public Eci(Vector pos, Vector vel, Julian date, bool IsAeUnits)
{
m_pos = pos;
m_vel = vel;
m_date = date;
m_VecUnits = (IsAeUnits ? VecUnits.UNITS_AE : VecUnits.UNITS_NONE);
}
// ///////////////////////////////////////////////////////////////////
// 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_VecUnits = VecUnits.UNITS_KM;
double mfactor = Globals.TWOPI * (Globals.OMEGA_E / Globals.SEC_PER_DAY);
double lat = geo.m_Lat;
double lon = geo.m_Lon;
double alt = geo.Altitude.Kilometers;
// 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_pos = new Vector();
m_pos.X = achcp * Math.Cos(theta); // km
m_pos.Y = achcp * Math.Sin(theta); // km
m_pos.Z = (Globals.XKMPER * s + alt) * Math.Sin(lat); // km
m_pos.W = Math.Sqrt(Globals.Sqr(m_pos.X) +
Globals.Sqr(m_pos.Y) +
Globals.Sqr(m_pos.Z)); // range, km
m_vel = new Vector();
m_vel.X = -mfactor * m_pos.Y; // km / sec
m_vel.Y = mfactor * m_pos.X;
m_vel.Z = 0.0;
m_vel.W = Math.Sqrt(Globals.Sqr(m_vel.X) + // range rate km/sec^2
Globals.Sqr(m_vel.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>
/// 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));
}
// /////////////////////////////////////////////////////////////////////
// Subtract a vector from this one.
public void Sub(Vector vec)
{
m_x -= vec.m_x;
m_y -= vec.m_y;
m_z -= vec.m_z;
m_w -= vec.m_w;
}
// ///////////////////////////////////////////////////////////////////////////
// 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;
}
// /////////////////////////////////////////////////////////////////////
protected Eci FinalPosition(double incl, double omega, double e,
double a, double xl, double xnode,
double xn, double tsince)
{
if ((e * e) > 1.0)
{
throw new Exception("Error in satellite data");
}
double beta = Math.Sqrt(1.0 - e * e);
// Long period periodics
double axn = e * Math.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 * Math.Sin(omega) + aynl;
// Solve Kepler's Equation
double capu = Globals.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 = Math.Sin(temp2);
cosepw = Math.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 (Math.Abs(epw - temp2) <= Globals.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 = Globals.XKE * Math.Sqrt(a) * esine * temp1;
double rfdot = Globals.XKE * Math.Sqrt(pl) * temp1;
temp2 = a * temp1;
double betal = Math.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 = Globals.AcTan(sinu, cosu);
double sin2u = 2.0 * sinu * cosu;
double cos2u = 2.0 * cosu * cosu - 1.0;
temp = 1.0 / pl;
temp1 = Globals.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 = Math.Sin(uk);
double cosuk = Math.Cos(uk);
double sinik = Math.Sin(xinck);
double cosik = Math.Cos(xinck);
double sinnok = Math.Sin(xnodek);
double cosnok = Math.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;
Vector vecPos = new Vector(x, y, z);
// Validate on altitude
double altKm = (vecPos.Magnitude() * (Globals.XKMPER / Globals.AE));
if ((altKm < Globals.EARTH_RAD) || (altKm > (2 * Globals.GEOSYNC_ALT)))
{
throw new Exception("Satellite orbit may have decayed");
}
// Velocity
double xdot = rdotk * ux + rfdotk * vx;
double ydot = rdotk * uy + rfdotk * vy;
double zdot = rdotk * uz + rfdotk * vz;
Vector vecVel = new Vector(xdot, ydot, zdot);
DateTime gmt = m_Orbit.EpochTime;
gmt = gmt.AddMinutes(tsince);
return new Eci(vecPos, vecVel, new Julian(gmt), true);
}
// ///////////////////////////////////////////////////////////////////
// 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));
}
public Eci(Vector pos, Vector vel, Julian date, bool IsAeUnits)
{
m_Position = pos;
m_Velocity = vel;
m_Date = date;
m_VectorUnits = (IsAeUnits ? VectorUnits.Ae : VectorUnits.None);
}
/// <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 = GetPosition(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.m_El += Globals.ToRadians((1.02 /
Math.Tan(Globals.ToRadians(Globals.ToDegrees(el) + 10.3 /
(Globals.ToDegrees(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;
}
/// <summary>
/// Calculates the dot product of this vector and another.
/// </summary>
/// <param name="vec">The second vector.</param>
/// <returns>The dot product.</returns>
public double Dot(Vector vec)
{
return (X * vec.X) + (Y * vec.Y) + (Z * vec.Z);
}
// /////////////////////////////////////////////////////////////////////
// Calculate the angle between this vector and another
public double Angle(Vector vec)
{
return Math.Acos(Dot(vec) / (Magnitude() * vec.Magnitude()));
}
/// <summary>
/// Creates a new instance of the class from ECI coordinates.
/// </summary>
/// <param name="eci">The ECI coordinates.</param>
public Eci(Eci eci)
{
Position = new Vector(eci.Position);
Velocity = new Vector(eci.Velocity);
}
/// <summary>
/// Creates a new instance of the class with the given position and
/// velocity components.
/// </summary>
/// <param name="pos">The position vector.</param>
/// <param name="vel">The velocity vector.</param>
public Eci(Vector pos, Vector vel)
{
Position = pos;
Velocity = vel;
}
/// <summary>
/// Creates a new instance of the class from XYZ coordinates.
/// </summary>
/// <param name="pos">The XYZ coordinates.</param>
public Eci(Vector pos)
: this(pos, new Vector())
{
}
/// <summary>
/// Creates an instance of the class with the given position, velocity, and time.
/// </summary>
/// <param name="pos">The position vector.</param>
/// <param name="vel">The velocity vector.</param>
/// <param name="date">The time associated with the position.</param>
public EciTime(Vector pos, Vector vel, Julian date)
: base(pos, vel)
{
Date = date;
}
/// <summary>
/// Creates a new vector from an existing vector.
/// </summary>
/// <param name="v">The existing vector to copy.</param>
public Vector(Vector v)
: this(v.X, v.Y, v.Z, v.W)
{
}
/// <summary>
/// Subtracts a vector from this vector.
/// </summary>
/// <param name="vec">The vector to subtract.</param>
public void Sub(Vector vec)
{
X -= vec.X;
Y -= vec.Y;
Z -= vec.Z;
W -= vec.W;
}
// /////////////////////////////////////////////////////////////////////
// Return the dot product
public double Dot(Vector vec)
{
return (m_x * vec.m_x) + (m_y * vec.m_y) + (m_z * vec.m_z);
}
/// <summary>
/// Calculates the distance between two vectors as points in XYZ space.
/// </summary>
/// <param name="vec">The second vector.</param>
/// <returns>The calculated distance.</returns>
public double Distance(Vector vec)
{
return Math.Sqrt(Math.Pow(X - vec.X, 2.0) +
Math.Pow(Y - vec.Y, 2.0) +
Math.Pow(Z - vec.Z, 2.0));
}
