Geostationary Satellite

A geostationary satellite must remain stationary relative to a ground observer, which requires its angular motion to exactly match the Earth's rotation. First, its orbital period must equal the Earth's rotational period of about 24 hours, so it completes one revolution as the planet turns once. Second, it must orbit in the equatorial plane; any inclined or polar orbit would cause the satellite to drift north and south daily, tracing a figure-eight rather than staying fixed. Third, it must move from west to east, the same sense as Earth's spin, otherwise it would appear to race across the sky. Applying $T=2\pi \sqrt{r^3/GM}$ with $T=24$ h yields the unique geostationary radius of about 42,000 km from the centre. The 12-hour polar option fails both the period and plane requirements. The 24-hour polar option fails the equatorial-plane condition. The 1-hour option corresponds to a low orbit. This is the NCERT definition of a geostationary orbit, and such satellites are the backbone of television, weather, and long-distance communication networks because a fixed ground antenna can point at them permanently without tracking. A related but distinct category is the polar sun-synchronous satellite, which deliberately uses an inclined orbit to scan different strips of the Earth and is therefore not geostationary. A magnitude check on the geostationary radius shows it lies roughly 36,000 km above the surface, far higher than low-Earth-orbit satellites. A sanity check confirms only matching period, plane, and direction together keep the satellite fixed overhead.