After some puzzling, Bradley finally arrived at the correct solution. The velocity of light (300,000 km/sec) is finite; the velocity of the earth around the sun is 30 km/sec, or 1/10,000 of the velocity of light. This causes the direction to stars to be displaced in much the same way as rain appears to slant in on a moving observer. The displacement is 1/10,000 of a radian or 20 arcseconds in the direction of the earth's velocity, precisely what was observed.
This phenomenon, called the aberration of starlight, was announced by Bradley in 1729. Although not the long-sought annual parallax, it did in fact prove the Copernican hypothesis by establishing that the earth was in fact moving (although few doubters remained in 1729). Furthermore, annual aberration of starlight represents a phenomenon that must be removed to get accurate stellar directions -- and it is a large effect (20 arc seconds).
Furthermore, Bradley stated in his paper that after correction for the effects of aberration he could have detected an annual parallax of as little as one arcsecond but saw none, and that therefore the stars he studied must be much farther away than anyone had conceived. "