Although the observed orbit is a long narrow ellipse, careful observations of the apparent relative positions of the two stars means that we can calculate the apparent orbit. Using some mathematics of various standard orbital models, we can determine the shape and size of the Alpha Centauri’s true orbit. (See Figure 3-1 above.)
The size of the ellipse of the orbit is measured by the eccentricity e1.00 This is slightly different than the eccentricity e given with the normal orbital elements - mainly due the orientational transformation. P and A, are the points of periastron and apastron, respectively, which for the α Centauri system can range between 11.9 A.U ( m.km.) and 34.9 AU (m.km.). If you could look down on the orbit like this from the distance between α Centauri and the Sun, the stars would orbit 8.5″ at closest approach and 26.5″ when furthest away - averaging some 17.5″. Periastron last occurred in July 1955 and will do so again in May 2035. Apastron similarly occurred in June 2004 and will again in April 2115. These date are space apart by the orbital period of 79.92 years. The widest positions observed in the apparent orbit do not correspond with the maximum distance between the stars because the orientation and the direction of the line between periastron and apastron lies askew than the observer.