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Orbital speed of a satellite

A satellite in a circular orbit is falling all the time, but the Earth's surface curves away just as fast. The centripetal force is gravity. The orbital speed depends on the distance from the Earth's centre, not on the satellite's mass. A low orbit gives high speed and a short period. The radius in the formula is the Earth's radius plus the height above the ground. The height alone is not enough, because gravity is measured from the centre.

Try it yourself

Satellite in orbit

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

speed in a circular orbit

Symbols

$r$	distance from the Earth's centre	m
$v$	orbital speed	m/s
$M$	mass of the Earth	kg

Example

A satellite orbits 400 km above the ground. The Earth's radius is 6.37·10⁶ m.

$r = 6.37 \cdot 10^{6} + 400 \cdot 10^{3} = 6.77 \cdot 10^{6}$ m, and $v \approx 7.67$ km/s.

A higher orbit gives a lower speed. A geostationary orbit lies much farther out than 400 km.

Practise circular motion and gravitation for free →

← The law of gravitation · Force on a current-carrying wire →

Part of Physics 2: Circular motion and gravitation.