You can't put a MacBook Pro battery in there, however you can upgrade it to the battery from the later unibody MacBook, you can get the part here, and the step-by-step installation guide is here.

I have replied to other questions with the same answer I am giving here. As apple releases new MacBooks the battery wattage is generally the same. The part that allows the computer to get more batter life is the fact that as Apple progresses they use CPUs and GPUs, along with many other components to allow the system to consume less power. If you had 2 light bulbs, but one use 5w per hour, and the other used 10w per hour, no matter which light you attach a battery to, the 10w light will always use more. The battery isn't the only factor that affects battery life. I hope that I am understood here. Putting a 2011 MacBook Pro battery into a 2010 MacBook Pro will not change the battery life of the 2010 model, only because that model has more power hungry chips.

Hope this helps.

What about a mid 2009 unibody macbook pro ?

Can i swap my old battery (~6 hours) with a new (~10 hours) battery ?

Thanks!