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Julian, Rob, Bill.
Firstly, thank you for your replies. They are much appreciated and have given much food for thought.
For an object spanning 60 degrees of arc I calculate that the length of the arc A-C-B would be 4.72% longer than the length of the chord A-B. 4% is not an insignificant amount. But of course an angle of 60 degrees is way beyond anything that will concern us in the night sky. Apart from the Milky Way, the largest object in our skies is possibly Barnard's Loop which, according to Wikipedia, spans about 10 degrees of arc. For such an angle the arc is only 0.13% longer than the chord. And by the time we get to more usual objects such as NGC 253 which spans 27.5 arc minutes the difference is only 0.001%. Add to that the uncertainty factors mentioned by Rob and it is clear that the question raised has little practical merit in the context of astronomical objects.
But it was an interesting mental exercise that kept the aging little grey cells ticking over and again I thank you for replying.
Last edited by DavidLJ; 24-09-2016 at 11:21 PM.
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