static void Main0(string[] args)
{
// Ground station
const double lon_Sta = 11.0 * OrbitConsts.RadPerDeg; // [rad]
const double lat_Sta = 48.0 * OrbitConsts.RadPerDeg; // [rad]
const double alt_h = 0.0e3; // [m]
GeoCoord StaGeoCoord = new GeoCoord(lon_Sta, lat_Sta, alt_h); // Geodetic coordinates
// Spacecraft orbit
double Mjd_Epoch = DateUtil.DateToMjd(1997, 01, 01, 0, 0, 0); // Epoch
const double a = 960.0e3 + OrbitConsts.RadiusOfEarth; // Semimajor axis [m]
const double e = 0.0; // Eccentricity
const double i = 97.0 * OrbitConsts.RadPerDeg; // Inclination [rad]
const double Omega = 130.7 * OrbitConsts.RadPerDeg; // RA ascend. node [rad]
const double omega = 0.0 * OrbitConsts.RadPerDeg; // Argument of latitude [rad]
const double M0 = 0.0 * OrbitConsts.RadPerDeg; // Mean anomaly at epoch [rad]
Vector kepElements = new Geo.Algorithm.Vector(a, e, i, Omega, omega, M0); // Keplerian elements
// Variables
double Mjd_UTC, dt;
// Station
var R_Sta = StaGeoCoord.ToXyzVector(OrbitConsts.RadiusOfEarth, OrbitConsts.FlatteningOfEarth); // Geocentric position vector
Matrix E = StaGeoCoord.ToLocalNez_Matrix(); // Transformation to
// local tangent coordinates
// Header
var info = "Exercise 2-4: Topocentric satellite motion" + "\r\n"
+ " Date UTC Az El Dist" + "\r\n"
+ "yyyy/mm/dd hh:mm:ss.sss [deg] [deg] [km]";
Console.WriteLine(info);
// Orbit
for (int Minute = 6; Minute <= 24; Minute++)
{
Mjd_UTC = Mjd_Epoch + Minute / 1440.0; // Time
dt = (Mjd_UTC - Mjd_Epoch) * 86400.0; // Time since epoch [s]
Geo.Algorithm.Vector r = Kepler.State(OrbitConsts.GM_Earth, kepElements, dt).Slice(0, 2); // Inertial position vector
Matrix U = Matrix.RotateZ3D(IERS.GetGmstRad(Mjd_UTC)); // Earth rotation
var enz = E * (U * r - R_Sta); // Topocentric position vector
double Azim = 0, Elev = 0, Dist;
GeoCoord.LocalEnzToPolar(enz, out Azim, out Elev, out Dist); // Azimuth, Elevation
info = DateUtil.MjdToDateTimeString(Mjd_UTC) + " " + String.Format("{0, 9:F3}", (Azim * OrbitConsts.DegPerRad)) + " " + String.Format("{0, 9:F3}", (Elev * OrbitConsts.DegPerRad))
+ " " + String.Format("{0, 9:F3}", (Dist / 1000.0));
Console.WriteLine(info);
}
;
Console.ReadKey();
}
static void Main0(string[] args)
{
// Constants
const double GM = 1.0; // Gravitational coefficient
const double e = 0.1; // Eccentricity
const double t_end = 20.0; // End time
Geo.Algorithm.Vector Kep = new Geo.Algorithm.Vector(1.0, e, 0.0, 0.0, 0.0, 0.0); // (a,e,i,Omega,omega,M)
Geo.Algorithm.Vector y_ref = Kepler.State(GM, Kep, t_end); // Reference solution
int[] Steps = { 50, 100, 250, 500, 750, 1000, 1500, 2000 };
// Variables
// Function call count
int iCase;
double t, h; // Time and step aboutSize
Geo.Algorithm.Vector y = new Geo.Algorithm.Vector(6); // State vector
RungeKutta4StepIntegrator Orbit = new RungeKutta4StepIntegrator(f_Kep6D, 6, (Action)nCallsPlus); // Object for integrating the
// differential equation
// defined by f_Kep6D using the
// 4th-order Runge-Kutta method
// Header
