How fast does gravity propagate? The standard answer, "at the speed of light," is correct for gravitational waves but misses something important. General relativity naturally splits gravity into two parts: a **constraint sector** that holds things in place and a **radiative sector** that sends out waves. The holding part fixes the gravitational field at each moment in time. The wave part carries energy at the speed of light. We show that these two parts can be cleanly separated using a mathematical tool called a "velocity gauge," built in direct analogy with a well-known construction in electromagnetism. In this framework, the apparent speed of the binding field is a freely chosen coordinate parameter (not a physical quantity) while gravitational waves always travel at *c* and all measurable quantities remain the same regardless of the choice. We also show that the standard post-Newtonian approximation, used to model binary star systems, already treats the binding field as instantaneous through high accuracy (3PN order), with wave-like propagation effects first appearing only in radiation reaction (2.5PN) and in wave-scattering corrections to the binding energy (4PN). The well-known absence of gravitational "aberration" in orbiting bodies is reinterpreted as a property of the constraint sector, not a measurement of wave speed. The 2017 observation of merging neutron stars (GW170817) measured the speed of gravitational waves; it did not and could not measure the "speed" of constraints, because constraints do not travel; they hold. We work strictly within general relativity and introduce no new physics.