The long-life battery for your laptop has part number PA3535U-1BRS. These batteries will all replace it:
http://www.pcbattery....ery_desc.php?id=83316
The 5200mAh version will probably give slightly longer usage time than the original battery which, I believe, was only 4000mAh and designed for 2½ hours maximum use.
The 6600mAh battery should add at least 50% extra to the time which you can use your laptop for. The 8800mAh version should give you at least double the charge time.
Chris