How many watts from solar panels do I need to establish to produce enough power to operate an appliance on a 15amp circuit?

The max for a 15 amp circuit is 15x.80x120=1440 watts. If the solar panels are rated at a low DC voltage, you will need to divide by the efficiency of the inverter. If the appliance draws less than 12 amps, you won't need as high of a rating. Interesting project. See http://www.otherpower.com/otherpower_solar_used.html