Geosynchronous orbit

Description

A geosynchronous orbit (sometimes abbreviated GSO) is an orbit around the Earth with an orbital period of one sidereal day (approximately 23 hours 56 minutes and 4 seconds), matching the Earth’s sidereal rotation period.
The synchronization of rotation and orbital period means that, for an observer on the surface of the Earth, an object in geosynchronous orbit returns to exactly the same position in the sky after a period of one sidereal day. Over the course of a day, the object’s position in the sky traces out a path, typically in the form of an analemma, whose precise characteristics depend on the orbit’s inclination and eccentricity.
All Earth geosynchronous orbits, whether circular or elliptical, have the same semi-major axis. In fact, orbits with the same period always share the same semi-major axis

Related formulas

Variables

αSemi-Major axis of geosynchronous orbit (km)
μstandard gravitational parameter (for Earth : 398600.4418) (km3/s2)
POrbital Period (Sidereal time) (sec)
πpi