by MarkBour » Thu Nov 02, 2017 5:09 pm
De58te wrote:So if nearby Andromeda Galaxy would be in the picture, what would Andromeda's apparent size be? M31 is twice the diameter of NGC 891, and it is about 12 times closer. Would that mean Andromeda would appear 14 times bigger than NGC 891, or 24 times bigger?
To really answer your question, ""what would Andromeda's apparent size be?", I guess one should set aside your estimates and just say (from Wikipedia) that Andromeda subtends an angle of about 3.167° along its long axis (angular diameter). And NGC891 is also listed by Wikipedia at 13.5' of angular diameter.
The hypothetical question, "How would the visual angle change if a small, distant object were doubled in size and brought 12 times closer?" would be answered as follows. The
tangent of the angle it subtends would be 24 times what it was. And the tangent is a non-linear function, but at sufficiently small angles, it is close to linear. So it is not a bad approximation to say that based on your estimates, you would expect Andromeda to appear about 24 times as large as NGC891.
Going in the reverse, if you cut the size of Andromeda in half and moved it 12 times as far away, it would subtend an angle that is pretty close to (3.167°/24) = 0.132°, or about 8' . You could do the math more carefully, converting to a tangent, dividing by 24, then converting back to an arctangent, and you get almost the same result (I get 7.9' using Excel).
[quote="De58te"]So if nearby Andromeda Galaxy would be in the picture, what would Andromeda's apparent size be? M31 is twice the diameter of NGC 891, and it is about 12 times closer. Would that mean Andromeda would appear 14 times bigger than NGC 891, or 24 times bigger?[/quote]
To really answer your question, ""what would Andromeda's apparent size be?", I guess one should set aside your estimates and just say (from Wikipedia) that Andromeda subtends an angle of about 3.167° along its long axis (angular diameter). And NGC891 is also listed by Wikipedia at 13.5' of angular diameter.
The hypothetical question, "How would the visual angle change if a small, distant object were doubled in size and brought 12 times closer?" would be answered as follows. The [i][b]tangent[/b][/i] of the angle it subtends would be 24 times what it was. And the tangent is a non-linear function, but at sufficiently small angles, it is close to linear. So it is not a bad approximation to say that based on your estimates, you would expect Andromeda to appear about 24 times as large as NGC891.
Going in the reverse, if you cut the size of Andromeda in half and moved it 12 times as far away, it would subtend an angle that is pretty close to (3.167°/24) = 0.132°, or about 8' . You could do the math more carefully, converting to a tangent, dividing by 24, then converting back to an arctangent, and you get almost the same result (I get 7.9' using Excel).