In astrodynamics and celestial dynamics, the orbital state vectors (sometimes state vectors) of an orbit are
Cartesian vectors of position (
r
{\displaystyle \mathbf {r} }
) and velocity (
v
{\displaystyle \mathbf {v} }
) that together with their time (epoch) (
t
{\displaystyle t}
) uniquely determine the trajectory of the orbiting body in space.: 154
Orbital state vectors come in many forms including the traditional Position-Velocity vectors, Two-line element set (TLE), and Vector Covariance Matrix (VCM).
∣r⟩,∣l⟩,∣i⟩, and ∣o⟩ can all be expressed as expressions for ∣u⟩ and ∣d⟩. So, given the state vector ∣ψ⟩ = α∣u⟩ + β∣d⟩, is it possible to know not only the probability of ∣u⟩ but also the probability of ∣r⟩ and ∣i⟩? ∣ψ⟩ can be expressed as an expression for ∣r⟩, ∣l⟩ or ∣i⟩, ∣o⟩.