Binary stars form due to gravitational interactions and the dynamics of stellar formation. During the collapse of a gas cloud, which forms stars, the cloud can fragment into multiple cores due to instabilities. Each core can form a star, and if these stars are close enough, their mutual gravitational attraction causes them to orbit each other, creating a binary star system.
The concept of gravitational equilibrium plays a role in the stable orbit of the binary stars. Each star's gravity pulls on the other, and they find a balance in their mutual orbits. This equilibrium prevents them from colliding or drifting apart, maintaining the binary system. However, the formation of binary stars is more about the initial conditions in the molecular cloud and the dynamics of their formation rather than just reaching gravitational equilibrium.
