public void GetEllipse(ref Vector3[] positions, int resolution)
{
if (resolution < 2)
{
positions = new Vector3[0];
return;
}
if (positions == null || positions.Length != resolution)
{
positions = new Vector3[resolution];
}
period = GetPeriod();
double slice = period / resolution;
OrbitData clone = new OrbitData(this);
positions[0] = (Vector3)(clone.Position * OrbitUtils.KM2AU);
for (int j = 1; j < resolution; j++)
{
clone.Epoch += slice;
positions[j] = (Vector3)(clone.Position * OrbitUtils.KM2AU);
}
}
// TODO: This function does not behave as expected and/or has not been successfully tested/implemented.
public static void GetPositionsAlongEllipse(ref Vector3[] positions, OrbitData orbit, int resolution)
{
if (resolution < 2)
{
positions = new Vector3[0];
return;
}
double a = orbit.SemiMajorAxis;
double ecc = orbit.Eccentricity;
double w = orbit.ArgumentOfPerifocus;
double nu = orbit.TrueAnomaly;
// Trigometrics for any values used more than once in calculations
double cosI = Math.Cos(orbit.Inclination);
double cosOm = Math.Cos(orbit.LongitudeOfAscendingNode);
double sinOm = Math.Sin(orbit.LongitudeOfAscendingNode);
double angle = TwoPI / resolution;
if (ecc < 1.0 && ecc >= 0.0)
{
if (positions == null || positions.Length != resolution)
{
positions = new Vector3[resolution];
}
for (int j = 0; j < resolution; j++)
{
// Radial distance [km]
double r = orbit.SemiMajorAxis * (1.0 - ecc * ecc) / (1.0 + ecc * Math.Cos(j * angle));
// Flight path angle [rad]
//double fpa = Math.Atan2(1.0 + ecc * Math.Cos(nu), ecc * Math.Sin(nu));
double fpa = Math.Atan(ecc * Math.Sin(nu) / (1.0 + ecc * Math.Cos(nu)));
double cosNuPlusW = Math.Cos(nu + w);
double sinNuPlusW = Math.Sin(nu + w);
float x = (float)(r * (cosNuPlusW * cosOm - sinNuPlusW * cosI * sinOm));
float y = (float)(r * (cosNuPlusW * sinOm + sinNuPlusW * cosI * cosOm));
float z = (float)(r * (sinNuPlusW * Math.Sin(orbit.Inclination)));
positions[j] = new Vector3(x, y, z);
}
}
else
{
Debug.LogWarning("Cannot draw orbital ellipse: orbit is parabolic/hyperbolic");
}
}
public LambertSolution(int nRevs, double TA, double pTA, double Vinf,
double C3, double Vimp, Vector3d arrDV,
double VimpDotProduct, OrbitData transferOrbit)
{
this.nRevs = nRevs;
this.TA = TA;
this.pTA = pTA;
this.Vinf = Vinf;
this.C3 = C3;
this.arrDV = arrDV;
this.Vimp = Vimp;
this.VimpDotProduct = VimpDotProduct;
this.TransferOrbit = transferOrbit;
}
/// <summary>
/// Calculates the change in velocity of an object from an impact/deflection
/// with a smaller body (e.g. kinetic impactor spacecraft) in the ecliptic plane.
/// </summary>
/// <returns>The delta V of <paramref name="deflected"/> in the ecliptic.</returns>
/// <param name="deflected">Orbit of the object being deflected at time of impact [km-s].</param>
/// <param name="impactor">Orbit of the impacting object at time of impact [km-s].</param>
/// <param name="massDeflected">Mass of the object being deflected [kg].</param>
/// <param name="massImpactor">Mass of the impacting object [kg].</param>
/// <param name="beta">The momentum enhancement factor from ejecta (1 = no enhacement).</param>
public static Vector3d CalculateDeflectionDeltaVEcliptic(OrbitData deflected, OrbitData impactor,
double massDeflected, double massImpactor, double beta = 1.0)
{
// Velocity of the impactor relative to the object being deflected.
