Standard Gravitational Parameter of the Earth

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

Value	3.986004418 × 10¹⁴ m³/s² Use in the calculator →
Status	Measured: ± 800,000 m³/s² (2 × 10⁻⁹ relative)
Source	WGS 84 / EGM96 geocentric gravitational constant
Categories	Astronomical

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 3 solvers

Escape Velocity

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

Orbital Period

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

Orbital Velocity

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

Revised 16 October 2026

Cite this page

formula.expert. (2026, October 16). Standard Gravitational Parameter of the Earth. https://formula.expert/constants/earth-gravitational-parameter