Past exam of the relativity course of the University of Cambridge / 2013 / Paper 1 / 1 / a

Use the angular-diameter ratio under a collinear boost, with motion along the common sightline and small angular radius $\vartheta$. For a boost toward the source, relativistic aberration of the incoming light gives $\tan ({\vartheta }^{\prime }/2)=e^{-\eta }\tan (\vartheta /2)$, where $\eta$ is the relative rapidity. Thus the observer seeing the smaller disk has angular diameter reduced by $e^{-\eta }$. The ratio two implies $e^{\eta }=2$, soThe answer is $0.60c$. Both observations occur at one event, so this is a relativistic aberration comparison rather than a change of geometrical distance during observation. Arbitrary transverse relative motion would require additional directional information; the stated motion toward the same distant target selects the collinear interpretation.