You can work that out easily - you won't get the required 2,160 frames from one battery.
Sony's ACV-Q900AM AC power adaptor with twin charger is well worth the money. I have never regretted buying it. It intelligently charges and maintains batteries well, doing two batteries, in sequence - and also powers the camera.
To do what you want, get Sony's charger/DC unit. It is discontinued but can be tracked down. You will not regret it. Try: http://www.amazon.com/Sony-AC-VQ900AM-A ... B000DZKR1E