Well after reading the article you linked I looked up some background on star's lifecycles and such, to make sure I understand a little of what's in there.
So I came up with that... here's what I think the results might be ... all very back of the envelope... (I love making up fantasy worlds
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#1 - one tenth the sun's mass at 200 AU, a red dwarf star. On Earth its light will appear 100 times less than the full moon, but still 15 times brighter than Venus - absolutely dominating the night sky apart from the moon. Its angry red glow will be visible at daytime too. Certainly ancient cultures would ascribe all sorts of powers to it. It takes 200 years for the star's position in the sky to move through one of the constellations of the zodiac so it might be used for grand prophecies pertaining to eras. But during the experience of one human being it will rise and set with whatever constellation it's in. Astronomers will realize early on it's different from the other planets, that move so much faster, but it's also not a 'fixed star.' As astronomy improves telescopes will reveal it to be a disc of light, and probably the notion that all the other stars are actually distant suns in their own right will be accepted quite readily. Equipment comparable to what we have today might indeed uncover planets, and sending a spacecraft there would certainly be a goal...
#2 - equal mass to the sun, on Earth it gives the light of ten full moons, and when up at night, that would not be night anymore. The twilight would be enough for travel and work outside to be possible even without artificial illumination, that would surely influence lifestyles and culture. It is so far outside any comparison with other stars that it would probably be considered a category of its own, we'd have the Sun, the Moon, and the Nem
Up at day it would still be inconsequential next to the sun (1/40000) but surely irritating to look at directly. Being much better illuminated, any planets around it would be much easier to detect by telescope. We'd certainly want to go there once we had space travel.
Anyway who says we wouldn't be the space invaders?
#3 - just one third more mass than the sun -- oops, the astronomy pages tell me, we wouldn't see anything, as we wouldn't be around...