position and velocity. For any object moving through space, the velocity vector is tangent to the trajectory. If is the unit vector tangent to the trajectory, then Derivation The velocity vector can be derived from position vector by differentiation with respect to time: An object's state vector can be used to compute its classical or Keplerian orbital elements and vice versa. Each representation has its advantages. The elements are more descriptive of the size, shape and orientation of an orbit, and may be used to quickly and easily estimate the object's state at any arbitrary time provided its motion is accurately modeled by the two-body problem with only small perturbations. On the other hand, the state vector is more directly useful in a numerical integration that accounts for significant, arbitrary, time-varying forces such as drag, thrust and gravitational perturbations from third bodies as well as the gravity of the primary body. The state vectors ( and ) can be easily used to compute the specific angular momentum vector as . Because even satellites in low Earth orbit experience significant perturbations from Earth's non-spherical shape, Solar Radiation Pressure, Moon Tidal Effects, and Atmospheric Drag, the Keplerian elements computed from the state vector at any moment are only valid for a short period of time and need to be recomputed often to determine a valid object state. Such element sets are known as osculating elements because they coincide with the actual orbit only at that moment. Orbital State Vectors come in many forms including the traditional Position-Velocity vectors, Two-line element set (TLE), and Vector Covariance Matrix (VCM). See also ECEF Earth-centered inertial Orbital plane Orbit determination State vector (navigation) References Orbits Vectors (mathematics and physics)