  The discovery that a substantial fraction of Kuiper Belt objects (KBOs)
exists in binaries with wide separations and roughly equal masses, has
motivated a variety of new theories explaining their formation. Goldreich et
al. (2002) proposed two formation scenarios: In the first, a transient binary
is formed, which becomes bound with the aid of dynamical friction from the sea
of small bodies (L^2s mechanism); in the second, a binary is formed by three
body gravitational deflection (L^3 mechanism). Here, we accurately calculate
the L^2s and L^3 formation rates for sub-Hill velocities. While the L^2s
formation rate is close to previous order of magnitude estimates, the L^3
formation rate is about a factor of 4 smaller. For sub-Hill KBO velocities (v
<< v_H) the ratio of the L^3 to the L^2s formation rate is 0.05 (v/v_H)
independent of the small bodies' velocity dispersion, their surface density or
their mutual collisions. For Super-Hill velocities (v >> v_H) the L^3 mechanism
dominates over the L^2s mechanism. Binary formation via the L^3 mechanism
competes with binary destruction by passing bodies. Given sufficient time, a
statistical equilibrium abundance of binaries forms. We show that the frequency
of long-lived transient binaries drops exponentially with the system's lifetime
and that such transient binaries are not important for binary formation via the
L^3 mechanism, contrary to Lee et al. (2007). For the L^2s mechanism we find
that the typical time, transient binaries must last, to form Kuiper Belt
binaries (KBBs) for a given strength of dynamical friction, D, increases only
logarithmically with D. Longevity of transient binaries only becomes important
for very weak dynamical friction (i.e. D \lesssim 0.002) and is most likely not
crucial for KBB formation.
