On the Jacobi capture origin of binaries with applications to the
  Earth-Moon system and black holes in galactic nuclei
  Close encounters between two bodies in a disk 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 set with a fractal dimension of 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. Their respective
1D cross sections differ within an order of magnitude, evaluated at a
heliocentric distance of 1 AU. The impact speed is well approximated by a
parabolic encounter, while the impact angles follow that of a uniform beam on a
circular target. 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
estimate a cosmic rate density of 0.083 < R < 14 Gpc^-3 yr^-1. 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.
