A Keplerian orbit represents the idealized trajectory of a celestial body moving under the influence of a single central gravitational mass, governed by the laws of planetary motion established by Johannes Kepler in the early 17th century. Unlike a simple circular path, this trajectory is typically an ellipse defined by six precise orbital elements that dictate its unique geometry and orientation in three-dimensional space. These elements(including the semi-major axis, eccentricity, and inclination) work in concert to determine not only the size and elongation of the orbit but also exactly how the orbital plane is tilted relative to a reference frame and where the body is located at any specific moment in time. Understanding these fundamental mechanics is essential to the field of astrodynamics, serving as the mathematical backbone for tracking satellites, predicting planetary positions, and planning complex spaceflight maneuvers.

Based on the diagrams and the simulation controls you have implemented, here is a bulleted description of the Keplerian orbital elements:

NOTE : The revolution speed of satellite is not calculated based on real physics. The purpose of this note is mainly for visualization of the shape of Kepellerian orbit and relative speed of a satellite (not absolute speed).

• Semi-Major Axis (a): Defines the overall size of the orbit. In your simulation, this controls how large the elliptical path appears relative to the central grid.
• Eccentricity (e): Determines the shape of the orbit, ranging from a perfect circle (e = 0) to a highly elongated ellipse (e → 1). A higher value flattens the green orbital disk in your 3D view.
• Inclination (i): Represents the vertical tilt of the orbital plane relative to the reference plane (the white grid/disk). It is the angle required to lift the orbital plane up from the line of nodes.
• Longitude of the Ascending Node (Ω): Defines the horizontal orientation of the orbital plane's "hinge" (the Line of Nodes) relative to a fixed reference direction. In your code, this rotates the intersection line (magenta) around the vertical Y-axis.
• Argument of Periapsis (ω): Defines the orientation of the ellipse within the orbital plane. It is the angle measured from the Ascending Node (pink marker) to the Periapsis (orange marker), determining where the closest point of approach is located.
• True Anomaly (ν): Specifies the precise position of the orbiting body (the satellite) along its path at a specific moment in time. It is the angle measured from the Periapsis to the satellite's current position vector.