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I'm wondering how our galaxy is tilted with respect to the Andromeda galaxy.

Seen from the Andromeda galaxy, what would our galaxy look like?

Would it appear as a spiral, or would it be seen edge-on, and appear long and thin?

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The "Galactic coordinates" of the Andromeda galaxy are l=121 degrees, b=-22 degrees.

That means the Andromeda galaxy is seen by us at an angle of 22 degrees to the plane of the Milky Way galaxy. Thus if you were at the Andromeda galaxy looking at the Milky Way, it would be neither face-on or edge on, but a bit closer to the latter than the former. You would still be able to see that the Milky Way had a spiral structure, because the plane of the Milky Way is much thinner than its diameter.

NB. This simple argument works because the Andromeda galaxy is more than ten times further away than the diameter of the Milky Way galaxy.

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    $\begingroup$ By way of comparison we see the Andromeda galaxy at an angle of about 13 degrees from the plane of the galaxy. Messier 88 is inclined by about 30 degrees $\endgroup$ – James K Jul 25 '17 at 12:25

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