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Measuring size
Probably a silly question but would be good to get an opinion.
If you are given both the angular size of, and the distance to, a celestial object simple math should allow the object's linear size to be calculated. For example, in the attached grossly exaggerated diagram assume that you are at position O and that the short arc represents a segment of your night sky. You observe a galaxy that spans locations A and B on the sky and determine that it subtends an angle of L. Source references state that the distance to the galaxy is d. It is easy to calculate the linear size of the line A-B. It is also easy to calculate the length of the arc A-C-B. But which of the two is the correct size of the galaxy? In this exaggerated view it is obvious that the arc is appreciably longer than the line. As angle L gets smaller so the length of the arc more closely approaches the length of the line. At the very small angles that are involved for distant galaxies the difference becomes almost vanishingly small but nevertheless it is still present.
What do you think is the better calculation of the object's size, the line A-B or the arc A-C-B? Would it make a difference if what you are measuring is the distance between two different objects located at the two points A and B assuming that they are both the same distance away from us?
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