Abstract
The Temporary Satellite Capture (TSC) of short-period comets, such as Oterma and Helin-Roman-Crockett, by Jupiter has intrigued astronomers for many years. A widely accepted approach to study TSC is to numerically integrate the equations of motion for the n-body problem using a wide range of initial conditions obtained from the heliocentric two-body problem; then, a search ensues for instances when the Joviocentric energy becomes negative. More recently, a preliminary analysis involving the application of Dynamical Systems Theory (DST) to the Sun-Jupiter-comet three-body problem has provided significant insight into the motion in the Sun-Jupiter system and offered a simple model to account for the TSC phenomena observed in Jupiter family short-period comets. The accuracy of this model can be immediately verified since ephemeris data is available for comet trajectories.
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Howell, K.C., Marchand, B.G. & Lo, M.W. Temporary Satellite Capture of Short-Period Jupiter Family Comets from the Perspective of Dynamical Systems. J of Astronaut Sci 49, 539–557 (2001). https://doi.org/10.1007/BF03546223
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DOI: https://doi.org/10.1007/BF03546223