The factor that prevents the planets in our solar system from floating away is the Sun's gravitational pull. Each planet, including Earth, is held in its orbit by the force of the Sun's gravity. The Sun, being the most massive object in the Solar System, exerts a strong gravitational force on all the planets, keeping them in their respective orbits around it. The mutual gravitational attractions among the planets themselves are considerably weaker and although they do affect their orbits slightly (through perturbations), it is the Sun's gravity that is the dominant force maintaing the structure of the Solar System.
