Physical Constants for Orbital Mechanics — physical

Usage

gravitational_constant

seconds_per_hour

seconds_per_day

seconds_per_year

mass_sun

mass_earth

mass_moon

mass_mars

mass_jupiter

mass_saturn

mass_venus

mass_mercury

mass_uranus

mass_neptune

mass_pluto

distance_earth_sun

distance_earth_moon

distance_mars_sun

distance_jupiter_sun

distance_venus_sun

distance_mercury_sun

distance_saturn_sun

distance_uranus_sun

distance_neptune_sun

distance_pluto_sun

speed_earth

speed_moon

speed_mars

speed_jupiter

speed_venus

speed_mercury

speed_saturn

speed_uranus

speed_neptune

speed_pluto

Format

An object of class numeric of length 1.

Numeric scalar in kilograms.

An object of class numeric of length 1.

Details

`gravitational_constant`: Newton's gravitational constant (6.6743 x 10^-11 m^3 kg^-1 s^-2). Source: CODATA 2018 recommended value. Use this with `create_system()` to scale gravity: `create_system(G = gravitational_constant * 10)`.

`seconds_per_hour`: 3,600 seconds. Convenient for setting `time_step` in lunar or close-orbit simulations.

`seconds_per_day`: 86,400 seconds. Convenient for setting `time_step` in planetary-scale simulations.

`seconds_per_year`: 31,557,600 seconds (365.25 days, the Julian year). Convenient for setting `duration` in `simulate_system()`.

`mass_sun`: Mass of the Sun (1.989 x 10^30 kg). Source: IAU 2015 nominal solar mass.

`mass_earth`: Mass of the Earth (5.972 x 10^24 kg). Source: IAU 2015 nominal Earth mass.

`mass_moon`: Mass of the Moon (7.342 x 10^22 kg). Source: JPL DE440 ephemeris.

`mass_mars`: Mass of Mars (6.417 x 10^23 kg). Source: JPL DE440 ephemeris.

`mass_jupiter`: Mass of Jupiter (1.898 x 10^27 kg). Source: JPL DE440 ephemeris.

`mass_saturn`: Mass of Saturn (5.683 x 10^26 kg). Source: JPL DE440 ephemeris.

`mass_venus`: Mass of Venus (4.867 x 10^24 kg). Source: JPL DE440 ephemeris.

`mass_mercury`: Mass of Mercury (3.301 x 10^23 kg). Source: JPL DE440 ephemeris.

`mass_uranus`: Mass of Uranus (8.681 x 10^25 kg). Source: JPL DE440 ephemeris.

`mass_neptune`: Mass of Neptune (1.024 x 10^26 kg). Source: JPL DE440 ephemeris.

`mass_pluto`: Mass of Pluto (1.309 x 10^22 kg). Source: JPL DE440 ephemeris. Pluto is a dwarf planet but is included for convenience.

`distance_earth_sun`: Semi-major axis of Earth's orbit around the Sun (1.496 x 10^11 m, ~149.6 million km). Earth's actual distance varies between ~147.1 million km (perihelion) and ~152.1 million km (aphelion).

`distance_earth_moon`: Semi-major axis of the Moon's orbit around Earth (3.844 x 10^8 m, ~384,400 km). The Moon's actual distance varies between ~363,300 km (perigee) and ~405,500 km (apogee).

`distance_mars_sun`: Semi-major axis of Mars's orbit around the Sun (2.279 x 10^11 m, ~227.9 million km). Mars has a notably eccentric orbit (e = 0.093), ranging from ~206.7 million km to ~249.2 million km.

`distance_jupiter_sun`: Semi-major axis of Jupiter's orbit around the Sun (7.785 x 10^11 m, ~778.5 million km).

`distance_venus_sun`: Semi-major axis of Venus's orbit around the Sun (1.082 x 10^11 m, ~108.2 million km). Venus has the most circular orbit of any planet (e = 0.007).

`distance_mercury_sun`: Semi-major axis of Mercury's orbit around the Sun (5.791 x 10^10 m, ~57.9 million km). Mercury has the most eccentric planetary orbit (e = 0.206), ranging from ~46.0 million km to ~69.8 million km.

`distance_saturn_sun`: Semi-major axis of Saturn's orbit around the Sun (1.434 x 10^12 m, ~1.434 billion km).

`distance_uranus_sun`: Semi-major axis of Uranus's orbit around the Sun (2.871 x 10^12 m, ~2.871 billion km).

`distance_neptune_sun`: Semi-major axis of Neptune's orbit around the Sun (4.495 x 10^12 m, ~4.495 billion km).

`distance_pluto_sun`: Semi-major axis of Pluto's orbit around the Sun (5.906 x 10^12 m, ~5.906 billion km). Pluto has a highly eccentric orbit (e = 0.249), ranging from ~4.437 billion km to ~7.376 billion km.

`speed_earth`: Mean orbital speed of Earth around the Sun (29,780 m/s).

`speed_moon`: Mean orbital speed of the Moon around Earth (1,022 m/s).

`speed_mars`: Mean orbital speed of Mars around the Sun (24,070 m/s).

`speed_jupiter`: Mean orbital speed of Jupiter around the Sun (13,060 m/s).

`speed_venus`: Mean orbital speed of Venus around the Sun (35,020 m/s).

`speed_mercury`: Mean orbital speed of Mercury around the Sun (47,360 m/s).

`speed_saturn`: Mean orbital speed of Saturn around the Sun (9,680 m/s).

`speed_uranus`: Mean orbital speed of Uranus around the Sun (6,800 m/s).

`speed_neptune`: Mean orbital speed of Neptune around the Sun (5,430 m/s).

`speed_pluto`: Mean orbital speed of Pluto around the Sun (4,740 m/s).

A Note on "Distance" Constants

Orbital distances are not truly constant. Every orbit is an ellipse, so the separation between two bodies changes continuously. The distances provided here are **semi-major axes** — the average of the closest approach (periapsis) and farthest point (apoapsis). The semi-major axis is the single most characteristic length scale of an elliptical orbit: it determines the orbital period via Kepler's Third Law, and when paired with the circular velocity at that distance, it produces a near-circular orbit that closely approximates the real trajectory.

For example, the Earth-Sun distance varies from about 147.1 million km (perihelion in January) to 152.1 million km (aphelion in July). The semi-major axis of 149.598 million km sits right in the middle and gives the correct orbital period of one year.