Modern astronomers now know that the celestial north pole was exactly aligned between Kochab and Mizar only in the year 2, 467 BC.

BBC: Pyramids lined up with the stars

And because the error in the Kochab-Mizar alignment can be readily calculated for any date, the error in each pyramid's orientation corresponds to a period of several years.

BBC: Pyramids lined up with the stars

Writing in the journal Nature, Kate Spence shows that the orientation errors of earlier and later pyramids faithfully track the slow drift of Kochab and Mizar with respect to true north.

BBC: Pyramids lined up with the stars