Before revision: Then, the Clohessy–Wiltshire equations are where is the orbital rate (in units of radians/second) of the target body, is the radius of the target body's circular orbit, is the standard gravitational parameter, If we define , the Clohessy–Wiltshire equations can be written as a linear time-invariant (LTI) system, where the state matrix is For a satellite in low earth orbit, and , implying , corresponding to an orbital period of about 93 minutes.
After revision: the state vector asThen, the Clohessy–Wiltshire equations are where is the orbital rate (in units of radians/second) of the target body, is the radius of the target body's circular orbit, is the standard gravitational parameter, If we define , the Clohessy–Wiltshire equations can be written as a linear time-invariant (LTI) system, where the state matrix is For a satellite in low earth orbit, and , implying , corresponding to an orbital period of about 93 minutes.