Why there is an asteroid belt between Mars and Jupiter, and not a planet?
In 1596, Johannes Kepler predicted, “Between Mars and Jupiter, I place a planet” in his book, Mysterium Cosmographicum. Later, the astronomer Johann Daniel Titius of Wittenberg declared in a footnote, “But should the Lord Architect have left that space empty? Not at all”. This conjecture was based on one simple fact that there was too large a gap between the orbits of Mars and Jupiter.
Let us start from the beginning the formation and evolution of Solar System began 4.6 billion years ago after the gravitational collapse of a solar nebula (a cloud of interstellar dust and gas), which formed a rotating disc of objects. Most of the collapsing matter collected in the center and formed the Sun. Rest formed the planets, moons etcetera. During the early years of Solar System, roughly first few million years, an accretion process of sticky collisions resulted in the assembly of particles which gradually attained bigger sizes and started attracting matter on their own, forming planetesimals (Planetesimals are smaller predecessors of Protoplanets). This led to the formation of planets.
Planetesimals present between Mars and Jupiter were muddled up due to the Jupiter’s strong gravity and thus refrained from forming a planet and continued to orbit the Sun as before. Shattering of planetesimals tended to dominate over accretion. Asteroids orbits continue to be perturbed whenever their period of revolution about the Sun forms an orbital resonance with Jupiter, gaining relative velocities to each other.
Half of the belt’s mass is contained in the four largest asteroids, Ceres, Vesta, Pallas, and Hygiea. The belt is spread over a large volume, which is mostly empty. The total number of asteroids present in the belt is in millions.
Formation of other types of rings
All giants planets of Solar System have rings. When an asteroid, comet or any large object pass too close to the planet it is torn apart by the planet’s gravity. There is a point around the planets which is called the Roche limit. In the celestial mechanism, the Roche limit or radius is the distance in which a celestial body is held together only by its own gravity and will disintegrate due to a second celestial body’s tidal forces (differential gravitational forces exerted by one body over other) exceeding first body’s gravitational self-attraction.
When an asteroid gets close to the Roche radius, it gets deformed by the tidal forces. Within the limit, the asteroid’s own gravity can no longer withstand the tidal forces and the body disintegrates. Particles closer to planet move more quickly than particles further away. The varying orbital speed eventually causes it to forms a ring. For the maths behind calculating this limit, see this:-