static void Main0(string[] args)
{
// Constants
const int N_Step = 720; // Maximum number of steps
// Variables
int i;
int N_Step1;
int N_Step2;
double Step;
double Mjd0_UTC;
Geo.Algorithm.Vector Y0 = new Geo.Algorithm.Vector(6);
Geo.Algorithm.Vector Kep = new Geo.Algorithm.Vector(6);
ForceModelOption Aux_ref = new ForceModelOption(), Aux = new ForceModelOption(); // Auxiliary parameters
double Max_J20, Max_J22, Max_J44, Max_J1010;
double Max_Sun, Max_Moon, Max_SRad, Max_Drag;
Geo.Algorithm.Vector[] Eph_Ref = new Geo.Algorithm.Vector[N_Step + 1];
Geo.Algorithm.Vector[] Eph_J20 = new Geo.Algorithm.Vector[N_Step + 1];
Geo.Algorithm.Vector[] Eph_J22 = new Geo.Algorithm.Vector[N_Step + 1];
Geo.Algorithm.Vector[] Eph_J44 = new Geo.Algorithm.Vector[N_Step + 1];
Geo.Algorithm.Vector[] Eph_J1010 = new Geo.Algorithm.Vector[N_Step + 1];
Geo.Algorithm.Vector[] Eph_Sun = new Geo.Algorithm.Vector[N_Step + 1];
Geo.Algorithm.Vector[] Eph_Moon = new Geo.Algorithm.Vector[N_Step + 1];
Geo.Algorithm.Vector[] Eph_SRad = new Geo.Algorithm.Vector[N_Step + 1];
Geo.Algorithm.Vector[] Eph_Drag = new Geo.Algorithm.Vector[N_Step + 1];
// Initialize UT1-UTC and UTC-TAI time difference
IERS = new IERS(-0.05, -30.00, 0.0, 0.0);
// Epoch state (remote sensing satellite)
Mjd0_UTC = DateUtil.DateToMjd(1999, 03, 01, 00, 00, 0.0);
Kep = new Vector(7178.0e3, 0.0010, 98.57 * OrbitConsts.RadPerDeg, 0.0, 0.0, 0.0);
Y0 = Kepler.State(OrbitConsts.GM_Earth, Kep, 0.0);
// Model parameters
Aux_ref.Mjd0_TT = Mjd0_UTC - IERS.GetTT_UTC(Mjd0_UTC) / 86400.0;
Aux_ref.Area = 5.0; // [m^2] Remote sensing satellite
Aux_ref.Mass = 1000.0; // [kg]
Aux_ref.CoefOfRadiation = 1.3;
Aux_ref.CoefOfDrag = 2.3;
Aux_ref.MaxDegree = 20;
Aux_ref.MaxOrder = 20;
Aux_ref.EnableSun = true;
Aux_ref.EnableMoon = true;
Aux_ref.EnableSolarRadiation = true;
Aux_ref.EnableDrag = true;
// Reference orbit
Step = 120.0; // [s]
N_Step1 = 50; // 100 mins
N_Step2 = 720; // 1 day
Aux = Aux_ref;
Ephemeris(Y0, N_Step2, Step, Aux, Eph_Ref);
// J2,0 perturbations
Aux.MaxDegree = 2; Aux.MaxOrder = 0;
Ephemeris(Y0, N_Step2, Step, Aux, Eph_J20);
// J2,2 perturbations
Aux.MaxDegree = 2; Aux.MaxOrder = 2;
Ephemeris(Y0, N_Step2, Step, Aux, Eph_J22);
// J4,4 perturbations
Aux.MaxDegree = 4; Aux.MaxOrder = 4;
Ephemeris(Y0, N_Step2, Step, Aux, Eph_J44);
// J10,10 perturbations
Aux.MaxDegree = 10; Aux.MaxOrder = 10;
Ephemeris(Y0, N_Step2, Step, Aux, Eph_J1010);
Aux.MaxDegree = 20; Aux.MaxOrder = 20;
// Solar perturbations
Aux.EnableSun = false;
Ephemeris(Y0, N_Step2, Step, Aux, Eph_Sun);
Aux.EnableSun = true;
// Lunar perturbations
Aux.EnableMoon = false;
Ephemeris(Y0, N_Step2, Step, Aux, Eph_Moon);
Aux.EnableMoon = true;
