  Understanding which stars explode leaving behind neutron stars and which
stars collapse forming black holes remains a fundamental astrophysical problem.
We derive an analytic explosion condition for spherically symmetric
core-collapse supernovae. The derivation starts with the exact governing
equations, considers the balance of integral forces, includes the important
dimensionless parameters, and includes an explicit set of self-consistent
approximations. The force explosion condition is $\tilde{L}_\nu\tau_g - 0.06
\tilde{\kappa} > 0.38$, and only depends upon two dimensionless parameters. The
first compares the neutrino power deposited in the gain region with the
accretion power, $\tilde{L}_\nu \tau_g = L_{\nu} \tau_g R_{\rm NS}/ ( G \dot{M}
M_{\rm NS})$. The second, $\tilde{\kappa} = \kappa \dot{M} / \sqrt{G M_{\rm NS}
R_{\rm NS}}$, parameterizes the neutrino optical depth in the accreted matter
near the neutron-star surface. Over the years, many have proposed approximate
explosion conditions: the critical neutrino-luminosity, ante-sonic, and
timescale conditions. We are able to derive these other conditions from the
force explosion condition, which unifies them all. Using numerical,
steady-state and fully hydrodynamic solutions, we test the explosion condition.
The success of these tests is promising in two ways. One, the force explosion
condition helps to illuminate the underlying physics of explosions. Two, this
condition may be a useful explosion diagnostic for more realistic,
three-dimensional radiation hydrodynamic core-collapse simulations.
