orbitalparametrar

Orbitalparametrar, or orbital parameters, are a set of quantities used to specify the orbit of a celestial body around a primary mass. They encode the size, shape, and orientation of the orbit as well as the body's position along the path at a specific time. In practice, these parameters enable the calculation of future positions and velocities and are fundamental to mission design, satellite tracking, and celestial mechanics.

The classical six-element set includes: semi-major axis a, eccentricity e, inclination i, longitude of the ascending node Omega, argument of periapsis omega, and the true anomaly nu at a specified epoch (or equivalently the mean anomaly M at that epoch). Often the epoch is accompanied by the central body's gravitational parameter mu (GM) and, optionally, the time of periapsis passage T. Together with mu, these elements define the instantaneous Keplerian orbit around the central body.

Osculating versus mean: Most commonly used are osculating orbital elements, which describe the instantaneous Keplerian orbit that would apply at that moment if all perturbations were removed. Under perturbations, these elements vary with time, requiring numerical propagation to predict future states. Mean elements provide averaged values over short-term perturbations and are used for long-term studies.

Reference frames and alternative parametrizations: The numerical values depend on the chosen reference frame and epoch, such as a particular inertial frame tied to J2000 or to the ecliptic. Other parameterizations exist, including equinoctial and non-singular elements, which are used to avoid singularities in special cases like zero inclination or circular orbits.