Var x = (position.X * Math.Cos(-aop)) - (position.Y * Math.Sin(-aop)) ĭouble foo = GMath.Clamp(x / a, -1, 1) //because sometimes we were getting a floating point error that resulted in numbers infinatly smaller than -1 Vector4 foo1 = Vector4.Cross(velocity, angularMomentum) / sgp Īnd EccentricAnomaly: public static double GetEccentricAnomalyFromStateVectors(Vector4 position, double a, double linierEccentricity, double aop) Vector4 angularMomentum = Vector4.Cross(position, velocity) Return Math.PI - Math.Abs(Math.Abs(a1 - a2) - Math.PI) Īnd eccentricity Vector found thus: public static Vector4 EccentricityVector(double sgp, Vector4 position, Vector4 velocity) Var θ5 = OrbitMath.TrueAnomaly(pos, aop) ĭouble angleΔ = 0.0000001 //this is the 'acceptable' amount of error, really only the TrueAnomalyFromEccentricAnomaly() calcs needed this.Īssert.AreEqual(0, Angle.DifferenceBetweenRadians(directAngle, aop - θ1), angleΔ) Īssert.AreEqual(0, Angle.DifferenceBetweenRadians(directAngle, aop - θ2), angleΔ) Īssert.AreEqual(0, Angle.DifferenceBetweenRadians(directAngle, aop - θ3), angleΔ) Īssert.AreEqual(0, Angle.DifferenceBetweenRadians(directAngle, aop - θ4), angleΔ) Īssert.AreEqual(0, Angle.DifferenceBetweenRadians(directAngle, aop - θ5), angleΔ) Īnd the following to compare the angles: public static double DifferenceBetweenRadians(double a1, double a2) Var θ4 = OrbitMath.TrueAnomalyFromEccentricAnomaly2(e, eccentricAnomaly) Var θ3 = OrbitMath.TrueAnomalyFromEccentricAnomaly(e, eccentricAnomaly) Var θ2 = OrbitMath.TrueAnomaly(ev, pos, vel) Var θ1 = OrbitMath.TrueAnomaly(sgp, pos, vel) Vector4 ev = OrbitMath.EccentricityVector(sgp, pos, vel) ĭouble specificOrbitalEnergy = Math.Pow(vel.Length(), 2) * 0.5 - sgp / pos.Length() ĭouble a = -sgp / (2 * specificOrbitalEnergy) ĭouble eccentricAnomaly = OrbitMath.GetEccentricAnomalyFromStateVectors(pos, a, ae, aop) ĭouble directAngle = Math.Atan2(pos.Y, pos.X) Recall is the proportion of true positives among all actual positives (both true positives and false negatives). It can be calculated as follows: Precision TP / (TP + FP) A precision score of 1.0 means that every anomaly detected corresponds to an actual abnormal event. Given position and velocity: pos = new Vector4() Īnd tested them with the following double parentMass = 1.989e30 ĭouble sgp = * (parentMass + objMass) / 3.347928976e33 It indicates how many detected anomalies correspond to actual abnormal events. So I found an edge case where most of the above calculations fail. Yeah so I was wrong, the above all do return the correct values after all. Just to clarify: My angles appear to be sort of correct, just pointing in the wrong quadrant depending on the position and or velocity vectors. How do I fix these so that I get a consistent results when position and velocity are negitive? These functions all agree if position.x, position.y and velocity.y are all positive. Positions are all relative to the parent body.

Return Math.Atan2(position.Y, position.X) - loP Var y = 1 - eccentricity * Math.Cos(eccentricAnomaly) Įdit: another way of doing it which Spectre pointed out: public static double TrueAnomaly(Vector4 position, double loP) Var x = Math.Cos(eccentricAnomaly) - eccentricity Public static double TrueAnomalyFromEccentricAnomaly2(double eccentricity, double eccentricAnomaly) Var y = Math.Cos(eccentricAnomaly) - eccentricity Var x = Math.Sqrt(1 - Math.Pow(eccentricity, 2)) * Math.Sin(eccentricAnomaly) Public static double TrueAnomalyFromEccentricAnomaly(double eccentricity, double eccentricAnomaly) Var q = Vector4.Dot(position, velocity) // dot product of r*v Var H = Vector4.Cross(position, velocity).Length() Public static double TrueAnomaly(double sgp, Vector4 position, Vector4 velocity) Var talen = eccentVector.Length() * position.Length() Var dotEccPos = Vector4.Dot(eccentVector, position) Public static double TrueAnomaly(Vector4 eccentVector, Vector4 position, Vector4 velocity) Here are the different ways I'm trying to calculate the True Anomaly: /// The two are related through the eccentric anomaly: let $M$ be the mean anomaly, $E$ be the eccentric anomaly, $e$ be the eccentricity, and $ u$ be the true anomaly.I'm attempting to convert from state vectors (position and speed) into Kepler elements, however I'm running into problems where a negative velocity or position will give me wrong results when trying to calculate true anomaly.

The true anomaly, in general, does not, except if the orbit is circular, in which case the mean anomaly and true anomaly are identical (well, not really, because circular orbits don't have a periapsis, but in the limiting case, this is true). The key difference is that the mean anomaly always increases linearly with time. Mean anomaly is the angle between the periapsis point and the imagined position of an object for the same elapsed time since periapsis for a circular orbit around the same body with the same orbital period. True anomaly is the actual measured angle in the orbital plane between the vector extending from the focus to the point of periapsis and the vector extending from the focus to the object's actual position.