True anomaly - circular orbit

Description

In celestial mechanics, true anomaly is an angular parameter that defines the position of a body moving along a Keplerian orbit. It is the angle between the direction of periapsis and the current position of the body, as seen from the main focus of the ellipse (the point around which the object orbits). The true anomaly is usually denoted by the Greek letters ν or θ, or the Latin letter f. The true anomaly f is one of three angular parameters (“anomalies”) that defines a position along an orbit, the other two being the eccentric anomaly and the mean anomaly.

For circular orbits the true anomaly is undefined, because circular orbits do not have a uniquely determined periapsis. Instead the argument of latitude u is used if rz< 0 (the z-component of the orbital position vector r), then replace u by 2π − u

Related formulas

Variables

uArgument of latitude (rad)
nA vector pointing towards the ascending node (i.e. the z-component of n is zero). (dimensionless)
rorbital position vector (m)