We can mention some of them; like the size, as we can see there is a big difference between their sizes; the solar system is that huge, while the atom is that very tiny system! Also the attraction force acting on the rotating bodies, like the planets in the solar system and the electrons in the atom, in which the planets are attracted to the sun due to the  gravitational forces, while the electrons are attracted to the nucleus due to the electrical forces.

    Both are considered as a component of a bigger state; as the solar system, which is too big, is a small piece from the universe, while the atoms are a very tiny pieces from the molecules, which are in turn pieces from the substances and matters. And the difference here is that the atoms compose the solar system, while the solar system doesn't compose the atom! 

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