// Solar radiation pressure perturbations
Aux.EnableSolarRadiation = false;
Ephemeris(Y0, N_Step2, Step, Aux, Eph_SRad);
Aux.EnableSolarRadiation = true;
// Drag perturbations
Aux.EnableDrag = false;
Ephemeris(Y0, N_Step2, Step, Aux, Eph_Drag);
Aux.EnableDrag = true;
// Find maximum over N_Step1 steps
Max_J20 = Max_J22 = Max_J44 = Max_J1010 = Max_Sun = Max_Moon = Max_SRad = Max_Drag = 0.0;
for (i = 0; i <= N_Step1; i++)
{
var refEph = Eph_Ref[i].Slice(0, 2);
Max_J20 = max(Norm(Eph_J20[i].Slice(0, 2) - refEph), Max_J20);
Max_J22 = max(Norm(Eph_J22[i].Slice(0, 2) - refEph), Max_J22);
Max_J44 = max(Norm(Eph_J44[i].Slice(0, 2) - refEph), Max_J44);
Max_J1010 = max(Norm(Eph_J1010[i].Slice(0, 2) - refEph), Max_J1010);
Max_Sun = max(Norm(Eph_Sun[i].Slice(0, 2) - refEph), Max_Sun);
Max_Moon = max(Norm(Eph_Moon[i].Slice(0, 2) - refEph), Max_Moon);
Max_SRad = max(Norm(Eph_SRad[i].Slice(0, 2) - refEph), Max_SRad);
Max_Drag = max(Norm(Eph_Drag[i].Slice(0, 2) - refEph), Max_Drag);
}
;
// Output
var info = "Exercise 3-4: Orbit Perturbations " + "\r\n" + "\r\n";
info += "Remote sensing satellite: " + "\r\n" + "\r\n";
info += " Maximum position errors within ";
Console.Write(info);
info = String.Format("{0, 8:F}", N_Step1 * Step / 60.0);
info += " min propagation interval " + "\r\n";
info += " J2,0 J2,2 J4,4 J10,10" + " Sun Moon SolRad Drag" + "\r\n";
info += " [m] [m] [m] [m]" + " [m] [m] [m] [m]";
Console.WriteLine(info);
info = String.Format("{0, 8:F}{1, 8:F}{2, 8:F}{3, 8:F}{4, 8:F}{5, 8:F}{6, 8:F}{7, 8:F}", Max_J20, Max_J22, Max_J44, Max_J1010, Max_Sun, Max_Moon, Max_SRad, Max_Drag);
Console.WriteLine(info);
Console.WriteLine();
// Find maximum over N_Step2 steps
for (i = N_Step1 + 1; i <= N_Step2; i++)
{
var refEph = Eph_Ref[i].Slice(0, 2);
Max_J20 = max(Norm(Eph_J20[i].Slice(0, 2) - refEph), Max_J20);
Max_J22 = max(Norm(Eph_J22[i].Slice(0, 2) - refEph), Max_J22);
Max_J44 = max(Norm(Eph_J44[i].Slice(0, 2) - refEph), Max_J44);
Max_J1010 = max(Norm(Eph_J1010[i].Slice(0, 2) - refEph), Max_J1010);
Max_Sun = max(Norm(Eph_Sun[i].Slice(0, 2) - refEph), Max_Sun);
Max_Moon = max(Norm(Eph_Moon[i].Slice(0, 2) - refEph), Max_Moon);
Max_SRad = max(Norm(Eph_SRad[i].Slice(0, 2) - refEph), Max_SRad);
Max_Drag = max(Norm(Eph_Drag[i].Slice(0, 2) - refEph), Max_Drag);
}
;
// Output
info = " Maximum position errors within ";
Console.Write(info);
info = String.Format("{0, 8:F}", N_Step2 * Step / 60.0);
info += " min propagation interval " + "\r\n";
info += " J2,0 J2,2 J4,4 J10,10" + " Sun Moon SolRad Drag" + "\r\n";
info += " [m] [m] [m] [m]" + " [m] [m] [m] [m]";
Console.WriteLine(info);
