  Close encounters between two bodies in a disc often result in a single
orbital deflection. However, within their Jacobi volumes, where the
gravitational forces between the two bodies and the central body become
competitive, temporary captures with multiple close encounters become possible
outcomes: a Jacobi capture. We perform 3-body simulations in order to
characterise the dynamics of Jacobi captures in the plane. We find that the
phase space structure resembles a Cantor-like set with a fractal dimension of
about 0.4. The lifetime distribution decreases exponentially, while the
distribution of the closest separation follows a power law with index 0.5. In
our first application, we consider the Jacobi capture of the Moon. We
demonstrate that both tidal captures and giant impacts are possible outcomes.
The impact speed is well approximated by a parabolic encounter, while the
impact angles follow that of a uniform beam on a circular target. Jacobi
captures at larger heliocentric distances are more likely to result in tidal
captures. In our second application, we find that Jacobi captures with
gravitational wave dissipation can result in the formation of binary black
holes in galactic nuclei. The eccentricity distribution is approximately
super-thermal and includes both prograde and retrograde orientations. We
conclude that dissipative Jacobi captures form an efficient channel for binary
formation, which motivates further research into establishing the universality
of Jacobi captures across multiple astrophysical scales.
