The altitude falls straight out of the period: match Earth\’s rotation and the orbit radius is fixed at about 42,164 km, or 35,786 km up. But the period to match is the sidereal day, 86,164 s — using 86,400 puts the answer roughly 77 km wrong.
Geostationary means holding station over one spot on the ground, so the orbital period has to equal one rotation of Earth relative to the stars — not relative to the Sun. The two differ by about four minutes a day because Earth also moves along its orbit. Radius scales as the two-thirds power of period, so a four-minute error becomes tens of kilometres, and there is only one radius that works: it is a consequence, not a design choice.
Geostationary is the special case of geosynchronous with zero inclination and zero eccentricity. An inclined geosynchronous orbit has the same period and altitude but traces a figure-of-eight over the ground, which is a different thing entirely — and real satellites need regular station-keeping regardless.
Estimate with the rule, then check it against the calculator that models it properly.
Open Orbital Mechanics →The altitude falls straight out of the period: match Earth\’s rotation and the orbit radius is fixed at about 42,164 km, or 35,786 km up. But the period to match is the sidereal day, 86,164 s — using 86,400 puts the answer roughly 77 km wrong. Geostationary means holding station over one spot on the ground, so the orbital period has to equal one rotation of Earth relative to the stars — not relative to the Sun.