Problem 1 of 6
How fast is the ISS going?
Given
Circular orbit at h = 420 km altitude. RE = 6378.137 km, μ = 398600.4418 km3/s2. Find the orbital speed and the period.
In a circular orbit gravity supplies exactly the centripetal force, so μ/r2 = v2/r. Measure r from the centre of the Earth, not from the ground.
- r = RE + h = 6378.137 + 4206798.137 km
- v = √(μ / r) = √(398600.4418 / 6798.137)7.657 km/s
- T = 2π √(r3 / μ) = 5578.2 s92.97 min
Answer. v = 7.66 km/s, T = 93.0 min. About 15.5 orbits per day.