The departure point for this timeline occurs way before 1900 AD, basically the orbital path of the Sun around the Galaxy is altered so that now its only 15,000 Astronomical Units away from Alpha Centauri A & B rather than 4.33 light years. This is about the distance of Alpha Centauri C or Proxima Centauri from those two stars. Alpha Centauri still appears in the constellation of Centaurus, but now the components A and B are distinctly seperate to the naked eye and the stars are correspondingly brighter as well.
How would this affect Earth's history, assuming the stars don't stir up the Oort cloud or haven't done so yet as to cause a major cometary impact with the Earth? The stars have been fairly close for all of recorded history and getting closer, although now it is approaching its minimal distance and in a few centuries they will be pulling farther away once again.
Alpha Centaur A is easily the brightest star in the night sky.