Satellite Orbits

Satellites — both natural (like the Moon) and artificial (like the International Space Station) — are held in orbit by gravitational attraction. Understanding orbital mechanics means applying Newton's law of gravitation together with circular motion principles. The key insight is that gravity provides the centripetal force needed for circular orbital motion.

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The Fundamental Orbital Equation

For a satellite of mass m in a circular orbit of radius r around a body of mass M, the gravitational force provides the centripetal force:

$\frac{GMm}{r^2} = \frac{mv^2}{r}$r2GMm​=rmv2​

The satellite mass m cancels:

$\frac{GM}{r} = v^2$rGM​=v2

Therefore the orbital speed is:

$v = \sqrt{\frac{GM}{r}}$v=rGM​​

This result has a profound implication: orbital speed depends only on the mass of the central body and the orbital radius, not on the mass of the satellite. A feather and a space station orbiting at the same altitude would need the same orbital speed.

Notice that orbital speed decreases with increasing radius. Satellites closer to Earth orbit faster than those further away. The ISS (altitude ~400 km) orbits at about 7.7 km s⁻¹, while geostationary satellites (altitude ~35,800 km) orbit at only about 3.1 km s⁻¹.

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Orbital Period