Stellar Aberration as an Inertial Velocimeter: Classical and Relativistic Analysis with Implications for Autonomous Deep-Space Navigation Sensor Design

A theoretical framework is proposed for an autonomous inertial velocimeter based on the phenomenon of stellar aberration, with direct application to deep-space navigation. Starting from classical geometric optics, the relation v = C · sin(β) between the transverse velocity of an observer and the aberration angle β of an external light source is derived, demonstrating that this relation is independent of the distance to the reference source. The corresponding relativistic correction is discussed, whose contribution is less than 0.01% for velocities below 10% of the speed of light. It is demonstrated that the principle requires a reference source in an inertial frame external to the spacecraft, and that no co-moving source can serve as a valid reference, by virtue of Einstein's Principle of Relativity. The Cosmic Microwave Background (CMB) is proposed as the optimal absolute reference, whose kinematic dipole anisotropy of 6.73 mK allows determination of both speed and direction of motion relative to the cosmological rest frame. A total instrument mass of ~25 kg and ~115 W is estimated, compatible with standard deep-space exploration missions.