var info = "Exercise 4-1: Runge-Kutta 4th-order integration" + "\r\n" + "\r\n"
+ " Problem D1 (e=0.1)" + "\r\n" + "\r\n"
+ " N_fnc Accuracy Digits " + "\r\n";
Console.WriteLine(info);
// Loop over test cases
for (iCase = 0; iCase < 8; iCase++)
{
// Step aboutSize
h = t_end / Steps[iCase];
// Initial values
t = 0.0;
y = new Geo.Algorithm.Vector(1.0 - e, 0.0, 0.0, 0.0, Math.Sqrt((1 + e) / (1 - e)), 0.0);
nCalls = 0;
// Integration from t=t to t=t_end
for (int i = 1; i <= Steps[iCase]; i++)
{
Orbit.Step(ref t, ref y, h);
}
// Output
info = String.Format("{0, 6:D}{1, 14:E4}{2, 9:F}", nCalls, (y - y_ref).Norm(), -Math.Log10((y - y_ref).Norm()));
Console.WriteLine(info);
}
;
Console.ReadKey();
}
static void Main0(string[] args)
{
// Constants
const double GM = 1.0; // Gravitational coefficient
const double e = 0.1; // Eccentricity
const double t_end = 20.0; // End time
Geo.Algorithm.Vector Kep = new Geo.Algorithm.Vector(1.0, e, 0.0, 0.0, 0.0, 0.0); // (a,e,i,Omega,omega,M)
Geo.Algorithm.Vector y_ref = Kepler.State(GM, Kep, t_end); // Reference solution
int[] Steps = { 100, 300, 600, 1000, 1500, 2000, 3000, 4000 };
// Variables
// Function call count
int iCase;
double t, h; // Time and step aboutSize
GaussJackson4OrderPredictor Orbit = new GaussJackson4OrderPredictor(f_Kep3D, 3, nCallsPlus); // Object for integrating the
// 2nd order diff. equation
// defined by f_Kep3D using the 4th-order GJ predictor
// Header
var info = "Exercise 4-2: Gauss-Jackson 4th-order predictor" + "\r\n";
info += " Problem D1 (e=0.1)" + "\r\n";
info += " N_fnc Accuracy Digits " + "\r\n";
Console.WriteLine(info);
// Loop over test cases
for (iCase = 0; iCase < 8; iCase++)
{
// Step aboutSize
var step = Steps[iCase];
h = t_end / step;
// Initial values
nCalls = 0;
t = 0.0;
var y = Orbit.GetState(e, t, h, step);
info = String.Format("{0, 6:D}{1, 14:E4}{2, 9:F}", nCalls, (y - y_ref).Norm(), -Math.Log10((y - y_ref).Norm()));
Console.WriteLine(info);
}
Console.ReadKey();
}
static void Main0(string[] args)
{
// Constants
const double GM = 1.0; // Gravitational coefficient
const double e = 0.9; // Eccentricity
const double t_end = 20.0; // End time
Geo.Algorithm.Vector Kep = new Geo.Algorithm.Vector(1.0, e, 0.0, 0.0, 0.0, 0.0); // (a,e,i,Omega,omega,M)
Geo.Algorithm.Vector y_ref = Kepler.State(GM, Kep, t_end); // Reference solution
// Variables
double t; // Time
double relerr, abserr; // Accuracy requirements
Geo.Algorithm.Vector y = new Geo.Algorithm.Vector(6); // State vector
AuxDataRecord Aux = new AuxDataRecord(); // Auxiliary satData
DeIntegrator Orbit = new DeIntegrator(f_Kep6D_, 6, Aux); // Object for integrating the
// differential equation
// defined by f_Kep6D_
// Header
var info = "Exercise 4-3: Step size control of DE multistep method" + "\r\n";
info += " Step t h r " + "\r\n";
Console.WriteLine(info);
// Initial values
t = 0.0;
y = new Geo.Algorithm.Vector(1.0 - e, 0.0, 0.0, 0.0, Math.Sqrt((1 + e) / (1 - e)), 0.0);
Aux.n_step = 0;
Aux.t = 0;
relerr = 0.0;
