In the battle of Yavin, the Empire wants to destroy a moon that is hidden behind the planet Yavin. They circle around the planet because the moon is hidden. Again: They are on a space station that can destroy planets! Planets! Like the one that is obstructing a clear shot on the rebel base (i.e. the moon).

The only reason I see for them not to simply blow up Yavin is that it may take too long for the Death Star to be able to shoot again. So, is there any information on how long it would take?

As a side note, I have an alternate theory of why they didn't destroy Yavin, maybe those guys' union forbade the Empire to unnecessarily expose them to radiation?

(Source: Irregular Webcomic #512)