The distance between two stars in a binary system is primarily determined by their masses and their initial conditions during formation. The mass of the stars is indeed a crucial factor in determining the possible separation between them. Additionally, the conservation of angular momentum during the formation of a binary system also plays a role.
When a binary star system forms, it starts from a large rotating cloud of gas and dust. As the cloud collapses under its gravity, it begins to spin faster due to the conservation of angular momentum. The collapsing cloud eventually fragments into two separate protostars, each with its own mass. The specific details of this process can be quite complex and depend on the initial conditions and dynamics of the system.
There is no single equation that can precisely determine the separation between the stars in a binary system because it depends on various factors and the specific history of each system. However, there are theoretical models and numerical simulations that can provide insights into the range of possible separations for binary star systems based on their masses and initial conditions.
Generally, more massive stars tend to have wider separations between them in binary systems. Smaller, lower-mass stars are more likely to have closer orbits. However, there is a wide range of possible configurations and separations, and it is influenced by other factors such as stellar interactions, orbital dynamics, and external influences.
It's important to note that the study of binary star systems is an active area of research, and our understanding is continually advancing as observations and simulations improve.