Vector3d vrel = impactor.Velocity - deflected.Velocity;
//Vector3d vhat = deflected.Velocity.normalized;
//Vector3d vrelhat = vrel.normalized;
//double Vimp = vrel.magnitude;
//double VimpDotP = Vector3d.Dot(vhat, vrelhat);
// Delta V from deflection, in the ecliptic plane.
return(vrel * beta * massImpactor / massDeflected);
}
/// <summary>
/// Copy constructor.
/// </summary>
/// <param name="other">Orbit to copy.</param>
public OrbitData(OrbitData other)
{
epoch = other.epoch;
mu = other.mu;
a = other.a;
ecc = other.ecc;
i = other.i;
Om = other.Om;
w = other.w;
M = other.M;
nu = other.nu;
E = other.E;
pos = other.pos;
vel = other.vel;
N = other.N;
period = other.period;
}
/// <summary>
/// Calculates the change in velocity of an object from an impact/deflection
/// with a smaller body (e.g. kinetic impactor spacecraft) in the as (ΔVA, ΔVC, ΔVN).
/// </summary>
/// <remarks>
/// The ACN coordinate system is a coordinate system set up at the center of mass
/// of the asteroid at the time of deflection and used to express the magnitude
/// and direction of the velocity change imparted to the asteroid. Its pricipal
/// directions are:
/// Along-track direction (A): in the asteroid's orbital plane and along the
/// direction of the asteroid's current velocity vector about the Sun,
/// Normal direction (N): perpendicular to the asteroid's orbit plane and is
/// aligned with the positive orbital angular momentum vector (<c>r x v</c>)
/// where r is the vector from the Sun to the asteroid's current position,
/// Cross-track direction (C): in the orbital plane, perpendicular to the
/// along-track direction (<c>C = N x A</c>), and positive in the general
/// direction of the Sun.
/// References: NDA Handbook v6.3
/// Transformation from ecliptic to ACN coordinate system
/// provided by Jason Anderson of Aerospace 07-2018.
/// </remarks>
/// <returns>The delta V of <paramref name="deflected"/> in the ACN coordinate system.</returns>
/// <param name="deflected">Orbit of the object being deflected at time of impact [km-s].</param>
/// <param name="impactor">Orbit of the impacting object at time of impact [km-s].</param>
/// <param name="massDeflected">Mass of the object being deflected [kg].</param>
/// <param name="massImpactor">Mass of the impacting object [kg].</param>
/// <param name="beta">The momentum enhacement factor from ejecta (1 = no enhancement).</param>
public static Vector3d CalculateDeflectionDeltaVInAcn(OrbitData deflected, OrbitData impactor,
double massDeflected, double massImpactor, double beta = 1.0)
{
Vector3d deltaVEcliptic = CalculateDeflectionDeltaVEcliptic(deflected, impactor, massDeflected, massImpactor, beta);
// Velocity unit vector of object to deflect.
Vector3d vhat = deflected.Velocity.normalized;
// Angular momentum vector unit vector: hhat = pos x vel
Vector3d hhat = Vector3d.Cross(deflected.Position, deflected.Velocity).normalized;
Vector3d along = vhat;
Vector3d normal = hhat.normalized;
Vector3d cross = Vector3d.Cross(normal, along);
double va = Vector3d.Dot(deltaVEcliptic, along);
double vc = Vector3d.Dot(deltaVEcliptic, cross);
double vn = Vector3d.Dot(deltaVEcliptic, normal);
return(new Vector3d(va, vc, vn));
}
/// <summary>
/// Gets a new Lambert solution.