info = String.Format("{0, 8:F}{1, 8:F}{2, 8:F}{3, 8:F}{4, 8:F}{5, 8:F}{6, 8:F}{7, 8:F}", Max_J20, Max_J22, Max_J44, Max_J1010, Max_Sun, Max_Moon, Max_SRad, Max_Drag);
Console.WriteLine(info);
Console.WriteLine();
// Epoch state (geostationary satellite)
Kep = new Vector(42166.0e3, 0.0004, 0.02 * OrbitConsts.RadPerDeg, 0.0, 0.0, 0.0);
Y0 = Kepler.State(OrbitConsts.GM_Earth, Kep, 0.0);
// Model parameters
Aux_ref.Area = 10.0; // [m^2] Geostationary satellite
// Reference orbit
Step = 1200.0; // [s]
N_Step1 = 72; // 1 day
N_Step2 = 144; // 2 days
Aux = Aux_ref;
Ephemeris(Y0, N_Step2, Step, Aux, Eph_Ref);
// J2,0 perturbations
Aux.MaxDegree = 2; Aux.MaxOrder = 0;
Ephemeris(Y0, N_Step2, Step, Aux, Eph_J20);
// J2,2 perturbations
Aux.MaxDegree = 2; Aux.MaxOrder = 2;
Ephemeris(Y0, N_Step2, Step, Aux, Eph_J22);
// J4,4 perturbations
Aux.MaxDegree = 4; Aux.MaxOrder = 4;
Ephemeris(Y0, N_Step2, Step, Aux, Eph_J44);
// J10,10 perturbations
Aux.MaxDegree = 10; Aux.MaxOrder = 10;
Ephemeris(Y0, N_Step2, Step, Aux, Eph_J1010);
Aux.MaxDegree = 20; Aux.MaxOrder = 20;
// Solar perturbations
Aux.EnableSun = false;
Ephemeris(Y0, N_Step2, Step, Aux, Eph_Sun);
Aux.EnableSun = true;
// Lunar perturbations
Aux.EnableMoon = false;
Ephemeris(Y0, N_Step2, Step, Aux, Eph_Moon);
Aux.EnableMoon = true;
// Solar radiation pressure perturbations
Aux.EnableSolarRadiation = false;
Ephemeris(Y0, N_Step2, Step, Aux, Eph_SRad);
Aux.EnableSolarRadiation = true;
// Drag perturbations
Aux.EnableDrag = false;
Ephemeris(Y0, N_Step2, Step, Aux, Eph_Drag);
Aux.EnableDrag = true;
// Find maximum over N_Step1 steps
Max_J20 = Max_J22 = Max_J44 = Max_J1010 = Max_Sun = Max_Moon = Max_SRad = Max_Drag = 0.0;
for (i = 0; i <= N_Step1; i++)
{
var refEph = Eph_Ref[i].Slice(0, 2);
Max_J20 = max(Norm(Eph_J20[i].Slice(0, 2) - refEph), Max_J20);
Max_J22 = max(Norm(Eph_J22[i].Slice(0, 2) - refEph), Max_J22);
Max_J44 = max(Norm(Eph_J44[i].Slice(0, 2) - refEph), Max_J44);
Max_J1010 = max(Norm(Eph_J1010[i].Slice(0, 2) - refEph), Max_J1010);
Max_Sun = max(Norm(Eph_Sun[i].Slice(0, 2) - refEph), Max_Sun);
Max_Moon = max(Norm(Eph_Moon[i].Slice(0, 2) - refEph), Max_Moon);
Max_SRad = max(Norm(Eph_SRad[i].Slice(0, 2) - refEph), Max_SRad);
Max_Drag = max(Norm(Eph_Drag[i].Slice(0, 2) - refEph), Max_Drag);
}
;
// Output
// Output
info = "Geostationary satellite: " + "\r\n";
info += " Maximum position errors within ";
Console.Write(info);
info = String.Format("{0, 8:F}", N_Step1 * Step / 60.0);
info += " min propagation interval " + "\r\n";
info += " J2,0 J2,2 J4,4 J10,10" + " Sun Moon SolRad Drag" + "\r\n";
info += " [m] [m] [m] [m]" + " [m] [m] [m] [m]";
Console.WriteLine(info);
info = String.Format("{0, 8:F}{1, 8:F}{2, 8:F}{3, 8:F}{4, 8:F}{5, 8:F}{6, 8:F}{7, 8:F}", Max_J20, Max_J22, Max_J44, Max_J1010, Max_Sun, Max_Moon, Max_SRad, Max_Drag);
