solar system is an autocratic state rather than a democracy

An example of an analogy used in popular science writing:

"It is of course, a pity that we cannot see the mysterious galactic centre around which our sun is spinning, along with billions of other stars. But in a way we know how it must look from the observations of other stellar systems of galaxies scattered through space far beyond the outermost limit of our Milky Way. It is not some supergiant star[*] keeping in subordination all the other members of the stellar system, as the sun reigns over the family of planets. The study of the central parts of other galaxies…indicates that they also consist of large multitudes of stars with the only difference that here the stars are crowded much more densely than in the outlying parts to which our sun belongs. If we think of the planetary system as an autocratic state where the Sun rules the planets, the Galaxy of stars may be likened to a kind of democracy in which some members occupy influential central places while the others have to be satisfied with more humble positions on the outskirts of their society."

…

"As we have already mentioned above, our Galaxy is not the only isolated society of stars floating about in the vast spaces of the universe."

[Capitalisation as in original]

George Gamow (1961) One, Two, Three…Infinity. Facts and speculations of science, Revised Edition, Dover Publications, Inc., New York.

This is an imaginative analogy, even if we now know it is unfounded. (* It is now considered that at the centre of the Milky Way galaxy there is a supergiant star, Sagittarius A* {a strong radio source not discovered till the 1970s} which is a supermassive black hole with a mass over four million times larger than our sun, around which other stars orbit.)

Read about analogy in science

Read examples of scientific analogies

Many examples of science analogies are listed in 'Creative comparisons: Making science familiar through language. An illustrative catalogue of figurative comparisons and analogies for science concepts'. Free Download.

The Sun ruling over the planets may be seen as metaphor, and the phrase and "the sun reigns over the family of planets" as something of a mixed metaphor.