rs-core

Core utilities

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Astronomical Constants and Functions

Core utility library by Ross Smith

#include "rs-core/astronomy.hpp"
namespace RS;

Contents

Astronomical constants

Sources:

Constant Symbol Value
astronomical_unit au 1.496×1011 m
light_year ly 9.461×1015 m
parsec pc 3.086×1016 m
earth_mass M_earth 5.972×1024 kg
earth_radius R_earth 6.378×106 m
standard_gravity g_0 9.807 m s-2
julian_day jd 86400 s
sidereal_day d_sid 86160 s
tropical_year y_trop 3.156×107 s
julian_year jy 3.156×107 s
sidereal_year y_sid 3.156×107 s
lunar_mass M_moon 7.346×1022 kg
lunar_radius R_moon 1.738×106 m
lunar_distance a_moon 3.844×108 m
sidereal_month sid_mon 2.361×106 s
synodic_month syn_mon 2.551×106 s
jupiter_mass M_jup 1.899×1027 kg
jupiter_radius R_jup 7.149×107 m
solar_mass M_sun 1.988×1030 kg
solar_radius R_sun 6.957×108 m
solar_temperature T_sun 5772 K
solar_luminosity L_sun 3.828×1026 W
solar_visual_magnitude Mv_sun 4.81 mag
solar_bolometric_magnitude Mbol_sun 4.74 mag
solar_bolometric_correction BC_sun -0.07 mag
bolometric_luminosity_constant L_0 3.013×1028 W
age_of_universe t_0 4.351×1017 s

Astronomical formulae

All of these assume that all arguments, and the return value, are expressed in SI units (apart from stellar magnitudes).

template <std::floating_point T>
    constexpr T mass_from_radius_density(T r, T d) noexcept;
template <std::floating_point T>
    constexpr T radius_from_mass_density(T m, T d) noexcept;
template <std::floating_point T>
    constexpr T density_from_mass_radius(T m, T r) noexcept;

Relationship between radius, density, and mass of a sphere.

template <std::floating_point T>
    constexpr T gravity_from_mass_radius(T m, T r) noexcept;

Relationship between mass, radius, and surface gravity of a body.

template <std::floating_point T>
    T distance_from_mass_period(T m, T p) noexcept;
template <std::floating_point T>
    T period_from_mass_distance(T m, T a) noexcept;

Relationship between primary mass, semimajor axis, and orbit period.

Formula: G M P2 = 4 π2 a3

template <std::floating_point T>
    T hill_radius(T m1, T m2, T a) noexcept;

Radius of the Hill sphere for a planet. Here m1 is the mass of the primary (star), m2 is the mass of the secondary (planet).

Formula: r = a (m2 / 3 m1)1/3

template <std::floating_point T>
    T luminosity_from_radius_temperature(T r, T t) noexcept;
template <std::floating_point T>
    T radius_from_luminosity_temperature(T l, T t) noexcept;
template <std::floating_point T>
    T temperature_from_luminosity_radius(T l, T r) noexcept;

Relationship between radius, effective temperature, and luminosity of a star.

Formula: L = 4 π σ r2 T4

template <std::floating_point T>
    constexpr T main_sequence_lifetime(T m, T l) noexcept;

Estimated main sequence lifetime of a star, given its mass and main sequence luminosity.

template <std::floating_point T>
    constexpr T schwarzschild_radius(T m) noexcept;

Schwarzschild radius of a black hole, given its mass.

Formula: r = 2 G M / c2

template <std::floating_point T>
    T delta_magnitude_to_ratio(T dm) noexcept;
template <std::floating_point T>
    T ratio_to_delta_magnitude(T r) noexcept;
template <std::floating_point T>
    T bolometric_magitude_to_luminosity(T m) noexcept;
template <std::floating_point T>
    T bolometric_luminosity_to_magnitude(T l) noexcept;

Relationship between stellar magnitude and luminosity.

template <std::floating_point T>
    T temperature_to_bc(T t) noexcept;

Estimated bolometric correction for a star, given its effective temperature.

Source: Guillermo Torres (2010), “On the Use of Empirical Bolometric Corrections for Stars”

template <std::floating_point T>
    T planet_distance_to_temperature(T l, T a) noexcept;
template <std::floating_point T>
    T planet_temperature_to_distance(T l, T t) noexcept;
template <std::floating_point T>
    T planet_distance_to_illumination(T l, T a) noexcept;
template <std::floating_point T>
    T planet_illumination_to_temperature(T i) noexcept;

Relationship between the luminosity of a star, the distance of a planet, the illumination per unit area, and the equilibrium temperature (assuming a blackbody planet).