  We construct approximate analytical solutions to the constraint equations of
general relativity for binary black holes of arbitrary mass ratio in
quasicircular orbit. We adopt the puncture method to solve the constraint
equations in the transverse-traceless decomposition and consider perturbations
of Schwarzschild black holes caused by boosts and the presence of a binary
companion. A superposition of these two perturbations then yields approximate,
but fully analytic binary black hole initial data that are accurate to first
order in the inverse of the binary separation and the square of the black
holes' momenta.
