What is the shape of the solar system and how is it maintained?
Circular and flat.
Newtonian physics explains this phenomena vis-à-vis gravity and the laws of motion. The sun's gravitational field reaches out to the furthest point of the solar system. Every object in the solar system is in motion and by the laws of physics, those object want to move in a straight line. The sun's gravity in turn pulls them out of that straight line and in turn sets up the object's (planet, asteroid, etc) orbit.