True anomaly - circular orbit with zero inclination

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 with zero inclination the argument of latitude is also undefined, because there is no uniquely determined line of nodes. One uses the true longitude instead as shown.

if vx > 0 (the x-component of the orbital velocity vector v.) then replace l by 2π − l.

Related formulas

Variables

lTrue longitude (rad)
rxx-component of the orbital position vector r (m)
rorbital position vector (m)