Circular Orbital Velocity
Circular Orbital Velocity
A satellite in a circular orbit moves at exactly the speed where gravity provides the needed centripetal force.
The orbital velocity is v = √(G·M/r). where G is the gravitational constant, M the planet mass and r the orbital radius.
Inputs
G := 6.674e-11 N·m^2/kg^2=6.67e-11 m^3/kg/s^2
M := 5.972e24 kg=5.97e+24 kg
r := 6.771e6 m=6.77e+06 m
Balance gravity against centripetal demand.
v := sqrt(G·M/r)=7672.32 m/s
Results
Low Earth orbit needs about 7.7 km/s. Higher orbits are slower; the orbital period follows from this speed and the circumference.
Assumptions & limitations
- Circular orbit.
- Spherical, non-rotating planet.
- No atmospheric drag.