Watch how you use a 240V inverter in a dripping wet paddock at 3 in the morning. Even with a high quality isolation transformer, I'd be rather nervous.
I use two laptops, one to drive the scope and autoguider and work the camera shutter, and one to do real time image analysis. Each uses a 40 AH deep cycle gel battery and one of those JayCar 12V-to-anything converters that Photon mentioned. One of the batteries also works the mount, and the other works the dew heater, but the laptops are the main guzzlers.
The 40 AH battery will drop from 13 volts to 12.5 over about 3 hours. Although its very nonlinear and temperature dependent, at laptop load, a 0.5 volt drop would represent roughly 60% charge still left. Don't like taking them flatter than 50% (about 12 volts) because of (a) margin for error, and (b) sulphation. You can wreck an 18 AH battery pretty quickly by repeatedly flattening it. You can get a lot more out of your battery if you turn the screen brightness to minimum, and actually switch the screen off when you're not looking at it.
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