Satellites in orbit: mechanics and applications
Types of orbits and cosmic velocities
Classification of Earth orbits
| Type | Typical altitude | Example use |
|---|---|---|
| LEO (low Earth orbit) | 300 - 2,000 km | Observation, ISS, constellations (Starlink) |
| MEO (medium Earth orbit) | ~20,000 km | Navigation (GPS, Galileo) |
| GEO (geostationary) | 35,786 km | Telecommunications, weather |
| SSO (Sun-synchronous) | 600 - 800 km, polar orbit | Earth imaging at a fixed local solar time |
Geostationary orbit
A geostationary satellite has a period equal to that of the Earth's rotation (sidereal day, T = 86,164 s) and a circular equatorial orbit. It stays fixed above a point on the equator, which explains its massive use for telecommunications and fixed satellite dishes.
Cosmic velocities
- First cosmic velocity (placing into low orbit, r ~ Earth's radius): v1 = sqrt(G*M/R) ~ 7.9 km/s
- Second cosmic velocity, called escape velocity (escaping the gravitational field): v2 = sqrt(2GM/R) = v1*sqrt(2) ~ 11.2 km/s
Escape velocity corresponds to zero mechanical energy (Em = 0): the object theoretically reaches infinity with zero speed.
Classic pitfall
A Sun-synchronous orbit is not geostationary: it is low and polar (inclination close to 90 degrees), chosen to fly over every point on the globe at the same local solar time, a valuable feature for comparing images taken on different dates.
Note
Kepler stated his laws for a fixed attracting center. Strictly speaking, for two bodies of comparable mass, one should use the reduced mass and the common center of mass, but the approximation M >> m is excellent for any artificial satellite around the Earth.