Summary: at relativistic speeds, if you compute a planet's relative distance using angular diameter (roughly proportional to 1/angular diameter), will that computed distance increase or decrease linearly, assuming you are traveling directly towards or directly away from the planet? Example:
A ship starts at Earth, accelerates to 0.8c, and travels to a planet P 10 light years away.
The ship pilot knows the diameter of P, and uses the angular diameter to compute his distance from P.
When the ship accelerates from 0 to 0.8c, P's angular diameter does not change (is that correct?), so the pilot defines that diameter to correspond to 10ly (he's using the reference frame of the Earth/planet for this definition only).
The journey takes 7.5 years ship clock time; as the ship approaches t=7.5, P's angular diameter tells the pilot his distance is approaching 0.
Question: does the distance as computed from the angular diameter (which is roughly the reciprocal of the angular diameter) decrease linearly during the pilot's journey? The angular diameter is perpendicular to direction of flight, so foreshortening shouldn't be an issue, but I could be wrong about this.
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