Editing True anomaly (section)

===From state vectors===
For elliptic orbits, the '''true anomaly''' {{mvar|ν}} can be calculated from [[orbital state vectors]] as:

:<math> \nu = \arccos { {\mathbf{e} \cdot \mathbf{r}} \over { \mathbf{\left |e \right |} \mathbf{\left |r \right |} }}</math>
::(if {{nowrap|'''r''' ⋅ '''v''' < 0}} then replace {{mvar|ν}} by {{nowrap|2{{pi}} − {{mvar|ν}}}})

where: 
* '''v''' is the [[orbital velocity vector]] of the orbiting body,
* '''e''' is the [[eccentricity vector]],
* '''r''' is the [[orbital position vector]] (segment ''FP'' in the figure) of the orbiting body.

====Circular orbit====
For [[circular orbit]]s the true anomaly is undefined, because circular orbits do not have a uniquely determined periapsis. Instead the [[argument of latitude]] ''u'' is used:

:<math> u = \arccos { {\mathbf{n} \cdot \mathbf{r}} \over { \mathbf{\left |n \right |} \mathbf{\left |r \right |} }}</math>
::(if {{nowrap|''r<sub>z</sub>'' < 0}} then replace {{nowrap|''u'' by 2{{pi}} − ''u''}})

where:
* '''n''' is a vector pointing towards the ascending node (i.e. the ''z''-component of '''n''' is zero).
* ''r<sub>z</sub>'' is the ''z''-component of the [[orbital position vector]] '''r'''

====Circular orbit with zero inclination====
For [[circular orbit]]s 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:

:<math> l = \arccos { r_x  \over { \mathbf{\left |r \right |}}}</math>
::(if {{nowrap|''v<sub>x</sub>'' > 0}} then replace {{mvar|l}} by {{nowrap|2{{pi}} − {{mvar|l}}}})

where:
* ''r<sub>x</sub>'' is the ''x''-component of the [[orbital position vector]] '''r'''
* ''v<sub>x</sub>'' is the ''x''-component of the [[orbital velocity vector]] '''v'''.