/// </summary>
/// <param name="from">Departure body orbit at time of impact.</param>
/// <param name="to">Arrival body orbit at time of impact.</param>
/// <param name="D">Number of days before impact the deflection is to occur.</param>
/// <param name="TOF_days">Time of flight [days]</param>
/// <param name="nRevs">Number of revolutions or -1 to search for optimal</param>
public static LambertSolution GetTransferOrbit(OrbitData from, OrbitData to,
double D, double TOF_days, int nRevs = -1)
{
Debug.Assert(Math.Abs(from.Epoch - to.Epoch) <= double.Epsilon);
// Make local copies of orbit parameters (passed by reference).
OrbitData dep = new OrbitData(from);
OrbitData arr = new OrbitData(to);
dep.Step(-(D + TOF_days));
arr.Step(-D);
Vector3d pos1 = dep.Position;
Vector3d vel1 = dep.Velocity;
Vector3d pos2 = arr.Position;
Vector3d vel2 = arr.Velocity;
Vector3d[] depDV = new Vector3d[2];
Vector3d[] arrDV = new Vector3d[2];
double[] TA = new double[2]; // Transfer angle
double[] Vinf = new double[2]; // Earth departure V-infinity
double[] C3 = new double[2];
int i;
if (nRevs < 0)
{
// Search for the best number of revolutions...
// Start the search with 0 and 1 revolutions.
for (i = 0; i < 2; i++)
{
nRevs = i;
// Calculate the Lambert arc from state1 to state2 in TOF days;
// Return the departure delta V and the arrival delta V.
CalcLambert(nRevs, pos1, vel1, pos2, vel2, TOF_days,
ref depDV[i], ref arrDV[i], out TA[i]);
// Earth departure V-infinity.
Vinf[i] = depDV[i].magnitude;
C3[i] = Vinf[i] * Vinf[i];
Debug.Log("Rev #" + nRevs + ": C3 = " + C3[i]);
}
// Storage index.
i = 1;
// Run until C3 does not improve.
while (C3[i == 1 ? 1 : 0] < C3[i == 1 ? 0 : 1])
{
// Alternate storing index.
i = (i == 0 ? 1 : 0);
// Next revolution.
nRevs++;
// Calculate the Lambert arc from state1 to state2 in TOF days;
// Return the departure delta V and the arrival delta V.
CalcLambert(nRevs, pos1, vel1, pos2, vel2, TOF_days,
ref depDV[i], ref arrDV[i], out TA[i]);
// Earth departure V-infinity.
Vinf[i] = depDV[i].magnitude;
C3[i] = Vinf[i] * Vinf[i];
Debug.Log("Rev #" + nRevs + ": C3 = " + C3[i]);
}
// Best solution is the previous iteration.
nRevs--;
i = (i == 0 ? 1: 0);
}
else
{
// Storage index.
i = 0;
// Calculate the Lambert arc from state1 to state2 in TOF days;
// Return the departure delta V and the arrival delta V.
CalcLambert(nRevs, pos1, vel1, pos2, vel2, TOF_days,
ref depDV[i], ref arrDV[i], out TA[i]);
// Earth departure V-infinity.
Vinf[i] = depDV[i].magnitude;
C3[i] = Vinf[i] * Vinf[i];
}
if (depDV[i] == Vector3d.zero)
{
return(null);
}
// Object impact velocity.
double Vimp = arrDV[i].magnitude;
// Planar transfer angle.
double pTA = Math.Atan2(pos2.y, pos2.x) - Math.Atan2(pos1.y, pos1.x);
if (pTA < 0.0)
{
pTA += OrbitUtils.TwoPI;
}
double VimpDotProduct = -arrDV[i].x * vel2.x - arrDV[i].y * vel2.y - arrDV[i].z * vel2.z / arrDV[i].magnitude / vel2.magnitude;
vel1 += depDV[i]; // Transfer orbit velocity at departure
OrbitData transferOrbit = new OrbitData(dep.Epoch, pos1, vel1, OrbitUtils.GM_SUN);
return(new LambertSolution(nRevs, TA[i], pTA, Vinf[i], C3[i], Vimp,
-arrDV[i], VimpDotProduct, transferOrbit));
}
