OrbitalQuantities.hpp

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// Vulcan Orbital Quantities
// Two-body orbital mechanics computations
#pragma once
 
#include <cmath>
#include <janus/janus.hpp>
#include <vulcan/core/Constants.hpp>
#include <vulcan/core/VulcanTypes.hpp>
 
namespace vulcan::orbital::quantities {

template <typename Scalar>
Scalar period(const Scalar &a, double mu = constants::earth::mu) {
    return 2.0 * M_PI * janus::sqrt(a * a * a / mu);
}

template <typename Scalar>
Scalar velocity(const Scalar &r, const Scalar &a,
                double mu = constants::earth::mu) {
    return janus::sqrt(mu * (2.0 / r - 1.0 / a));
}

template <typename Scalar>
Scalar energy(const Scalar &a, double mu = constants::earth::mu) {
    return -mu / (2.0 * a);
}

template <typename Scalar>
Scalar escape_velocity(const Scalar &r, double mu = constants::earth::mu) {
    return janus::sqrt(2.0 * mu / r);
}

template <typename Scalar>
Scalar circular_velocity(const Scalar &r, double mu = constants::earth::mu) {
    return janus::sqrt(mu / r);
}

template <typename Scalar>
Scalar mean_motion(const Scalar &a, double mu = constants::earth::mu) {
    return janus::sqrt(mu / (a * a * a));
}

template <typename Scalar>
Scalar semi_latus_rectum(const Scalar &a, const Scalar &e) {
    return a * (1.0 - e * e);
}

template <typename Scalar>
Scalar radius_at_anomaly(const Scalar &a, const Scalar &e, const Scalar &nu) {
    return a * (1.0 - e * e) / (1.0 + e * janus::cos(nu));
}
 
} // namespace vulcan::orbital::quantities