In astronomy, the **true anomaly** (, also written ) is the angle between the direction *z-s* of periapsis and the current position *p* of an object on its orbit, measured at the focus *s* of the ellipse (the point around which the object orbits). In the diagram below, true anomaly is the angle *z-s-p*.
## Calculation from state vectors For elliptic orbits **true anomaly** can be calculated from orbital state vectors as: - (if then replace
*T* by 2π − *T*) where: For circular orbits this can be simplified to: - (if then replace
*T* by 2π − *T*) where: - is vector pointing towards the ascending node (i.e. the z-component of is zero).
For circular orbits with the inclination of zero this can be simplified further to: - (if then replace
*T* by 2π − *T*) where: ## Other relations The relation between *T* and *E*, the eccentric anomaly, is: or equivalently The relations between the radius (position vector magnitude) and the anomalies are: and where *a* is the orbit's semi-major axis (segment *cz*).
## See also |