claudes_game/src/orbital_mechanics.h

#ifndef ORBITAL_MECHANICS_H
#define ORBITAL_MECHANICS_H

#include "physics.h"

static const double PARABOLIC_TOLERANCE = 1e-3;

struct OrbitalElements {
    union {
        double semi_major_axis;       // for elliptical (e<1) and hyperbolic (e>1)
        double semi_latus_rectum;     // for parabolic (e≈1)
    };
    double eccentricity;
    double true_anomaly;
    double inclination;
    double longitude_of_ascending_node;
    double argument_of_periapsis;
};

void orbital_elements_to_cartesian(OrbitalElements elements, double parent_mass,
                                    Vec3* out_position, Vec3* out_velocity);

OrbitalElements cartesian_to_orbital_elements(Vec3 position, Vec3 velocity, double parent_mass);

// Initial guess for Newton-Raphson: M + e·sin(M) + (e²/2)·sin(2M)
double get_initial_trial_value(double mean_anomaly, double eccentricity);

// Elliptical Kepler equation solver: E - e·sin(E) = M
double solve_kepler_elliptical(double mean_anomaly, double eccentricity);

// Hyperbolic Kepler equation solver: H - e·sinh(H) = M
double solve_kepler_hyperbolic(double mean_anomaly, double eccentricity);

// Conversions between anomaly types
double eccentric_to_true_anomaly(double eccentric_anomaly, double eccentricity);
double hyperbolic_to_true_anomaly(double hyperbolic_anomaly, double eccentricity);

// Unified mean anomaly to true anomaly conversion
// Automatically dispatches to elliptical or hyperbolic based on eccentricity
double mean_anomaly_to_true_anomaly(double mean_anomaly, double eccentricity);

// Barker's equation: D + D³/3 = M, where D = tan(ν/2)
double solve_barker_equation(double mean_anomaly);

OrbitalElements propagate_orbital_elements(const OrbitalElements& elements, double dt, double parent_mass);

#endif