What keeps the solar system in balance?
As a physicist I would say Gravitational Force.
The Solar System is quite a complicated system of bodies that you can immagine as a system of particles in movement around a very massive body, the Sun.
All these movements are governed by Gravitational Force.
The gravitational force between two objects of mass
So basically the Sun keeps all the objects around it bound through this force and each smaller object keeps the moons or asteroinds around them bound as well.
Every now and then you have the interference, in this carefully ordered dance, of external actions due to the passing of comets or external occurences (death of a star or other) but always the "glue" that at the end prevails is Gravitational Force.