abserr = 1.0e-8;
// Integration from t=t to t=t_end
Orbit.Init(t, relerr, abserr);
Orbit.Integ(t_end, y);
Console.ReadKey();
}
static void Main0(string[] args)
{
// Ground station
const double lon_Sta = 11.0 * OrbitConsts.RadPerDeg; // [rad]
const double lat_Sta = 48.0 * OrbitConsts.RadPerDeg; // [rad]
const double alt_h = 0.0e3; // [m]
GeoCoord Sta = new GeoCoord(lon_Sta, lat_Sta, alt_h); // Geodetic coordinates
// Fixed media satData at ground site
const double T0 = 273.2; // Temperature at 0 deg C [K]
const double pa = 1024.0; // Partial pressure of dry air [mb]
const double fh = 0.7; // Relative humidity
// Spacecraft orbit
double Mjd_Epoch = DateUtil.DateToMjd(1997, 01, 01); // Epoch
const double a = 42164.0e3; // Semimajor axis [m]
const double e = 0.000296; // Eccentricity
const double i = 0.05 * OrbitConsts.RadPerDeg; // Inclination [rad]
const double Omega = 150.7 * OrbitConsts.RadPerDeg; // RA ascend. node [rad]
const double omega = 0.0 * OrbitConsts.RadPerDeg; // Argument of latitude [rad]
const double M0 = 0.0 * OrbitConsts.RadPerDeg; // Mean anomaly at epoch [rad]
Vector Kep = new Vector(a, e, i, Omega, omega, M0); // Keplerian elements
// Variables
int Hour;
double Mjd_UTC, dt;
double Azim = 0, Elev = 0, Elev0 = 0, Dist;
double Ns, eh, T, TC;
Vector dElev = new Vector(2);
Vector R_Sta = new Vector(3);
Vector r = new Vector(3), s = new Vector(3);
Matrix U = new Matrix(3, 3), E = new Matrix(3, 3);
double[] Tv = { 303.0, 283.0 }; // Temperature [K]
// Station
R_Sta = Sta.ToXyzVector(OrbitConsts.RadiusOfEarth, OrbitConsts.FlatteningOfEarth); // Geocentric position vector
E = Sta.ToLocalNez_Matrix(); // Transformation to
// local tangent coordinates
// Header
var endl = "\r\n";
var info = "Exercise 6-4: Tropospheric Refraction" + endl + endl;
Console.Write(info);
// Orbit
for (Hour = 0; Hour <= 8; Hour++)
{
Mjd_UTC = Mjd_Epoch + 3.0 * Hour / 24.0; // Modified Julian Date [UTC]
dt = (Mjd_UTC - Mjd_Epoch) * 86400.0; // Time since epoch [s]
r = Kepler.State(OrbitConsts.GM_Earth, Kep, dt).Slice(0, 2); // Inertial position vector
U = Matrix.RotateZ3D(IERS.GetGmstRad(Mjd_UTC)); // Earth rotation
s = E * (U * r - R_Sta); // Topocentric position vector
GeoCoord.LocalEnzToPolar(s, out Azim, out Elev, out Dist); // Azimuth, Elevation
if (Hour == 0)
{
Elev0 = Elev; // Store initial elevation
info = "E0 [deg] " + String.Format("{0, 10:F3}", Elev0 * OrbitConsts.DegPerRad) + endl + endl;
Console.Write(info);
info = " Date UTC E-E0 dE_t1 dE_t2 " + endl
+ "yyyy/mm/dd hh:mm:ss.sss [deg] [deg] [deg]" + endl;
Console.Write(info);
}
;
for (int Ti = 0; Ti <= 1; Ti++)
{ // Evaluate at 2 temperatures
T = Tv[Ti]; // Map to scalar
TC = T - T0; // Temperature [C]
eh = 6.10 * fh * Math.Exp(17.15 * TC / (234.7 + TC)); // Partial water pressure
Ns = 77.64 * pa / T + 3.734e5 * eh / (T * T); // Refractivity
dElev[Ti] = Ns * 1.0e-6 / Math.Tan(Elev); // Tropospheric refraction
}
;
info = DateUtil.MjdToDateTimeString(Mjd_UTC)
