orbital state vector

This set of six variables, together with time, are called the orbital state vectors.

That is, the orbit that coincides with the current orbital state vectors (position and velocity).

For elliptic orbits true anomaly can be calculated from orbital state vectors as:

In astrodynamics semi-major axis a can be calculated from orbital state vectors:

Keplerian elements can be obtained from orbital state vectors (x-y-z coordinates for position and velocity) by manual transformations or with computer software.

Eccentricity of an orbit can be calculated from orbital state vectors as a magnitude of eccentricity vector:

These can be described as orbital state vectors, but this is often an inconvenient way to represent an orbit, which is why Keplerian elements are commonly used instead.

Simplified perturbations models are a set of five mathematical models (SGP, SGP4, SDP4, SGP8 and SDP8) used to calculate orbital state vectors of satellites and space debris relative to the Earth-centered inertial coordinate system.