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http://www.wired.com/geekdad/2009/09/top-10-unanswered-questions-in-geeky-movies/
I didn't think Han had even bothered to attempt to pay off Jabba's debts though
the Massassi Temple on Yavin IV was an old jedi temple around this time period? bah I don't remember... I used to be big into Young Jedi Knights >.>)
When the rebels are evacuating Hoth, Han specifically says he's not going to the rendevous point because he's got debts to pay off. He wasn't planning to take Leia along but was forced too because the Falcon would be the last ship to leave before the defense cannons were shut down by the AT-AT assault on the power generators.
Even if it did hit the core accurately, the sudden lack of gravity from Yavin means all it's moons would start drifting in random directions. That is of course, provided that the explosion from Yavin didn't send the moons flying in all directions or cover them in the remnant gasses that used to make up Yavin.
I'm willing to bet it can't fire it's primary weapon in rapid succession without having to recharge. Yes, I know the second Death Star could, but they could have changed any number of on board systems for rapid fire.