Abstract: Accurate identification of end-diastole (ED) and end-systole (ES) in echocardiography underpins the quantification of ventricular function, yet manual selection of these key frames is subjective and introduces clinically significant inter-operator variability. Recent self-supervised methods either prescribe strict periodic trajectories or learn an unconstrained low-dimensional motion subspace from reconstruction or registration objectives. The former offers interpretability but imposes restrictive assumptions on temporal progression, whereas the latter leaves cardiac phase implicit and ED/ES must be recovered through post-hoc geometric processing of the learned trajectory. We translate the physiological observation that cardiac phase is a one-dimensional signal into a prior by constraining the latent motion component to a single-parameter latent orbit, i.e., a global linear trajectory in latent space indexed by a bounded scalar phase variable. Mapping this variable through a sinusoidal nonlinearity yields an oscillatory motion signal with consistent temporal ordering, enabling direct identification of ED and ES from the learned phase signal. This inductive bias allows the model to capture an interpretable representation of the cardiac cycle, while maintaining flexibility to capture irregular heartbeats. Trained on EchoNet-Dynamic without annotations, our minimal single-parameter cardiac phase model learns an effective latent orbit, significantly improves upon the previous state of the art in ED localisation and matches it in ES localisation while using a more constrained representation and fewer training epochs. This demonstrates that a principled physiological inductive bias can match or exceed the performance of more complex representations. Code is available at: https://github.com/BonniciJ/OrbitalEcho/