Console.WriteLine(info);
Console.WriteLine();
// Find maximum over N_Step2 steps
for (i = N_Step1 + 1; i <= N_Step2; i++)
{
var refEph = Eph_Ref[i].Slice(0, 2);
Max_J20 = max(Norm(Eph_J20[i].Slice(0, 2) - refEph), Max_J20);
Max_J22 = max(Norm(Eph_J22[i].Slice(0, 2) - refEph), Max_J22);
Max_J44 = max(Norm(Eph_J44[i].Slice(0, 2) - refEph), Max_J44);
Max_J1010 = max(Norm(Eph_J1010[i].Slice(0, 2) - refEph), Max_J1010);
Max_Sun = max(Norm(Eph_Sun[i].Slice(0, 2) - refEph), Max_Sun);
Max_Moon = max(Norm(Eph_Moon[i].Slice(0, 2) - refEph), Max_Moon);
Max_SRad = max(Norm(Eph_SRad[i].Slice(0, 2) - refEph), Max_SRad);
Max_Drag = max(Norm(Eph_Drag[i].Slice(0, 2) - refEph), Max_Drag);
}
;
// Output
info = " Maximum position errors within ";
Console.Write(info);
info = String.Format("{0, 8:F}", N_Step2 * Step / 60.0);
info += " min propagation interval " + "\r\n";
info += " J2,0 J2,2 J4,4 J10,10" + " Sun Moon SolRad Drag" + "\r\n";
info += " [m] [m] [m] [m]" + " [m] [m] [m] [m]";
Console.WriteLine(info);
info = String.Format("{0, 8:F}{1, 8:F}{2, 8:F}{3, 8:F}{4, 8:F}{5, 8:F}{6, 8:F}{7, 8:F}", Max_J20, Max_J22, Max_J44, Max_J1010, Max_Sun, Max_Moon, Max_SRad, Max_Drag);
Console.WriteLine(info);
Console.WriteLine();
Console.ReadKey();
}
static void Main0(string[] args)
{
// Variables
int i; // Loop counter
double MJD_GPS, MJD_TT; // Modified Julian Date (GPS,TT)
double MJD_UTC, MJD_UT1; // Modified Julian Date (UTC,UT1)
Matrix P = new Matrix(3, 3), N = new Matrix(3, 3); // Precession/nutation matrix
Matrix Theta = new Matrix(3, 3); // Sidereal Time matrix
Matrix S = new Matrix(3, 3), dTheta = new Matrix(3, 3); // and derivative
Matrix Pi = new Matrix(3, 3); // Polar motion matrix
Matrix U = new Matrix(3, 3), dU = new Matrix(3, 3); // ICRS to ITRS transformation and derivative
Vector r_WGS = new Vector(3), v_WGS = new Vector(3); // Position/velocity in the Earth-fixed frame
Vector r = new Vector(3), v = new Vector(3); // Position/velocity in the ICRS
Vector y = new Vector(6), Kep = new Vector(6); // Satte vector and Keplerian elements
// Header
var endl = "\r\n";
var info = "Exercise 5-2: Velocity in the Earth-fixed frame"
+ endl + endl;
Console.WriteLine(info);
// Earth Orientation Parameters (UT1-UTC[s],UTC-TAI[s], x["], y["])
// (from IERS Bulletin B #135 and C #16; valid for 1999/03/04 0:00 UTC)
IERS IERS = new IERS(0.6492332, -32.0, 0.06740, 0.24173);
// Date
MJD_GPS = DateUtil.DateToMjd(1999, 03, 04, 0, 0, 0.0);
MJD_UTC = MJD_GPS - IERS.GetGPS_UTC(MJD_GPS) / 86400.0;
MJD_UT1 = MJD_UTC + IERS.GetUT1_UTC(MJD_UTC) / 86400.0;
MJD_TT = MJD_UTC + IERS.GetTT_UTC(MJD_UTC) / 86400.0;
