private void ApplyBoost(out Vector2D[] x, out Vector2D[] v)
{
double h = 3.0;
int numSteps = 7000;
x = new Vector2D[numSteps + 1];
v = new Vector2D[numSteps + 1];
for (int i = 0; i < numSteps + 1; i++)
{
x[i] = new Vector2D();
v[i] = new Vector2D();
}
x[0].x = 15e6;
x[0].y = 1e6;
v[0].x = 2e3;
v[0].y = 4e3;
bool boostDone = false;
for (int step = 0; step < numSteps; step++)
{
if (h * step >= 2.0 * 3600.0 && !boostDone)
{
v[step] += 300.0 * v[step] / v[step].Length();
boostDone = true;
}
Vector2D acceleration0 = Acceleration(x[step]);
Vector2D xE = x[step] + h * v[step];
Vector2D vE = v[step] + h * acceleration0;
x[step + 1] = x[step] + h * 0.5 * (v[step] + vE);
v[step + 1] = v[step] + h * 0.5 * (acceleration0 + Acceleration(xE));
}
}
public Vector2D Acceleration(Vector2D moonPosition, Vector2D spaceshipPosition)
{
Vector2D vectorToEarth = -spaceshipPosition;
Vector2D vectorToMoon = moonPosition - spaceshipPosition;
Vector2D acc = G * (earthMass * vectorToEarth / Math.Pow(vectorToEarth.Length(), 3) + moonMass * vectorToMoon / Math.Pow(vectorToMoon.Length(), 3));
return acc;
}
private Vector2D Acceleration(double time, Vector2D position)
{
Vector2D moonPos = MoonPosition(time);
Vector2D vectorFromMoon = position - moonPos;
Vector2D vectorFromEarth = position;
Vector2D acc = -gravitationalConstant * (earthMass * vectorFromEarth / Math.Pow(vectorFromEarth.Length(), 3) + moonMass * vectorFromMoon / Math.Pow(vectorFromMoon.Length(), 3));
return acc;
}
private void CalculateError(int numSteps, out double h, out double e)
{
h = totalTime / numSteps;
Vector2D[] x = new Vector2D[numSteps + 1];
Vector2D[] v = new Vector2D[numSteps + 1];
for (int i = 0; i < numSteps + 1; i++)
{
x[i] = new Vector2D();
v[i] = new Vector2D();
}
x[0].x = radius;
v[0].y = speed;
for (int step = 0; step < numSteps; step++)
{
x[step + 1] = x[step] + h * v[step];
v[step + 1] = v[step] + h * Acceleration(x[step]);
}
e = (x[numSteps] - x[0]).Length();
}
private Vector2D Acceleration(Vector2D spaceshipPosition)
{
Vector2D vectorToEarth = -spaceshipPosition;//earth located at origin
return gravitationalConstant * earthMass * vectorToEarth / Math.Pow(vectorToEarth.Length(), 3);
}
private void TotalEnergy(out Vector2D[] x, out double[] energy)
{
int numSteps = 20000;
double h = 5.0;//s
x = new Vector2D[numSteps + 1]; // m
Vector2D[] v = new Vector2D[numSteps + 1]; // m / s
energy = new double[numSteps + 1];// J = kg m2 / s2
for (int i = 0; i < numSteps + 1; i++)
{
x[i] = new Vector2D();
v[i] = new Vector2D();
}
x[0].x = 15e6;
x[0].y = 1e6;
v[0].x = 2e3;
v[0].y = 4e3;
for (int step = 0; step < numSteps; step++)
{
x[step + 1] = x[step] + h * v[step];
v[step + 1] = v[step] + h * Acceleration(x[step]);
}
for (int step = 0; step < numSteps + 1; step++)
{
energy[step] = 0.5 * spacecraftMass * Math.Pow(v[step].Length(), 2) - gravitationalConstant * earthMass * spacecraftMass / x[step].Length();
}
}
private void Orbit(out Vector2D x, out Vector2D v)
{
x = new Vector2D(); // m
v = new Vector2D(); // m / s
x.x = 15e6;
x.y = 1e6;
v.x = 2e3;
v.y = 4e3;
StringBuilder sb = new StringBuilder();
sb.Append("x.x,x.y,s" + Environment.NewLine);
sb.Append(x.x + "," + x.y + "," + 4 + Environment.NewLine);
double currentTime = 0.0d; // s
double h = 100.0d;// s
double hNew = h;// s, will store the adaptive step size of the next step
double tolerance = 5e5;//m
while (currentTime < totalTime)
{
Vector2D acceleration0 = Acceleration(x);
Vector2D xE = x + h * v;
Vector2D vE = v + h * acceleration0;
Vector2D xH = x + h * 0.5 * (v + vE);
Vector2D vH = v + h * 0.5 * (acceleration0 + Acceleration(xE));
x = xH;
v = vH;
double error = (xE - xH).Length() + totalTime * ((vE - vH).Length());
hNew = h * Math.Sqrt(tolerance / (error + 1e-50));
hNew = Math.Min(1800.0d, Math.Max(0.1d, hNew));
sb.Append(x.x + "," + x.y + "," + 1 + Environment.NewLine);
currentTime += h;
h = hNew;
}
sb.Append(0 + "," + 0 + "," + 0 + Environment.NewLine);
File.WriteAllText("adaptive_step_size.csv", sb.ToString());
}
private void HeunsMethod(int numSteps, out Vector2D[] x, out Vector2D[] v, out double error)
{
double h = totalTime / numSteps;
x = new Vector2D[numSteps + 1];
v = new Vector2D[numSteps + 1];
for (int i = 0; i < numSteps + 1; i++)
{
x[i] = new Vector2D();
v[i] = new Vector2D();
}
x[0].x = radius;
v[0].y = speed;
for (int step = 0; step < numSteps; step++)
{
x[step + 1] = x[step] + h * v[step];
v[step + 1] = v[step] + h * Acceleration(x[step]);
}
error = (x[numSteps] - x[0]).Length();
hArray.Add(h);
eulerErrorArray.Add(error);
//Heun's Method
for (int step = 0; step < numSteps; step++)
{
Vector2D initialAcceleration = Acceleration(x[step]);
Vector2D xE = x[step] + h * v[step];
Vector2D vE = v[step] + h * initialAcceleration;
x[step + 1] = x[step] + h * 0.5 * (v[step] + vE);
v[step + 1] = v[step] + h * 0.5 * (initialAcceleration + Acceleration(xE));
}
error = (x[numSteps] - x[0]).Length();
heunsErrorArray.Add(error);
}
private Vector2D MoonPosition(double time)
{
double moonAngle = moonInitialAngle + 2.0 * Math.PI * time / moonPeriod;
Vector2D position = new Vector2D();
position.x = moonDistance * Math.Cos(moonAngle);
position.y = moonDistance * Math.Sin(moonAngle);
return position;
}
