Binary star system exist because they are revolving around a common center, and its outwards momentum is holding them in place.

The binary systems are formed from splitting of one star or in the formation of the star itself. In your atom model, chemical bonds like bringing together two atoms and they form stable bonds is not possible. If you say this gravitational atom model have more close relation with real atom model than differences, then I could also say two magnets in space which spins around each other due to magnetic force and the centrifugal force(which came from inertia at initial conditions) balancing is also analogous to an atom. You have to perfectly set the velocites and magnetic moments but you will get something like a binary system. I would conclude there are bigher differences than simple structural similiarities to a (wrong) model of atom