Quoting:
I've always wanted to know why. At the end of the movie when the death star was waiting to clear that planet in order to blow up the rebel base...why did'nt they just blow the planet up to get it out of the way, and then there would have been a clear shot...no waiting. Because it cost them in the end. :o
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Here's my theory...

The Death Star only has one shot per time frame.  If it wastes that shot on planet #1, it will have to recharge for a while before it can blast planet #2.  So that's why they cleared the planet.

Wasn't the other thing a star, actually?

Quoting:
The object blocking the Death Star was a gas giant named Yavin, several times the size of the Death Star.  I believe the Rebel base was on a small moon called Yavin-4.
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Thanks Secret, eh-hehehe...hey, I thought eet was Alderaan?

Quoting:
Because the budget for special effects had been exhausted ?  ;)
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Or because the script told them to go around? ;)

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Thanks Secret, eh-hehehe...hey, I thought eet was Alderaan?
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Morocco Mole, my old friend, we meet again.  :)  Actually, Alderaan was Princess Leia's home planet.  It was the first (and only) planet blown up by the Death Star.