However, it results in a set of elements that let you predict future positions.
True anomaly full#
All of those give you, at any instant, the full position and motion in 3D of the satellite at a specific instance in time.Ī more clever approach still uses 6 elements- the minimum regardless of what dimensional or grid layout you choose. You could use spherical coordinates, or Euler angles. You could use (x,y,z) for the position and (vx,vy,vz) for the velocities. Since we live in 3-D space, it's equivalent to 3 spatial dimensions and 3 velocities. but what does that actually mean? Here's a brief mini course in orbital mechanics.Īny orbit requires 6 elements to specify the position and motion fully. Thanks to Futurogogist and Spektre for their help.'Project Calliope' will have a nearly circular polar low-earth orbit. 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) Given position and velocity: pos = new Vector4() Īnd tested them with the following double parentMass = 1.989e30 ĭouble sgp = * (parentMass + objMass) / 3.347928976e33 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: /// 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.
0 kommentar(er)
