Standard Gravitational Parameter of the Earth

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

Value	3.986004418e14 m³/s²
Status	Measured: ± 800,000 m³/s² (2.0e-09 relative)
Source	WGS 84 / EGM96 geocentric gravitational constant
Categories	Astronomical earth orbital-mechanics

Learning zone

This single number, not Earth's mass, is what satellite navigation runs on. GPS broadcasts orbital elements that a receiver propagates using GM⊕, and an error of one part in a million would drift the constellation by metres within hours. Laser ranging to retroreflectors and Doppler tracking of low satellites determine it to about one part in 10⁹ — the quoted value includes the mass of the atmosphere, which matters at that precision.

Handy consequences fall straight out of it: circular orbital speed at radius r is √(GM⊕/r), giving 7.67 km/s for the ISS, and the geostationary radius where the period matches one sidereal day works out to 42 164 km, or about 35 786 km above the equator.

Used by these solvers

Orbital Velocity

v = \sqrt{\frac{GM}{r}}

Orbital Period

T = 2\pi \sqrt{\frac{r^{3}}{GM}}

Escape Velocity

v = \sqrt{\frac{2GM}{r}}