Let , , be a Cartesian coordinate system in a reference frame whose origin corresponds to the location of the Sun, and which is such that the planet's unperturbed orbit lies in the plane , with the angular momentum vector pointing in the positive -direction, and the perihelion situated on the positive -axis. Let , , be a cylindrical coordinate system in the same reference frame.
We know from the analysis of Chapter 4 thatand . Moreover, the planet's mean orbital angular velocity is and are the planet's orbital major radius and eccentricity, respectively. Note that, for the unperturbed orbit, the quantities , , , , , and are all constant in time. We also have , , and are the planet's true anomaly, eccentric anomaly, and mean anomaly, respectively. (See Chapter 4.)