Keplerian Orbital Elements

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This Demonstration visualizes the influence of the Keplerian elements of a celestial body (e.g., a planet or asteroid orbiting around the Sun) on its orbit in 3-space.

Contributed by: Christoph Lhotka (January 2009)
Inspired by: Jeff Bryant
Open content licensed under CC BY-NC-SA



Keplerian or osculating orbital elements are the natural set of variables to describe the motion of a celestial body (planet, asteroid, satellite) in 3-space: while in the 2-body problem the full set of Cartesian coordinates changes with time, the corresponding Keplerian elements are all constant except for the mean anomaly . The semi-major axis and the eccentricity define the form of the ellipse; the inclination , periapsis , and node define the orientation of the ellipse in 3-space. The only variable to the system is the mean anomaly , defining the position of the planet in its orbit.

Snapshot 1: form of the ellipse (change )

Snapshot 2: orientation of the ellipse in 3-space (change )

Snapshot 3: position of the body in the ellipse (change )

Many more general -body systems (solar system, lunar, or artificial satellite motion) can be modelled as perturbed two-body problems, where the Keplerian elements may oscillate around their mean values.

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