Orbital Radius
Orbital radius is the distance from the center of the body being orbited to the satellite or other orbiting object. In satellite communications, it normally refers to the distance from the center of the Earth to a communications satellite. Orbital radius is closely related to orbital altitude, but the two terms are not the same. Orbital altitude is measured from the Earth’s surface to the satellite, whereas orbital radius is measured from the Earth’s center to the satellite.
For a circular Earth orbit, the relationship is straightforward: the orbital radius is equal to the Earth’s radius plus the satellite’s altitude. Using the Earth’s mean radius of about 6,371 km, a satellite at an altitude of 1,000 km has an orbital radius of about 7,371 km. A geostationary (GEO) satellite has an altitude of about 35,786 km, giving an orbital radius of about 42,164 km. This larger value is the one used in orbital mechanics calculations, because gravity acts as though the Earth’s mass were concentrated at its center.
Orbital radius is especially important in applying Kepler's laws. Kepler's third law relates the orbital period to the size of the orbit, and for a circular orbit the relevant size is the orbital radius. Satellites with a larger orbital radius take longer to complete one orbit. This is why low Earth orbit satellites circle the Earth in roughly 90 to 120 minutes, medium Earth orbit satellites take several hours, and geostationary satellites complete one orbit in one sidereal day.
For elliptical orbits, the term orbital radius requires more care because the satellite’s distance from the Earth’s center changes continuously during the orbit. The satellite is closest to the Earth at perigee and farthest away at apogee. Therefore, an elliptical orbit does not have a single constant orbital radius. Instead, it has a perigee radius, an apogee radius, and a semi-major axis. The semi-major axis is particularly important because it determines the orbital period. It is equal to half the longest diameter of the ellipse and, for an Earth orbit, is measured from the center of the Earth to the midpoint between perigee and apogee along the major axis.
Orbital radius also affects satellite speed. In a circular orbit, a satellite closer to the Earth must travel faster to remain in orbit, while a satellite farther from the Earth travels more slowly. In an elliptical orbit, the satellite’s speed changes: it moves fastest at perigee, where its orbital radius is smallest, and slowest at apogee, where its orbital radius is largest. This behavior follows from conservation of energy and angular momentum and is described by Kepler's second law.
In satellite communications, orbital radius affects several practical design issues. It influences free-space path loss, propagation delay, Earth coverage, visibility time, antenna pointing, Doppler shift, and the number of satellites needed for continuous coverage. A small orbital radius gives low delay and lower path loss, but a smaller coverage area and rapid apparent motion across the sky. A large orbital radius gives broader coverage and slower apparent motion, but greater path loss and longer delay.
The distinction between orbital altitude and orbital radius is therefore more than a matter of terminology. Altitude is convenient for describing how high a satellite is above the Earth, but orbital radius is the quantity most directly used in orbital dynamics. For this reason, calculations involving orbital period, gravitational force, orbital velocity, and geostationary orbit generally use orbital radius rather than altitude.