+ String.Format("{0, 10:F3}", (Elev - Elev0) * OrbitConsts.DegPerRad)
+ String.Format("{0, 10:F3}", dElev[0] * OrbitConsts.DegPerRad) + String.Format("{0, 10:F3}", dElev[1] * OrbitConsts.DegPerRad) + endl;
Console.Write(info);
}
;
Console.ReadKey();
}
static void Main0(string[] args)
{
// Ground station
const double lon_Sta = 11.0 * OrbitConsts.RadPerDeg; // [rad]
const double lat_Sta = 48.0 * OrbitConsts.RadPerDeg; // [rad]
const double alt_h = 0.0e3; // [m]
GeoCoord Sta = new GeoCoord(lon_Sta, lat_Sta, alt_h); // Geodetic coordinates
// Spacecraft orbit
double Mjd_Epoch = DateUtil.DateToMjd(1997, 01, 01); // Epoch
const double a = 960.0e3 + OrbitConsts.RadiusOfEarth; // Semimajor axis [m]
const double e = 0.0; // Eccentricity
const double i = 97.0 * OrbitConsts.RadPerDeg; // Inclination [rad]
const double Omega = 130.7 * OrbitConsts.RadPerDeg; // RA ascend. node [rad]
const double omega = 0.0 * OrbitConsts.RadPerDeg; // Argument of latitude [rad]
const double M0 = 0.0 * OrbitConsts.RadPerDeg; // Mean anomaly at epoch [rad]
Vector Kep = new Vector(a, e, i, Omega, omega, M0); // Keplerian elements
// Light time iteration
const int I_max = 2; // Maxim. number of iterations
// Variables
int Iteration, Step; // Loop counters
double Mjd_UTC, t; // Time
double rho, range; // Range 1-way/2-way
double tau_up, tau_down; // Upleg/downleg light time
Vector R_Sta = new Vector(3); // Earth-fixed station position
Vector r_Sta = new Vector(3); // Inertial station position
Vector r = new Vector(3); // Inertial satellite position
Vector rho_up = new Vector(I_max + 1), rho_down = new Vector(I_max + 1); // Upleg/downleg range
Matrix U = new Matrix(3, 3); // Earth rotation matrix
// Station
R_Sta = Sta.ToXyzVector(OrbitConsts.RadiusOfEarth, OrbitConsts.FlatteningOfEarth); // Geocentric position vector
// Header
var endl = "\r\n";
var info = "Exercise 6-1: Light time iteration" + endl + endl
+ " Date UTC Distance " +
"Down It 1 It 2 Up It 1 Range" + endl
+ "yyyy/mm/dd hh:mm:ss.sss [m] " +
" [m] [mm] [m] [m] " + endl;
Console.WriteLine(info);
// Orbit
for (Step = 0; Step <= 6; Step++)
{
// Ground-received time
t = 360.0 + 180.0 * Step; // Time since epoch [s]
Mjd_UTC = Mjd_Epoch + t / 86400.0; // Modified Julian Date [UTC]
U = Matrix.RotateZ3D(IERS.GetGmstRad(Mjd_UTC)); // Earth rotation matrix
r_Sta = U.Transpose() * R_Sta; // Inertial station position
// Light time iteration for downleg satellite -> station
tau_down = 0.0;
for (Iteration = 0; Iteration <= I_max; Iteration++)
{
r = Kepler.State(OrbitConsts.GM_Earth, Kep, t - tau_down).Slice(0, 2); // Spacecraft position
rho = (r - r_Sta).Norm(); // Downleg range
tau_down = rho / OrbitConsts.SpeedOfLight; // Downleg light time
rho_down[Iteration] = rho;
}
;
// Light time iteration for upleg station -> satellite
tau_up = 0.0;
for (Iteration = 0; Iteration <= I_max; Iteration++)
{
U = Matrix.RotateZ3D(IERS.GetGmstRad(Mjd_UTC - (tau_down + tau_up) / 86400.0));
r_Sta = U.Transpose() * R_Sta; // Inertial station pos.
