topo.ElevationRad = (Math.PI / 2.0);
}
#endif
return(topo);
}
/// <summary>
/// Calculate satellite ECI position/velocity for a given time.
/// </summary>
/// <param name="tsince">Target time, in minutes-past-epoch format.</param>
/// <returns>AU-based position/velocity ECI coordinates.</returns>
/// <remarks>
/// 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.
/// The algorithm uses NORAD's Simplified General Perturbation 4 near earth
/// orbit model.
/// </remarks>
public override EciTime GetPosition(double tsince)
{
// For m_perigee less than 220 kilometers, the isimp flag is set and
// the equations are truncated to linear variation in square root of 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 || (m_aodp * (1.0 - m_satEcc) / Globals.Ae) < (220.0 / Globals.Xkmper + Globals.Ae);
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_aodp * m_tsi * c1sq;
double temp = d2 * m_tsi * m_c1 / 3.0;
d3 = (17.0 * m_aodp + m_s4) * temp;
d4 = 0.5 * temp * m_aodp * m_tsi *
(221.0 * m_aodp + 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 = Orbit.MeanAnomaly + m_xmdot * tsince;
double omgadf = Orbit.ArgPerigee + m_omgdot * tsince;
double xnoddf = 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 = Orbit.BStar * m_c4 * tsince;
double templ = m_t2cof * tsq;
if (!isimp)
{
double delomg = m_omgcof * tsince;
double delm = m_xmcof * (Math.Pow(1.0 + m_eta * Math.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 + Orbit.BStar * m_c5 * (Math.Sin(xmp) - m_sinmo);
templ = templ + t3cof * tcube + tfour * (t4cof + tsince * t5cof);
}
double a = m_aodp * Globals.Sqr(tempa);
double e = m_satEcc - tempe;
double xl = xmp + omega + xnode + m_xnodp * templ;
double xn = Globals.Xke / Math.Pow(a, 1.5);
return(FinalPosition(m_satInc, omgadf, e, a, xl, xnode, xn, tsince));
}
// ///////////////////////////////////////////////////////////////////////////
// getLookAngle()
// Return the topocentric (azimuth, elevation, etc.) coordinates for a target
// object described by the input ECI coordinates.
public CoordTopo getLookAngle(Eci eci)
{
// Calculate the ECI coordinates for this Site object at the time
// of interest.
Julian date = eci.Date;
Eci eciSite = new Eci(m_geo, date);
// The Site ECI units are km-based; ensure target ECI units are same
if (!eci.UnitsAreKm())
{
throw new Exception("ECI units must be kilometer-based");
}
Vector vecRgRate = new Vector(eci.Velocity.X - eciSite.Velocity.X,
eci.Velocity.Y - eciSite.Velocity.Y,
eci.Velocity.Z - eciSite.Velocity.Z);
double x = eci.Position.X - eciSite.Position.X;
double y = eci.Position.Y - eciSite.Position.Y;
double z = eci.Position.Z - eciSite.Position.Z;
double w = Math.Sqrt(Globals.Sqr(x) + Globals.Sqr(y) + Globals.Sqr(z));
Vector vecRange = new Vector(x, y, z, w);
// The site's Local Mean Sidereal Time at the time of interest.
double theta = date.toLMST(Longitude);
double sin_lat = Math.Sin(Latitude);
double cos_lat = Math.Cos(Latitude);
double sin_theta = Math.Sin(theta);
double cos_theta = Math.Cos(theta);
double top_s = sin_lat * cos_theta * vecRange.X +
sin_lat * sin_theta * vecRange.Y -
cos_lat * vecRange.Z;
double top_e = -sin_theta * vecRange.X +
cos_theta * vecRange.Y;
double top_z = cos_lat * cos_theta * vecRange.X +
cos_lat * sin_theta * vecRange.Y +
sin_lat * vecRange.Z;
double az = Math.Atan(-top_e / top_s);
if (top_s > 0.0)
{
az += Globals.PI;
}
if (az < 0.0)
{
az += 2.0 * Globals.PI;
}
double el = Math.Asin(top_z / vecRange.W);
double rate = (vecRange.X * vecRgRate.X +
vecRange.Y * vecRgRate.Y +
vecRange.Z * vecRgRate.Z) / vecRange.W;
CoordTopo topo = new CoordTopo(az, // azimuth, radians
el, // elevation, radians
vecRange.W, // range, km
rate); // rate, km / sec
#if WANT_ATMOSPHERIC_CORRECTION
// Elevation correction for atmospheric refraction.
// Reference: Astronomical Algorithms by Jean Meeus, pp. 101-104
// Note: Correction is meaningless when apparent elevation is below horizon
topo.m_El += Globals.Deg2Rad((1.02 /
Math.Tan(Globals.Deg2Rad(Globals.Rad2Deg(el) + 10.3 /
(Globals.Rad2Deg(el) + 5.11)))) / 60.0);
if (topo.m_El < 0.0)
{
topo.m_El = el; // Reset to true elevation
}
if (topo.m_El > (Globals.PI / 2))
{
topo.m_El = (Globals.PI / 2);
}
#endif
return(topo);
}