Gravitation is one of the central forces playing an important role in formation of natural systems like galaxies and planets. Gravitational forces between particles of a gaseous cloud transform the cloud into spherical shells and disks of higher density during gravitational contraction. The density can reach that of a solid body. The theoretical model was tested to model the formation of a spiral galaxy and Saturn. The formations of a spiral galaxy and Saturn and its disk are simulated using a novel N-body self-gravitational model. It is demonstrated that the formation of the spirals of the galaxy and disk of the planet is the result of gravitational contraction of a slowly rotated particle cloud that has a shape of slightly deformed sphere for Saturn and ellipsoid for the spiral galaxy. For Saturn, the sphere was flattened by a coefficient of 0.8 along the axis of rotation. During the gravitational contraction, the major part of the cloud transformed into a planet and a minor part transformed into a disk. The thin structured disk is a result of the electromagnetic interaction in which the magnetic forces acting on charged particles of the cloud originate from the core of the planet.