// Earth-fixed state vector of GPS satellite #PRN15
// (from NIMA ephemeris nim09994.eph; WGS84(G873) system)
r_WGS = new Vector(19440.953805e+3, 16881.609273e+3, -6777.115092e+3); // [m]
v_WGS = new Vector(-8111.827456e-1, -2573.799137e-1, -30689.508125e-1); // [m/s]
// ICRS to ITRS transformation matrix and derivative
P = IERS.PrecessionMatrix(OrbitConsts.MJD_J2000, MJD_TT); // IAU 1976 Precession
N = IERS.NutMatrix(MJD_TT); // IAU 1980 Nutation
Theta = IERS.GreenwichHourAngleMatrix(MJD_UT1); // Earth rotation
Pi = IERS.PoleMatrix(MJD_UTC); // Polar motion
S[0, 1] = 1.0; S[1, 0] = -1.0; // Derivative of Earth rotation
dTheta = OrbitConsts.RotationSpeedOfEarth_Rad * S * Theta; // matrix [1/s]
U = Pi * Theta * N * P; // ICRS to ITRS transformation
dU = Pi * dTheta * N * P; // Derivative [1/s]
// Transformation from WGS to ICRS
r = U.Transpose() * r_WGS;
v = U.Transpose() * v_WGS + dU.Transpose() * r_WGS;
// Orbital elements
y = r.Stack(v);
Kep = Kepler.Elements(OrbitConsts.GM_Earth, y);
// Output
info = "Date" + endl + endl
+ " " + DateUtil.MjdToDateTimeString(MJD_GPS) + " GPS" + endl
+ " " + DateUtil.MjdToDateTimeString(MJD_UTC) + " UTC" + endl
+ " " + DateUtil.MjdToDateTimeString(MJD_UT1) + " UT1" + endl
+ " " + DateUtil.MjdToDateTimeString(MJD_TT) + " TT " + endl + endl;
Console.WriteLine(info);
info = "WGS84 (G873) State vector:" + endl + endl;
info += " Position ";
for (i = 0; i < 3; i++)
{
info += String.Format("{0, 10:F6}", r_WGS[i] / 1000.0);
}
;
info += " [km]";
Console.WriteLine(info);
info = " Velocity ";
for (i = 0; i < 3; i++)
{
info += String.Format("{0, 10:F6}", v_WGS[i] / 1000.0);
}
;
info += " [km/s]" + endl + endl;
Console.WriteLine(info);
info = "ICRS-ITRS transformation" + endl + endl
+ String.Format("{0, 10:F6}", U) + endl;
info += "Derivative of ICRS-ITRS transformation [10^(-4)/s]" + endl + endl
+ String.Format("{0, 10:F6}", dU * 1.0e4) + endl;
info += "ICRS State vector:" + endl;
Console.WriteLine(info);
info = " Position ";
for (i = 0; i < 3; i++)
{
info += String.Format("{0, 14:F6}", r[i] / 1000.0);
}
;
info += " [km]";
Console.WriteLine(info);
info = " Velocity ";
for (i = 0; i < 3; i++)
{
info += String.Format("{0, 14:F6}", v[i] / 1000.0);
}
;
info += " [km/s]" + endl + endl;
Console.WriteLine(info);
info = "Orbital elements:" + endl + endl
+ " Semimajor axis " + String.Format("{0, 10:F3}", Kep[0] / 1000.0) + " km" + endl
+ " Eccentricity " + String.Format("{0, 10:F7}", Kep[1]) + endl
+ " Inclination " + String.Format("{0, 10:F3}", Kep[2] * OrbitConsts.DegPerRad) + " deg" + endl
+ " RA ascend. node " + String.Format("{0, 10:F3}", Kep[3] * OrbitConsts.DegPerRad) + " deg" + endl
