Similarities:

(i) In an atom, the protons and neutrons are tightly packed in the nucleus and electrons revolve around it in fixed orbits.

(ii) In the solar system, the Sun is in the centre and the planets revolve around it in fixed orbits.

Differences:

(i) In an atom, the electrons can jump from one orbit to another.

(ii) In the solar system, the planets remain in their orbits. They cannot change their orbits.