What are the facts?

1. Alderaan is destroyed by the Deathstar. 
2. The 2nd incomplete(though claimed to be fully operational) Death Star is shown firing its primary weapon in rapid succession in the battle over Endor in RoTJ.
3. Obi-Won dies the same day as the Deathstar participates in the battle of Yarvin, according to Vader.
5. The Deathstar has recharged and is capable of destroying the moon on which the rebel base is located. 


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 Deathstar 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 Yarvin. This time line also matches up with other EU works which give the destruction of Alderaan and the battle of Yarvin almost a 2 week window in which they happened.