+ " Arg. of perigee " + String.Format("{0, 10:F3}", Kep[4] * OrbitConsts.DegPerRad) + " deg" + endl
+ " Mean anomaly " + String.Format("{0, 10:F3}", Kep[5] * OrbitConsts.DegPerRad) + " deg" + endl;
Console.WriteLine(info);
Console.ReadKey();
}
static void Main0(string[] args)
{
// Variables
double MJD_UTC; // Modified Julian Date (UTC)
double MJD_UT1; // Modified Julian Date (UTC)
double MJD_TT; // Modified Julian Date (TT)
Matrix P = new Matrix(3, 3); // Precession matrix (ICRS -> mean-of-date)
Matrix N = new Matrix(3, 3); // Nutation matrix (mean-of-date -> true-of-date)
Matrix Theta = new Matrix(3, 3); // Sidereal Time matrix (tod -> pseudo-Earth-fixed)
Matrix Pi = new Matrix(3, 3); // Polar motion matrix (pseudo-Earth-fixed -> ITRS)
// Header
var info = "Exercise 5-1: Transformation from celestial "
+ "to terrestrial reference system" + "\r\n";
Console.WriteLine(info);
// Earth Orientation Parameters (UT1-UTC[s],UTC-TAI[s], x["], y["])
// (from IERS Bulletin B #135 and C #16; valid for 1999/03/04 0:00 UTC)
IERS IERS = new IERS(0.6492332, -32.0, 0.06740, 0.24173);
// Date
MJD_UTC = DateUtil.DateToMjd(1999, 03, 04, 0, 0, 0.0);
MJD_UT1 = MJD_UTC + IERS.GetUT1_UTC(MJD_UTC) / 86400.0;
MJD_TT = MJD_UTC + IERS.GetTT_UTC(MJD_UTC) / 86400.0;
// IAU 1976 Precession
// (ICRF to mean equator and equinox of date)
P = IERS.PrecessionMatrix(OrbitConsts.MJD_J2000, MJD_TT);
// IAU 1980 Nutation
// (Transformation to the true equator and equinox)
N = IERS.NutMatrix(MJD_TT);
// Apparent Sidereal Time
// Rotation about the Celestial Ephemeris Pole
Theta = IERS.GreenwichHourAngleMatrix(MJD_UT1); // Note: here we evaluate the equation of the
// equinoxes with the MJD_UT1 time argument
// (instead of MJD_TT)
// Polar motion
// (Transformation from the CEP to the IRP of the ITRS)
Pi = IERS.PoleMatrix(MJD_UTC); // Note: the time argument of polar motion series
// is not rigorously defined, but any differences
// are negligible
// Output
var endl = "\r\n";
info = "Date" + "\r\n"
+ " " + DateUtil.MjdToDateTimeString(MJD_UTC) + " UTC" + endl
+ " " + DateUtil.MjdToDateTimeString(MJD_UT1) + " UT1" + endl
+ " " + DateUtil.MjdToDateTimeString(MJD_TT) + " TT " + endl + endl + endl;
Console.WriteLine(info);
info = "IAU 1976 Precession matrix (ICRS to tod)" + endl
+ P.ToString();
Console.WriteLine(info);
info = "IAU 1980 Nutation matrix (tod to mod)" + endl
+ N.ToString();
Console.WriteLine(info);
info = "Earth Rotation matrix" + endl
+ Theta.ToString();
Console.WriteLine(info);
info = "Polar motion matrix" + endl
+ Pi.ToString();
Console.WriteLine(info);
info = "ICRS-ITRS transformation" + endl
+ (Pi * Theta * N * P).ToString();
Console.WriteLine(info);
Console.ReadKey();
}