It's quite clear that that the two systems have the same behavior, and We can remember what Rutherford said when he wanted to describe the atom, he resembled it by the solar system, the nucleus is the sun and the electrons are the planets.

   But let's have a closer look towards the systems. Both systems have Orbits, and the rotating bodies in each orbit have different energy.

   Although analogy is clear in the seen behavior but it's also clear in the applied formulas; as the gravitation force between any two huge bodies like in the case of the planets and sun is given by F=G Mm/r2, while the electrostatic force given from coulomb's law which keeps the electrons in their orbits F=k Qq/r2

   So we can see clearly that the two formulas are similar to each other. The force in the two cases is equal to the multiplication of a constant and two factors of the formula ( Masses in case of gravitation and charges in case of coulomb's law) divided by the square of the distance between the factors.

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