rho = (r - r_Sta).Norm(); // at ground transmit time
tau_up = rho / OrbitConsts.SpeedOfLight; // Upleg light time
rho_up[Iteration] = rho;
}
;
// Two-way range
range = 0.5 * (rho_down[I_max] + rho_up[I_max]);
info = DateUtil.MjdToDateTimeString(Mjd_UTC)
+ String.Format("{0,15:F3}{1,9:F3}{2,9:F3}{3,8:F3}{4,12:F3}", rho_down[0], rho_down[1] - rho_down[0], (rho_down[2] - rho_down[1]) * 1000.0, rho_up[1] - rho_up[0], range);
Console.WriteLine(info);
}
Console.ReadKey();
}
static void Main(string[] args)
{
// Constants
const double relerr = 1.0e-13; // Relative and absolute
const double abserr = 1.0e-6; // accuracy requirement
const double a = OrbitConsts.RadiusOfEarth + 650.0e3; // Semi-major axis [m]
const double e = 0.001; // Eccentricity
const double inc = OrbitConsts.RadPerDeg * 51.0; // Inclination [rad]
double n = Math.Sqrt(OrbitConsts.GM_Earth / (a * a * a)); // Mean motion
Matrix Scale = Matrix.CreateDiagonal(new Geo.Algorithm.Vector(1, 1, 1, 1 / n, 1 / n, 1 / n)); // Velocity
Matrix scale = Matrix.CreateDiagonal(new Geo.Algorithm.Vector(1, 1, 1, n, n, n)); // normalization
const double t_end = 86400.0;
const double step = 300.0;
// Variables
int i, j; // Loop counters
double Mjd0; // Epoch (Modified Julian Date)
double t; // Integration time [s]
double max, max_Kep; // Matrix error norm
AuxParam7 Aux1 = new AuxParam7(), Aux2 = new AuxParam7(); // Auxiliary parameter records
// Model parameters for reference solution (full 10x10 gravity model) and
// simplified variational equations
// Epoch state and transition matrix
Mjd0 = OrbitConsts.MJD_J2000;
Aux1.Mjd_0 = Mjd0; // Reference epoch
Aux1.n_a = 10; // Degree of gravity field for trajectory computation
Aux1.m_a = 10; // Order of gravity field for trajectory computation
Aux1.n_G = 10; // Degree of gravity field for variational equations
Aux1.m_G = 10; // Order of gravity field for variational equations
Aux2.Mjd_0 = Mjd0; // Reference epoch
Aux2.n_a = 2; // Degree of gravity field for trajectory computation
Aux2.m_a = 0; // Order of gravity field for trajectory computation
Aux2.n_G = 2; // Degree of gravity field for variational equations
Aux2.m_G = 0; // Order of gravity field for variational equations
DeIntegrator Int1 = new DeIntegrator(VarEqn, 42, Aux1); // Object for integrating the variat. eqns.
DeIntegrator Int2 = new DeIntegrator(VarEqn, 42, Aux2); //
Geo.Algorithm.Vector y0 = new Geo.Algorithm.Vector(6), y = new Geo.Algorithm.Vector(6); // State vector
Geo.Algorithm.Vector yPhi1 = new Geo.Algorithm.Vector(42), yPhi2 = new Geo.Algorithm.Vector(42); // State and transition matrix vector
Matrix Phi1 = new Matrix(6, 6), Phi2 = new Matrix(6, 6); // State transition matrix
Matrix Phi_Kep = new Matrix(6, 6); // State transition matrix (Keplerian)
y0 = Kepler.State(OrbitConsts.GM_Earth, new Geo.Algorithm.Vector(a, e, inc, 0.0, 0.0, 0.0));
for (i = 0; i <= 5; i++)
{
yPhi1[i] = y0[i];
for (j = 0; j <= 5; j++)
{
yPhi1[6 * (j + 1) + i] = (i == j ? 1 : 0);
}
}
yPhi2 = new Geo.Algorithm.Vector(yPhi1);
// Initialization
t = 0.0;
Int1.Init(t, relerr, abserr);
Int2.Init(t, relerr, abserr);
// Header
var endl = "\r\n";
var info = "Exercise 7-1: State transition matrix" + endl
+ endl
+ " Time [s] Error (J2) Error(Kep)" + endl;
// Steps
while (t < t_end)
{
// New output time
t += step;
// Integration
