File:Comparison of Eccentricity.gif

Summary[edit]

Notes[edit]

Two orbiting bodies have orbital elements that differ only in eccentricity. They are each independent two-body systems overlaid for purposes of illustration, and do not illustrate a three body system. The orbital period, a function of the semi-major axis, the aggregate mass of the two body system, and the gravitational constant, is the same for both systems, and independent of eccentricity. Due to Kepler's second law, however, a line joining the orbiting body and the center of mass of the system sweeps out equal areas during equal intervals of time. Consequently, for highly eccentric orbits, an orbiting body near periapsis, and the center of mass necessarily exhibits a large radial velocity. At apoapsis, with the body distant from the center of mass, a correspondingly small angular velocity ensues. This gives rise to a slingshot effect absent in circular orbits of zero eccentricity. The sling-shot effect becomes more marked as eccentricity approaches unity.

The plotting system employed R. H. Battin's universal formula to compute position and velocity for equal time steps from the periapsis passage. See Kaplan, Marshall H. Modern Spacecraft Dynamics and Control 1976 John Wiley and Sons ISBN 0-471-45703-5 pp 306 -308. Computations implemented in python, imagery generated using the TK Widget toolkit. Animation composited in Adobe After Effects; animated GIF generated and optimized in Gimp 2.2.

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