Past exam of the relativity course of the University of Cambridge / 2022 / Section A / 1 / Solution

Use angular size under a collinear relativistic boost. For a small distant source, the two angular diameters have ratio $e^{|\eta |}$, where $\eta$ is the relative rapidity. Thus $e^{|\eta |}=2$, and the relative velocity satisfiesThe speed is therefore $0.6c$. The observers are momentarily coincident, so this is relativistic aberration, rather than a difference in their distance from the planet. The observer moving faster towards the planet measures the smaller angular diameter under the source-direction aberration convention.