Keplerian Orbit Elements

Every orbit in the solar system, every satellite, every exoplanet, is catalogued by the same six numbers. Two of them set the ellipse itself: the semi-major axis a is its size and the eccentricity e is how stretched it is. Three more orient that ellipse in space against a reference plane: the inclination i tilts the orbit out of the plane, the longitude of the ascending node Omega swings the tilt around, and the argument of periapsis omega rotates the closest point within the orbital plane. The sixth, the true anomaly nu, just says where the body is right now, and it sweeps faster near the star and slower far away, Kepler's second law. The scene renders the orbit in 3D against an explicit reference frame: the reference plane (the ecliptic), the vernal-equinox direction ♈, and the line of nodes where the orbital plane cuts the reference plane. Each element is drawn as the angle arc that defines it, Ω measured in the reference plane from ♈ to the ascending node, i as the tilt between the two planes at that node, ω in the orbital plane from the node to periapsis, and ν from periapsis to the body now, so you can see exactly what every slider changes. The diagnostic is the distance and speed around the orbit, peaking and plunging as the body swings through periapsis.