Int1.Integ(t, ref yPhi1); // Reference
Int2.Integ(t, ref yPhi2); // Simplified
//info= setprecision(5) + setw(12)+yPhi1 + endl;
//info= setprecision(5) + setw(12) + yPhi2 + endl;
// Extract and normalize state transition matrices
for (j = 0; j <= 5; j++)
{
Phi1.SetCol(j, yPhi1.Slice(6 * (j + 1), 6 * (j + 1) + 5));
}
for (j = 0; j <= 5; j++)
{
Phi2.SetCol(j, yPhi2.Slice(6 * (j + 1), 6 * (j + 1) + 5));
}
Phi1 = Scale * Phi1 * scale;
Phi2 = Scale * Phi2 * scale;
// Keplerian state transition matrix (normalized)
Kepler.TwoBody(OrbitConsts.GM_Earth, y0, t, ref y, ref Phi_Kep);
Phi_Kep = Scale * Phi_Kep * scale;
// Matrix error norms
max = Max(Matrix.CreateIdentity(6) - Phi1 * InvSymp(Phi2));
max_Kep = Max(Matrix.CreateIdentity(6) - Phi1 * InvSymp(Phi_Kep));
// Output
// info = String.Format( "{0, 10:F }{1, 10:F }{2, 10:F } ", t, max , max_Kep );
info = String.Format("{0, 10:F2}{1, 10:F2}{2, 12:F2}", t, max, max_Kep);
Console.WriteLine(info);
}
;
// Output
info = endl
+ "Time since epoch [s]" + endl
+ endl
+ String.Format("{0, 10:F}", t) + endl
+ endl;
Console.Write(info);
info = "State transition matrix (reference)" + endl
+ endl
+ Phi1 + endl;
Console.Write(info);
info = "J2 State transition matrix" + endl
+ endl
+ Phi2 + endl;
Console.Write(info);
info = "Keplerian State transition matrix" + endl
+ endl
+ Phi_Kep + endl;
Console.Write(info);
Console.ReadKey();
}
static void Main0(string[] args)
{
// Ground station
const double lon_Sta = 11.0 * OrbitConsts.RadPerDeg; // [rad]
const double lat_Sta = 48.0 * OrbitConsts.RadPerDeg; // [rad]
const double alt_h = 0.0e3; // [m]
GeoCoord Sta = new GeoCoord(lon_Sta, lat_Sta, alt_h); // Geodetic coordinates
// Earth rotation
Vector omega_vec = new Vector(0.0, 0.0, OrbitConsts.RotationSpeedOfEarth_Rad); // Earth rotation vector
// Spacecraft orbit
double Mjd_Epoch = DateUtil.DateToMjd(1997, 01, 01); // Epoch
const double a = 960.0e3 + OrbitConsts.RadiusOfEarth; // Semimajor axis [m]
const double e = 0.0; // Eccentricity
const double i = 97.0 * OrbitConsts.RadPerDeg; // Inclination [rad]
const double Omega = 130.7 * OrbitConsts.RadPerDeg; // RA ascend. node [rad]
const double omega = 0.0 * OrbitConsts.RadPerDeg; // Argument of latitude [rad]
const double M0 = 0.0 * OrbitConsts.RadPerDeg; // Mean anomaly at epoch [rad]
Vector Kep = new Vector(a, e, i, Omega, omega, M0); // Keplerian elements
// Radar Modelling
const int I_max = 3; // Maximum light time iterations
const double Count = 1.0; // Doppler count time [s]
// Variables
int Iteration, Step; // Loop counters
double Mjd_UTC, t; // Time
double rho; // Range 1-way
double range1, range0; // Range 2-way at end, begin of count
double range_rate; // Range rate
double Doppler; // Instantaneous Doppler
double tau_up, tau_down; // Upleg/downleg light time
double rho_up = 0, rho_down = 0; // Upleg/downleg range
Vector R_Sta = new Vector(3); // Earth-fixed station position
Vector r_Sta = new Vector(3); // Inertial station position
Vector r = new Vector(3); // Inertial satellite position
Vector x = new Vector(3), v = new Vector(3); // Earth-fixed satellite position, velocity
Vector u = new Vector(3); // Unit vector satellite station
Matrix U = new Matrix(3, 3); // Earth rotation matrix
// Station
R_Sta = Sta.ToXyzVector(OrbitConsts.RadiusOfEarth, OrbitConsts.FlatteningOfEarth); // Geocentric position vector
