Stability of Macroscopic Binary Systems

The Darwin instability effect in the binary systems(di-planets, di-stars, and di-galaxies) is analyzed within the model based on the Regge-like laws. All possible binary stars are found satisfying the Darwin instability condition that requires to search for other mechanism triggering the merger of the contact binary objects. New analytical formulas are obtained for the orbital rotation period and the relative distance between components of the binary system. The decreasing and increasing periods as functions of mass asymmetry are related, respectively, with the non-overlapping and overlapping stage of the binary object evolution.