Escape velocity and internal propagation speed are generally regarded as independent properties of self-gravitating bodies. Escape velocity is determined by the global gravitational potential, whereas propagation speed depends primarily on local material properties such as density and elastic response. Here we report a previously unrecognized correspondence between these quantities across a range of gravity-shaped bodies. Observational data for Earth, Mars, Venus, the Moon, and the Sun indicate that characteristic internal propagation velocities closely match the corresponding escape velocities despite substantial differences in composition, thermodynamic state, and evolutionary history.The observed relation spans more than two orders of magnitude in characteristic velocity and appears to hold for both planetary and stellar interiors. For tidally locked bodies such as the Moon, a geometric correction associated with non-radial propagation yields the same scaling behavior. The correspondence is quantified through the dimensionless ratio �� = �� ��������/�� ��, which remains close to unity across the investigated bodies within observational uncertainty.The relation was originally identified as a consequence of a broader framework in which gravitational potential is associated with cumulative relativistic interaction delay. Within that framework, equating the relativistic time-dilation factors associated with finite-speed propagation and gravitational potential leads directly to the observed scaling. Although the physical origin of the correspondence remains open, the results suggest an unexpected connection between internal propagation processes and gravitational potential. Future planetary, lunar, and helioseismic observations may provide additional tests of the proposed relation.