Web Simulation 

 

 

 

 

Keplerian Orbit 

Sections

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.

Simulation

The interactive simulator is below. Use the controls to explore the concepts described above.

Orbital Elements

A Keplerian orbit is fully specified by six orbital elements: three that fix the size and shape of the ellipse, and three angles that fix its orientation and the body's position.

Note on speed: the revolution speed of the satellite is not calculated from real physics. This visualization conveys the shape of the Keplerian orbit and the relative speed of the satellite (faster near periapsis, slower near apoapsis), not its absolute speed.

Element

Symbol

Role

Semi-Major Axis

a

Overall size of the orbit; controls how large the elliptical path appears relative to the central grid.

Eccentricity

e

Shape, from a perfect circle (e = 0) to a highly elongated ellipse (e → 1). Higher values flatten the green orbital disk.

Inclination

i

Vertical tilt of the orbital plane relative to the reference plane (white grid) — the angle that lifts the plane up from the line of nodes.

Longitude of Ascending Node

Ω

Horizontal swivel of the plane's "hinge" (Line of Nodes) about the vertical axis, relative to a fixed reference direction.

Argument of Periapsis

ω

Orientation of the ellipse within its plane: the angle from the Ascending Node (pink) to Periapsis (orange), setting where the closest approach is.

True Anomaly

ν

Where the body is now: the angle from Periapsis to the satellite's current position vector at a given moment.