So what is the draw when the compressor is running and what percentage of the day is the compressor running.
Until we have a fair estimate for that, any numbers being thrown around are wild guesses that may or may not work.
Let's run some sample numbers and you can update based on your real life numbers:
- Assume 3amps at 120v when the compressor is running
- Assume 50% duty cycle
3amps * 120v = 360watts
50% duty cycle means 360w for 12hours or 4320w-hr which equals 360 amp-hr (at 12v).
Let's call it 5000w-hr as no system is 100% efficient.
Solar panels don't put out their rated output all the time. On average figure on about 4hr at the rated output since early and late day, it's a tiny fraction of the rating and you get nothing at night.
5000w-hr divided by 4hr = 1250w of solar panels needed.
Assuming roughly half the power is used at night, you need about 360amp-hr of battery storage since you can only use about 50% of a lead acid batteries rated power without damaging it (lithium are a different game but also more complicated and expensive).
Also make sure you have an inverter capable of starting the compressor. A 400w inverter will likely fail as the startup amperage is often 3 times what the continuous amperage is, so that 360w can quickly jump to over 1000w.
Another consideration what other 12v draws will be on. You may have some minor draws, you don't notice because by themselves they aren't enough to run down the batteries after a couple days but when added to a big draw, they could cause problems.
Now update with your real life numbers but as you can see, it's not a trivial project and if you just randomly add solar panels, they may not do what you want.