Here’s how they did it:
 

Astronomers can now measure how fast the Earth is moving compared to the radiation filling all of space. (Our motion causes one kind of Doppler Shift in the radiation we observe in the direction that we are moving and another kind in the opposite direction.)

This cosmic background radiation (CBR) provides a “frame of reference” for the universe at large, against which we can measure our motion. From that measured motion, we subtract (1.)  the motion of the Earth around the Sun and (2.) the motion of the Sun around the center of the Milky Way. The motion that’s left is the motion of our Galaxy through the universe!

And how fast is the Milky Way Galaxy moving? The speed turns out to be an astounding 1.3 million miles per hour. 

There is thought to be a large concentration of mass in the in the direction of Leo and Virgo, since all the galaxies near the Milky Way seem to be streaming in that direction. Astronomers believe there is a huge concentration of matter in this direction. Some people call it The Great Attractor.

Funny. That’s what people call me, too.

  “Indy Beagle.
The Great Attractor.“
          Aroo.