Explainer
How long does it take to orbit the Earth?
At the space station's altitude of about 420 km, one orbit of the Earth takes about 93 minutes at roughly 7.66 km/s. The higher the orbit, the slower and longer it is: GPS satellites take about 12 hours, and at 35,786 km an orbit takes one sidereal day, so the satellite seems to hang still over one spot.
The formula
For a circular orbit the period is T = 2π√(r³/GM), where r is the distance from Earth's centre (Earth's radius, 6,371 km, plus the altitude) and GM is Earth's gravitational parameter, 398,600.4418 km³/s².
The speed is v = √(GM/r). Both depend only on r, which is why every satellite at the same height moves at the same speed, whatever it weighs.
Three worked examples
Space station, 420 km: r = 6,791 km, v is about 7.66 km/s and one orbit takes about 92.8 minutes.
GPS, 20,200 km: r = 26,571 km, v is about 3.87 km/s and one orbit takes about 11 hours 58 minutes.
Geostationary, 35,786 km: r = 42,157 km, v is about 3.07 km/s and one orbit takes about 23 hours 56 minutes, matching Earth's own spin.
What the formula leaves out
Real orbits are rarely perfect circles, and low orbits lose height to thin air. The circular formula is still the right first answer, and the one mission planners start from.
Quick answers
Why do higher orbits take longer?
Gravity is weaker further out, so the speed needed to stay in orbit is lower, and the path around is longer.
What is the lowest possible orbit?
Around 160 km is the practical minimum; below that, air drag pulls a satellite down within days.