An astronomical body's Hill radius is the radius of the sphere (Hill sphere) within which smaller bodies would tend to orbit the body. Outside the radius, the body would be drawn to orbit around the next larger body which the initial body is orbiting. For example, the Moon is within Earth's Hill radius because otherwise it would not retain a stable orbit around Earth but would end up in orbit around the Sun. It might take multiple orbits before the smaller body breaks away.
The Hill sphere lies between the L1 and L2 Lagrangian points; of the two bodies. The formula for the Hill radius for a body (e.g., Earth) orbiting another (e.g., the Sun) is:
r ≈ a(1-e)3√(m/3M)
The term tidal radius is often used when discussing entire star clusters or galaxies, distinguishing whether the dynamics of a body at that distance is determined by the cluster/galaxy or some separate entity.