Theory / Orbits
Orbits: why satellites do not fall
A satellite is always falling toward the Earth. It never reaches the ground because it moves sideways so fast.
A fall that never ends
Imagine throwing a stone horizontally. The faster you throw it, the farther it lands. At a high enough speed, the Earth’s surface curves away at the same rate the stone falls, and it never meets the ground. That is an orbit.
The force that keeps the satellite on its curve is gravity. No engine is running: the satellite simply follows the path that gravity and its speed give it.
Height, speed and period
The higher the satellite, the weaker gravity is there, and the lower the speed needed to stay in orbit. That is why low satellites go around much faster than high ones.
The time for one full lap, the period, comes from Kepler’s third law:
T = 2π · √( a³ / μ )
Here, a is the orbit radius (Earth’s radius plus altitude) and μ is Earth’s gravitational parameter, about 398,600 km³/s². For a satellite at 400 km altitude, like the International Space Station, the result is roughly 92 minutes per lap.
Three ideas to describe an orbit
- Altitude: how far from the surface the satellite is. It sets the period and how much of the planet it sees. See LEO, MEO and GEO.
- Inclination: the angle between the orbit plane and the Equator. It sets the latitude range the satellite reaches: 0° stays over the Equator and 90° passes over the poles.
- Shape: circular or elliptical. In the games we use circular orbits for simplicity.
Inclination is not the same thing as the satellite’s attitude. Attitude is where the satellite points; inclination is the route it follows.
Changing orbit
Satellites change altitude with thrusters, spending fuel. The most common maneuver speeds the satellite up to move it onto an elliptical orbit, then speeds it up again at the highest point to make the orbit circular. Going up requires speeding up, yet the satellite ends up slower in the final orbit.
Where this shows up in the games
In Last Transmission, each lane has a different speed: the low one spins fast and the high one slowly. Changing lanes costs fuel, as in a real maneuver, but here the change is instant.
In Sky Beacon, altitude sets how much of the ship’s horizon each satellite reaches.
Sources
Maini, A. K.; Agrawal, V. Satellite Technology: Principles and Applications, 3rd ed., Wiley. ESA, “Types of orbits”. NASA Earth Observatory, catalog of Earth satellite orbits.