Temporary satellite capture of short-period Jupiter family comets from the perspective of dynamical systems

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.