Very New to Solar

Motor nameplate amperage ratings are genrally high. They are for the most part what is known as locked rotor amperages. But for the purpose of calculating a PV system for a specific load such as the motor you describe, it would not be a bad idea to use it as is, because of all the potential power losses intrinsic to a PV/battery/inverter power system and of course, the weather. So...

120 vac multiplied by 12 amps equals 1,440 watts.
1,440 watts times 24 hours = 34,560 watt hours or 35 kWh.
Since PV output will last the equivalent of about 6 hours of the day, that leaves 18 hours of reserved time for another power source. But to offset the total energy needed with a grid interactive PV system one still needs to use the entire 35 kWh load in this example. So...

35 kWh divided by 6 equals a 6,000 watt or 6 kW PV array, not mention a grid interactive inverter that can send this power back onto the grid, preferably through a bi-directional meter. That will depend largely on your local electric power supplier or EPP.

6 kW PV array times $5.00 a watt equals $30,000.00, chances are your paying about $0.09 a kWh to your EPP? If so that same 35 kWh is costing you about $600.00 for 6 months unless it runs 12 months a year. So think about that. With that PV array, the other half of the year it will be "earning" almost $600.00 in savings. In other words in the summer the pool doesn't cost you anything and during the winter your earning money, in a manner of speaking.

All in all your looking at a payback period of about 25 years or more.

Is it worth while? All I can say to that is, not for me it wouldn't be. I live off grid.

Thanks for all the help.