Geosta

Meet Geosta, a satellite who keeps pace with Earth's spin, so she seems to hang still in the sky.

From Kepler's third law, the period of an orbit fixes its radius: r = (GMT²/4π²)^(1/3). Choose a period equal to one sidereal day, Earth's true rotation period of about 23 hours 56 minutes, and put the orbit over the equator, moving eastward. The satellite then turns with the planet and stays above one spot.

With Earth's GM and T ≈ 86,164 s, the radius comes out at about 42,164 kilometres from Earth's centre, about 35,786 kilometres above the surface (computed). The writer Arthur C. Clarke popularised the idea of using such orbits for communications in 1945.

Because the satellite never moves in the sky, a dish on the ground can point at it permanently. Satellite TV, many weather satellites and some communications satellites use this orbit.

The orbit is very high, so signals take about a quarter second for the round trip, which is noticeable in calls. Sun and Moon pulls and Earth's uneven shape slowly push satellites off station, so they need regular small corrections.