The faster the disk rotates, the broader the 21-cm emission line will be. Infrared is used to lessen the effect of the dust in our galaxy and in the other spiral galaxy. The luminosity of the galaxy is found from the width of the 21-cm emission line and the distance is then derived using the apparent brightness and the inverse square law. Edwin Hubble and Milton Humason found distances to the spiral nebulae. This relation is called the Hubble Law and the Hubble constant is the slope of the line.
More distant galaxy has greater redshift.
It is easy to find the recession speeds of galaxies from their redshifts. The Hubble Law shows that there is actually not a violation of the Copernican principle. Every other galaxy or galaxy cluster is moving away from everyone else. Every galaxy would see the same Hubble Law. For now, use the figure above to see how a uniform expansion gives us the Hubble Law.