And I said 79 years, but it would be closer to 1 year, assuming the planet was in a similar orbit to ours around Alpha. Maybe that oscillation is minor relative to a yearly cycle. I don't know how much it would change the planet's orbit over time, though.
Not all that much.
At periapse, the stars are still 11 AU distance. The period would be 26 Earth years if stars stayed at the same distance, which they do not.
While the orbital period of Ab, in habitable zone, would be 1,3 Earth years.
So 20 orbits in notional circular orbit.
While Moon has about 13 orbits in 1 year.
Sun does perturb orbit of Moon. What happens?
The plane of Moon´s orbit changes rapidly, and so does the apside line.
But the inclination of Moon´s orbit to ecliptic remains small and constant, and the eccentricity varies periodically within small limits.
So, for the planets of Alpha Centauri, I should expect this kind of periodic, small amplitude perturbations.
Any actual computations of what the periods of those are?