Analogy between Bohr
Atom and Planetary Orbits

This similarity between a planetary model and the Bohr Model of the atom ultimately arises because the attractive gravitational force in a solar system and the attractive Coulomb (electrical) force between the positively charged nucleus and the negatively charged electrons in an atom are mathematically of the same form.

Although the form is the same, the intrinsic strength of the Coulomb interaction is much larger than that of the gravitational interaction; in addition, there are positive and negative electrical charges so the Coulomb interaction can be either attractive or repulsive, but gravitation is always attractive in our present Universe.