using System; using UnityEngine; namespace NewHorizons.Components.Orbital { public class OrbitalParameters : IOrbitalParameters { public float Inclination { get; set; } public float SemiMajorAxis { get; set; } public float LongitudeOfAscendingNode { get; set; } public float Eccentricity { get; set; } public float ArgumentOfPeriapsis { get; set; } public float TrueAnomaly { get; set; } public float Period { get; set; } public Vector3 InitialPosition { get; private set; } public Vector3 InitialVelocity { get; private set; } public static OrbitalParameters FromTrueAnomaly(Gravity primaryGravity, Gravity secondaryGravity, float eccentricity, float semiMajorAxis, float inclination, float argumentOfPeriapsis, float longitudeOfAscendingNode, float trueAnomaly) { var orbitalParameters = new OrbitalParameters(); orbitalParameters.Inclination = inclination; orbitalParameters.SemiMajorAxis = semiMajorAxis; orbitalParameters.LongitudeOfAscendingNode = longitudeOfAscendingNode; orbitalParameters.Eccentricity = eccentricity; orbitalParameters.ArgumentOfPeriapsis = argumentOfPeriapsis; // If primary gravity is linear and the orbit is eccentric its not even an ellipse so theres no true anomaly if (primaryGravity.Power == 1 && eccentricity != 0) { trueAnomaly = 0; } orbitalParameters.TrueAnomaly = trueAnomaly; // Have to calculate the rest var primaryMass = primaryGravity.Mass; var secondaryMass = secondaryGravity.Mass; var power = primaryGravity.Power; var period = (float)(GravityVolume.GRAVITATIONAL_CONSTANT * (primaryMass + secondaryMass) / (4 * Math.PI * Math.PI * Math.Pow(semiMajorAxis, power))); orbitalParameters.Period = period; // All in radians var f = Mathf.Deg2Rad * trueAnomaly; var p = semiMajorAxis * (1 - (eccentricity * eccentricity)); // Semi-latus rectum var r = p / (1 + eccentricity * Mathf.Cos(f)); var G = GravityVolume.GRAVITATIONAL_CONSTANT; var mu = G * (primaryMass); var r_p = semiMajorAxis * (1 - eccentricity); var r_a = semiMajorAxis * (1 + eccentricity); float v; // For linear if (primaryGravity.Power == 1) { // Have to deal with a limit if (eccentricity == 0) { var v2 = 2 * mu * (Mathf.Log(r_a / r) + (1 / 2f)); v = Mathf.Sqrt(v2); } else { var coeff = (r_p * r_p) / (r_p * r_p - r_a * r_a); var v2 = 2 * mu * (coeff * Mathf.Log(r_p / r_a) + Mathf.Log(r_a / r)); v = Mathf.Sqrt(v2); } } // For inverseSquare else { v = Mathf.Sqrt(G * primaryMass * ((2f / r) - (1f / semiMajorAxis))); } // Origin is the focus var x = r * Mathf.Cos(f); var y = r * Mathf.Sin(f); // Forgot to take the derivative of r as well with respect to f var denominator = Mathf.Pow(eccentricity * Mathf.Cos(f) + 1, 2); var dx = -p * Mathf.Sin(f) / denominator; var dy = p * (eccentricity + Mathf.Cos(f)) / denominator; var dir = Rotate(new Vector3(x, 0f, y).normalized, longitudeOfAscendingNode, inclination, argumentOfPeriapsis); var velocityDir = Rotate(new Vector3(dx, 0f, dy).normalized, longitudeOfAscendingNode, inclination, argumentOfPeriapsis); var pos = r * dir; var vel = v * velocityDir; orbitalParameters.InitialPosition = pos; orbitalParameters.InitialVelocity = vel; return orbitalParameters; } public static Vector3 Rotate(Vector3 vector, float longitudeOfAscendingNode, float inclination, float argumentOfPeriapsis) { var R1 = Quaternion.AngleAxis(longitudeOfAscendingNode, Vector3.up); var R2 = Quaternion.AngleAxis(argumentOfPeriapsis, Vector3.up); var R3 = Quaternion.AngleAxis(inclination, R1 * Vector3.left); return R3 * R2 * R1 * vector; } public OrbitalParameters GetOrbitalParameters(Gravity primaryGravity, Gravity secondaryGravity) { return FromTrueAnomaly(primaryGravity, secondaryGravity, Eccentricity, SemiMajorAxis, Inclination, ArgumentOfPeriapsis, LongitudeOfAscendingNode, TrueAnomaly); } } }