# What is the apparent magnitude of the Milky Way from the viewpoint of the Large Magellanic Cloud?

Wikipedia contains the essentially unsourced claim that

From a viewpoint in the LMC, the Milky Way's total apparent magnitude would be −2.0—over 14 times brighter than the LMC appears to us on Earth—and it would span about 36° across the sky, the width of over 70 full moons.

Is this the case?

The distance to the lmc is about 160000 light-years, and the diameter of the galaxy is about 100000 light-years. So by trigonometry the apparent diameter would be about $$2\arctan(0.5\times 100000/160000)=35^\circ$$ And that is close enough to the quote value to be a difference in rounding.
The absolute magnitude of the milky way is quoted taken as -21.3 So a naive calculation of apparent magnitude based on a distance modulus of $$5\log_{10}(160000/3.26 -1)=23.4$$ would be $$-21.3 + 23.4 = 2.1$$. That is quite a long way from the quoted value. But note that calculating a magnitude of such a extended object isn't of much use instead you would normally consider surface brightness.