= Jack Wisdom
{c}
<Jack Wisdom> is a planetary scientist whose work applies <Hamiltonian mechanics>, <chaotic dynamics> and numerical methods to the motion of bodies in the <Solar system>. His MIT profile documents contributions to long-duration integrations and mapping methods for planetary motion.<Jack Wisdom profile by MIT CSAIL>[research biography, numerical mappings and solar-system dynamics]{ref}
His 1983 study of the three-to-one <Kirkwood gap> investigated how an <orbital resonance> with Jupiter can produce large changes in an asteroid's <orbital eccentricity>. It compared a simplified mapping with direct numerical integration, showing that the sudden eccentricity changes were not merely artifacts of the faster model.<Chaotic Behavior and the Origin of the 3 1 Kirkwood Gap by Jack Wisdom>[Icarus56,51–74; abstract and sections1–2]{ref}
The three-to-one label means that an asteroid completes approximately three orbits for one orbit of Jupiter. Using <Kepler's third law> in an ideal solar two-body approximation gives
$$
\frac{a}{a_J}\simeq\left(\frac{T}{T_J}\right)^{2/3}=3^{-2/3}\simeq0.481.
$$
This locates the resonance approximately; it does not by itself establish that every trajectory there is unstable. The dynamical calculation asks how repeated perturbations alter the orbit over time. That distinction connects a simple period ratio to the harder problem of explaining an observed depletion of asteroids.
\Image[https://www.csail.mit.edu/sites/default/files/styles/headshot/public/images/people/profile/jack-2019_0.png?h=7ca0fd64&itok=OjFJloSD]
{title=Jack Wisdom, identified headshot on MIT CSAIL's profile}
{description=External portrait from <Jack Wisdom profile by MIT CSAIL>.}
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