Learn Spanish (Latin America): Los anillos de ese planeta son muy hermosos.

Even though planeta ends in -a, it is actually a masculine noun (el planeta). Because it is masculine, you must use the masculine word for "that," which is ese. Many Spanish words ending in -ta or -ma that come from Greek are masculine, like el problema and el mapa.

Why does the sentence say los anillos de ese planeta instead of using an apostrophe 's?

Spanish doesn't use an apostrophe 's to show that something belongs to someone or something. Instead, you always use the word de (of). You have to flip the English structure and say "the rings of that planet" (los anillos de ese planeta).

Why do we use son instead of están for "are" in this sentence?

We use son (from the verb ser) because being beautiful is seen as a fundamental, permanent characteristic of these rings. You would use estar for temporary states or conditions, but here we are describing an inherent trait.

Could I use aquel planeta instead of ese planeta?

Yes! Ese means "that" (often something relatively close to the listener), while aquel means "that one way over there" (far from both the speaker and listener). Since planets are far out in space, aquel planeta would sound very natural if you wanted to emphasize the distance.