Satellite Orbit Ops — RAAN, Coverage Radius, Eclipse Fraction

The orbit is governed by balancing the satellite's inertia with Earth's gravity. The key relationship gives the orbital period, which you see calculated automatically in the simulator.

Here, $T$ is the orbital period (seconds), $R_e = 6371$ km is Earth's radius, $h$ is the altitude above Earth (km), and $\mu = 3.986\times10^{14}$ m³/s² is Earth's standard gravitational parameter.

The satellite's orbital velocity, also displayed, is derived from the same principles. A higher orbit means a longer path but a slower speed.

Here, $v$ is the orbital velocity (m/s). This is the speed needed to maintain a circular orbit at altitude $h$. Notice in the simulator: LEO satellites zip around at ~7.8 km/s, while GEO satellites cruise at ~3.1 km/s.

Earth Observation & Weather Satellites: These often use Sun-synchronous orbits, a special type of LEO with high inclination. By adjusting RAAN and inclination precisely, the satellite passes over the same location at the same local solar time every day, ensuring consistent lighting for images. The simulator shows how changing inclination alters ground coverage.

Global Communications (GEO): Television and weather broadcast satellites use Geostationary orbit. As shown when you set altitude to ~35,786 km and inclination to 0°, the satellite stays over a fixed longitude, providing continuous coverage to nearly a third of the Earth's surface with a single satellite.

Satellite Constellations (LEO): Systems like Starlink or GPS use many satellites in lower orbits. In the simulator, see how a LEO satellite has a short period (~90 minutes). Multiple satellites in different orbital planes (set by varying RAAN and true anomaly) are needed to ensure at least one is always in view from any point on Earth.

Space Station & Crewed Missions: The International Space Station orbits in LEO at about 400 km altitude. At this height, you can see the high orbital velocity in the simulator. This low altitude reduces the energy required for crew and cargo launches but means the station experiences atmospheric drag and requires periodic re-boosts.

There are several key points you should be especially mindful of when starting to use the simulator. First is the assumption of "perfectly circular orbits." This tool calculates using circular orbits for simplicity, but in reality, most satellite orbits are elliptical. For instance, an Earth observation satellite can have an altitude difference of hundreds of kilometers between its perigee (closest point to Earth) and apogee. While circular orbit calculations are excellent as a first approximation, actual designs must always consider elliptical orbit parameters (eccentricity).

Next is overlooking dependencies between parameters. For example, you might memorize that "Geostationary Orbit (GEO) is at an altitude of about 36,000 km with 0-degree inclination," but this is true only for an ideal case where Earth is a perfect sphere and there is no gravitational influence from other celestial bodies (perturbations). In reality, Earth is slightly flattened (an oblate spheroid), so to strictly maintain a 0-degree inclination, a satellite will gradually drift on its own. Preventing this requires regular orbital control maneuvers (thruster firings). When adjusting parameters in the simulator, get into the habit of asking, "If I change this value, which other values will be affected?"

Finally, the interpretation of "coverage radius." The tool calculates the "area of Earth's surface visible from the satellite" geometrically. However, in practical communication or observation operations, this entire area is not uniformly usable. For example, near the edge of the horizon, radio signals can be attenuated by the atmosphere or experience significant delays. Keep in mind that the practical service area is often considerably smaller than the calculated coverage radius.