Until its final revision by Longomontanus in 1600, Tycho's lunar theory was fundamentally Copernican: Tycho (or Longomontanus) had been able to represent the Variation by simply putting an extra circle, AB in Figure A.3.1, into the center of Copernicus's theory. By making the center of the deferent (B) revolve around the earth (A) at twice the synodic velocity of the moon, he produced displacements that mounted to ±45' 20′ when the moon was in the octants and yet vanished in syzygy and quadrature. But the Variation was not the only extra circle grafted onto the traditional theory. The center of the large epicycle also moved on a new circle, CD, producing a periodic displacement up to ±11'.

This correction appears without a prior hint of any kind in either Tycho's log notes or his letters and would therefore be unknown if Tycho had not allowed Jöstel to “prepublish” his theory in 1599. What it represented, although somewhat imperfectly, was a phenomenon called the annual equation. When it finally attained recognition as a legitimate lunar phenomenon and was explained by Newton a hundred years later, it was seen as an annual variation of the speed of the moon in its orbit, owing to the annual fluctuation of the sun's distance from (and hence influence on) the earth–moon system.

That Tycho also associated the phenomenon with the sun in some sense is obvious from the fact that his period for it was a year.