Learn Turkish: Gökyüzü umutsuz, bu yağmurun dineceği yok. - The sky is hopeless; this rain has no intention of stopping.

This uses the core structure of this lesson: Verb + -(y)AcAk (future participle) + possessive + yok. Literally, it means 'its future-stopping does not exist.' In Turkish, this pattern is frequently used to express that someone or something shows absolutely no sign, intention, or likelihood of doing a particular action.

Why is yağmur in the genitive case (yağmurun)?

It is part of a genitive-possessive phrase. The core phrase is yağmurun dineceği (the rain's future-stopping). Because the nominalized verb dinecek takes the third-person possessive suffix -i (which softens the k to ğ), the subject performing the action (yağmur) must take the genitive suffix -un to link them together.

Could I use the verb durmak instead of dinmek here?

You could say duracağı yok, and people would understand you, but dinmek is much more natural here. While durmak means a physical halt like a car or a person stopping, dinmek means to calm down, subside, or cease. It is the specific verb used for things like rain, wind, pain, or crying.

Is it common to use umutsuz (hopeless) for inanimate things like the sky?