The equation relating a galaxy’s recessional velocity to its distance using redshift observations is Hubble’s law.
In its simplest form, Hubble’s law is written v = H₀d: a galaxy’s recession velocity, v, is approximately equal to the Hubble constant, H₀, multiplied by its distance, d. It describes the large-scale expansion of the universe rather than galaxies simply flying away from one central explosion through otherwise empty space.
Astronomers estimate recession velocity from a galaxy’s redshift, the displacement of spectral lines toward longer, redder wavelengths. Distances are measured independently using astronomical distance indicators. When many galaxies are compared, more distant galaxies generally show larger recession velocities, producing the Hubble–Lemaître relation.
The law has limits. Nearby galaxies can have substantial peculiar velocities caused by local gravitational interactions, and the exact expansion relation depends on cosmological parameters and epoch. The symbol H₀ is called the Hubble constant, although its measured value remains the subject of the modern Hubble tension. Hubble’s law is therefore a foundational approximation within observational cosmology, not one of the optical laws governing lenses or circuits.