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Hi David,
You should note a couple of things ...
1. Most of the objects (e.g. globular clusters, nebulae, galaxies) do not have a definite boundary. They fade outwards gradually. In binoculars, Omega Centauri looks barely 15' across, in a telescope it might look 36', in images maybe 50'. The bigger the aperture or the longer the exposure, the bigger it will look. So any angular size is bound to be an approximation.
2. The distance to these objects is approximate. In fact, it is more likely to be a range of distances. Example, galaxy M66 in the NED database gives its distance as anywhere between 3.86 and 15.6 megaparsecs with a mean of approximately 9.8 megaparsec. One parsec = 3.26 light years.
The errors in these two will far outweigh the small difference in using the arc as against the chord.
Regards, Rob
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