// Header
var endl = "\r\n";
var info = "Exercise 6-2: Range Rate Modelling" + endl + endl
+ " Date UTC Range Rate Doppler Difference" + endl
+ "yyyy/mm/dd hh:mm:ss.sss [m/s] [m/s] [m/s] " + endl;
Console.WriteLine(info);
// Orbit
for (Step = 0; Step <= 6; Step++)
{
// Ground-received time
t = 360.0 + 180.0 * Step; // Time since epoch [s]
Mjd_UTC = Mjd_Epoch + t / 86400.0; // Modified Julian Date [UTC]
U = Matrix.RotateZ3D(IERS.GetGmstRad(Mjd_UTC)); // Earth rotation matrix
r_Sta = U.Transpose() * R_Sta; // Inertial station position
// Light time iteration at count interval end for downleg satellite -> station
tau_down = 0.0;
for (Iteration = 0; Iteration <= I_max; Iteration++)
{
r = Kepler.State(OrbitConsts.GM_Earth, Kep, t - tau_down).Slice(0, 2); // Spacecraft position
rho = (r - r_Sta).Norm(); // Downleg range
tau_down = rho / OrbitConsts.SpeedOfLight; // Downleg light time
rho_down = rho;
}
;
// Light time iteration at count interval end for upleg station -> satellite
tau_up = 0.0;
for (Iteration = 0; Iteration <= I_max; Iteration++)
{
U = Matrix.RotateZ3D(IERS.GetGmstRad(Mjd_UTC - (tau_down + tau_up) / 86400.0));
r_Sta = U.Transpose() * R_Sta; // Inertial station pos.
rho = (r - r_Sta).Norm(); // at ground transmit time
tau_up = rho / OrbitConsts.SpeedOfLight; // Upleg light time
rho_up = rho;
}
;
// Two-way range at end of count interval
range1 = 0.5 * (rho_down + rho_up);
// Station position at begin of count interval
U = Matrix.RotateZ3D(IERS.GetGmstRad(Mjd_UTC - Count / 86400.0)); // Earth rotation matrix
r_Sta = U.Transpose() * R_Sta; // Inertial station position
// Light time iteration at count interval begin for downleg satellite -> station
tau_down = 0.0;
for (Iteration = 0; Iteration <= I_max; Iteration++)
{
r = Kepler.State(OrbitConsts.GM_Earth, Kep, t - tau_down - Count).Slice(0, 2); // Spacecraft position
rho = (r - r_Sta).Norm(); // Downleg range
tau_down = rho / OrbitConsts.SpeedOfLight; // Downleg light time
rho_down = rho;
}
;
// Light time iteration at count interval begin for upleg station -> satellite
tau_up = 0.0;
for (Iteration = 0; Iteration <= I_max; Iteration++)
{
U = Matrix.RotateZ3D(IERS.GetGmstRad(Mjd_UTC - (tau_down + tau_up + Count) / 86400.0));
r_Sta = U.Transpose() * R_Sta; // Inertial station pos.
rho = (r - r_Sta).Norm(); // at ground transmit time
tau_up = rho / OrbitConsts.SpeedOfLight; // Upleg light time
rho_up = rho;
}
;
// Two-way range at begin of count interval
range0 = 0.5 * (rho_down + rho_up);
// Two-way average range rate
range_rate = (range1 - range0) / Count;
// Instantaneous Doppler modelling at mid of count interval
U = Matrix.RotateZ3D(IERS.GetGmstRad(Mjd_UTC - (Count / 2.0) / 86400)); // Earth rotation matrix
x = U * Kepler.State(OrbitConsts.GM_Earth, Kep, t - (Count / 2.0)).Slice(0, 2); // Spacecraft position
v = U * Kepler.State(OrbitConsts.GM_Earth, Kep, t - (Count / 2.0)).Slice(3, 5) // Spacecraft velocity
- omega_vec.Cross3D(x);
u = (x - R_Sta) / (x - R_Sta).Norm(); // Unit vector s/c-station
Doppler = v.Dot(u); // Instantaneous Doppler
// Output
info = DateUtil.MjdToDateTimeString(Mjd_UTC) + String.Format("{0, 12:F3}{1, 12:F3}{2, 12:F3}", range_rate, Doppler, range_rate - Doppler);
Console.WriteLine(info);
}
Console.ReadKey();
}
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();
}
