The Moon's orbit is an ellipse, and the whole ellipse slowly rotates, taking eight years and ten months to come back round.

The Sun's pull tugs hardest on whichever side of the orbit is nearest it, and the result is that the line joining perigee to apogee sweeps forward. Newton could not make his own theory produce the observed rate and said so; the discrepancy was not resolved until Clairaut carried the calculation further in 1749.