= 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> satisfies
$$
\boxed{\frac{|v|}{c}=\tanh(\log2)=\frac{2^2-1}{2^2+1}=\frac35.}
$$
The 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.
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