At the risk of sounding naive, can't we calculate A Centauri's pull or that of Sirius?
But, binary mechanics are not so easily explained. Different mathematicians develop different models.
Most are based around Kepler's Third Law. Calculate the mass. Force is proportional to mass.
Sirius is in a Binary System, so the mechanics would need to address that factor. Alpha Centauri is in a three star system. Even more difficult.
My father knew the workings of the internal combustion engine. I'm just happy to drive the car.