What are the facts?
Alderaan is destroyed by the Death Star.
The incomplete (though claimed to be fully operational) Death Star II is shown firing its primary weapon in rapid succession in the battle over Endor in RotJ.
Obi-Wan dies the same day as the Death Star participates in the battle of Yavin, according to Vader.
The Death Star has recharged and is capable of destroying the moon on which the rebel base is located.
What else do we know or suspect?
- Right before Alderaan's destruction, Leia announces that the rebel base is on Dantooine.
- The empire sends scouts to Dantooine to determine if this is the case.
Governor Tarkin: You're far too trusting. Dantooine is too remote to make an effective demonstration - but don't worry; we will deal with your rebel friends soon enough.
Officer Cass: Our scout ships have reached Dantooine.
- Both Tarkin and the Rebels act as if they the moon is going to be destroyed when the Death Star is in range, and both have detailed schematics of the Death Star and should know its capabilities.
According to the movies, their is no plot inconsistencies here. Whether or not it takes time to recharge the primary weapon, and how long after Alderaan is destroyed before Luke arrives on the Death Star is inconsequential.
Now taking in the single source of now worthless expanded universe cannon, should it take the Death Star 24 hours to recharge the weapon to destroy a planet, then logically it is over 24 hours between the destruction of Alderaan and the battle of Yavin. This time line also matches up with other EU works which give the destruction of Alderaan and the battle of Yavin almost a 2 week window in which they happened.