Constants library

Mass of the Earth measured

M_\oplus = 5.9722 \times 10^{24}\ \text{kg}

kgMass of the Earth, 5.9722 × 10²⁴ kg — the unit in which rocky exoplanets are weighed, and limited in precision only by G.

a_\oplus = 6,378,137\ \text{m}

mSemi-major axis of the WGS 84 reference ellipsoid, exactly 6 378 137 m — the equatorial radius every GPS receiver is built around.

b_\oplus = 6356752.314245\ \text{m}

mSemi-minor axis of the WGS 84 ellipsoid, 6 356 752.3 m — 21.4 km shorter than the equatorial radius because the Earth is spinning.

R_\oplus = 6371008.8\ \text{m}

mMean radius (2a + b)/3 of the WGS 84 ellipsoid, about 6371 km — the single figure used when a spherical Earth is good enough.

GM_\oplus = 3.986004418 \times 10^{14}\ \text{m}^{3}\text{/s}^{2}

m³/s²The geocentric gravitational constant GM⊕, 3.986 004 418 × 10¹⁴ m³/s², known to nine digits and used by every GPS satellite.

v_\oplus = 29,780\ \text{m/s}

m/sMean speed of the Earth along its orbit, about 29.78 km/s — roughly 107 000 km/h, and it varies with distance from the Sun.

a_{\oplus,\mathrm{orb}} = 1.495982612 \times 10^{11}\ \text{m}

mEarth's actual mean orbital distance, 1.000 002 61 au — close to the astronomical unit but a measured quantity, not the definition.

e_\oplus = 0.0167086\ \text{—}

—Eccentricity of Earth's orbit at J2000, 0.0167 — nearly circular, yet enough to vary sunlight at the top of the atmosphere by 6.8 per cent.

\varepsilon = 0.4090928\ \text{rad}

radObliquity of the ecliptic at J2000, 23.4393° or 0.409 rad — the tilt of Earth's spin axis that causes the seasons.

v_{\mathrm{esc},\oplus} = 11,186\ \text{m/s}

m/sSpeed needed to break free of Earth's gravity from the surface, about 11.19 km/s, ignoring atmospheric drag and the planet's rotation.

T_{\mathrm{sid}} = 86164.0905\ \text{s}

sEarth's rotation period relative to the fixed stars, 23 h 56 min 4.09 s — about four minutes shorter than the solar day.

d = 86,400\ \text{s}

sThe civil day of exactly 86 400 SI seconds — a defined unit that Earth's actual rotation now overruns by a millisecond or two.

T_{\mathrm{sid}}^{\mathrm{yr}} = 31558149.8\ \text{s}

sOne orbit of the Sun relative to the fixed stars, 365.2564 days — about 20 minutes longer than the tropical year of the seasons.

T_{\mathrm{trop}} = 31556925.2\ \text{s}

sEquinox to equinox, 365.2422 days — the year the seasons follow, and the quantity every calendar reform has tried to approximate.