New MacBook Battery for a Mid-2009 MC240LL/A Model

I am interested in purchasing a new battery for my white macbook. This was my first laptop and I killed the battery by leaving it plugged in ALL the time (darn Sims 3..didn't want it to shut off on me mid game!) so it can barely hold a charge and I need it for a long airplane flight coming up. I again, have a MC240LL/A model, and on my battery itself says A1185..so it is a removable one. (Although on the box from when I purchased my macbook says Model No: A1181 so I'm not entirely sure what that means.) Anyway, I do not want to get a battery through apple as I am a poor college student, and am looking at batteries from ebay. I am also clueless when it comes to computers and was planning on purchasing this battery...

http://www.ebay.com/itm/6-Cell-Laptop-Battery-for-Apple-MacBook-13-13-3-A1181-A1 185-MA561-MA566-White-/310405753618?pt=Laptop_Batteries&hash=item48459feb12#ht_3 031wt_1176

But now after reading further I don't see my macbook model listed so I'm assuming that this battery wont work on my computer then? Even though it is the same battery model (A1185)? I need help...because I can't find any replacement batterys for my computer model, but most are either A1185 or A1181..the same as my laptops battery.

Help! My plane leaves in 3 weeks!

-Erin