public static float GetT0(GravitySystem gravitySystem)
{
GravitySystem parentSystem = gravitySystem.parentSystem;
// No Central body, thus no prediction
if (!parentSystem)
{
return(0);
}
float x = gravitySystem.localStartPosition.x;
float y = gravitySystem.localStartPosition.y;
float q = instance.gravityConstant * parentSystem.GetMass();
float a = gravitySystem.localStartPosition.magnitude;
float T = 2 * Mathf.PI * Mathf.Sqrt(Mathf.Pow(a, 3) / q);
float xt0 = -(Mathf.Acos(x / a) * T) / (2 * Mathf.PI);
float yt0 = -(Mathf.Asin(y / a) * T) / (2 * Mathf.PI);
string s = gravitySystem.name + "\n";
s += "X: " + x + " xT0: " + xt0 + "\n";
s += "Y: " + y + " yT0: " + yt0 + "\n";
print(s);
float t0 = 0;
t0 = y > 0 ? xt0 : yt0;
t0 = y < 0 && x < 0 ? -xt0: t0;
return(t0);
}
/*
* Circular Orbit Prediction
*
* x(t)=acos( (2π(t−t0)) / T)
* y(t)=asin( (2π(t−t0)) / T)
*
* T=2π * sqrt( a^3 / q )
*
* of the central body
* q = G * M
*/
public static OrbitPrediction GetStaticOrbitPrediction(float t, GravitySystem gravitySystem)
{
GravitySystem parentSystem = gravitySystem.parentSystem;
// No Central body, thus no prediction
if (!parentSystem)
{
return(new OrbitPrediction(t, gravitySystem));
}
float q = instance.gravityConstant * parentSystem.GetMass();
float a = gravitySystem.localStartPosition.magnitude;
float T = 2 * Mathf.PI * Mathf.Sqrt(Mathf.Pow(a, 3) / q);
float t0 = gravitySystem.t0;
float x = a * Mathf.Cos((2 * Mathf.PI * (t - t0)) / T);
float y = a * Mathf.Sin((2 * Mathf.PI * (t - t0)) / T);
float xV = -a *Mathf.Sin((2 * Mathf.PI * (t - t0)) / T) * (2 * Mathf.PI) / T;
float yV = a * Mathf.Cos((2 * Mathf.PI * (t - t0)) / T) * (2 * Mathf.PI) / T;
Vector2 localPosition = new Vector2(x, y);
Vector2 localVelocity = new Vector2(xV, yV);
return(new OrbitPrediction(t, localPosition, localVelocity));
}
/// <summary>
/// In Editor
/// </summary>
public void CheckSystem()
{
mass = 0;
if (!renderer)
{
renderer = GetComponentInChildren <SpriteRenderer>();
}
//Radius of Influence
GravitySystem parentSystem = null;
if (transform.parent)
{
parentSystem = transform.parent.GetComponent <GravitySystem>();
}
if (parentSystem)
{
float distToParentSytem = ((Vector2)parentSystem.transform.position - (Vector2)transform.position).magnitude;
radiusOfInfluence = OrbitMath.CircleOfInfluence(distToParentSytem, GetMass(), parentSystem.GetMass());
}
else
{
radiusOfInfluence = 10000;
}
// Add Siblings in RadiusOfInfluence
if (parentSystem)
{
GravitySystem[] siblingSystems = parentSystem.GetChildSystems();
foreach (GravitySystem siblingSystem in siblingSystems)
{
if (siblingSystem == this)
{
continue;
}
float distance = Vector2.Distance(transform.position, siblingSystem.transform.position);
if (distance < radiusOfInfluence && siblingSystem.GetMass() < GetMass())
{
siblingSystem.transform.SetParent(transform);
}
if (distance < siblingSystem.radiusOfInfluence && siblingSystem.GetMass() > GetMass())
{
transform.SetParent(siblingSystem.transform);
}
}
}
// Check if this system exited another System
if (parentSystem)
{
float distance = Vector2.Distance(transform.position, parentSystem.transform.position);
if (distance > parentSystem.radiusOfInfluence)
{
transform.SetParent(parentSystem.transform.parent);
}
}
}