Parmenter,
It can be done but YOU MUST KNOW how much power the fridge PLUS all the other loads that you expect to run will use.
I think one of the very first things you should do is purchase and install a SOC meter and get it going immediately. There are other ways to estimate real power useage but this thing will tell you without all the estimates. If the fridge, your 120Vac unit is only on 120V when at the dock then another purchase might be a KILL A WATT meter.
P3 International P4400 Kill A Watt Electricity Usage Monitor - Amazon.com
Then you will have a good reading and using the results of both as required you can come up with a plan.
If you are currently running the fridge from an inverter run from the batteries then the SOC will give you what you need. If you run the fridge separately then both may be required and then do the calculations to figure all out.
A story I've told before but here goes again. A friend, a retired EE, set up his boat to do without a gen. He does carry a 2K watt Honda for emergencies but seldom uses it.
3X 135 w solar panels run his boat and by 14:00 hr on a sunny summer day here in B.C. Canada his batteries are recharged. His panels are flat mounted with no provision for a tilt to follow the sun which in most cases at anchor is useless.
He has a 12vdc full size single wide combo fridge/freezer fridge and a 12vdc Waeco chest freezer. Both use the Danfoss compressor, the BD35 which when running draw about 4.0 - 4.2A. I don't know what the duty cycle is but I would guess based on my Danfoss , in hot weather about 60%.
He uses 6 X golf cart batteries for a bank of about 660A/Hrs. They have all the other stuff aboard , water pumps, lighting, radio, and whatever else they need. The system keeps up as long as they get the sun each day.
I BELIEVE they can actually go 2 days if one is cloudy because of course the panels still pick up enough to get through to the third day. After that they may need to run the boat or the gen. On a cloudy day, not rainy, he still gets 20-40% charge, I believe, but it is down, depending on cloud density.
I should note that he did things a bit differently from many. His systems panels are wired in series so the panel set sends a nominal 36volts to the controller. He bought the controller of course to take that into account + it self adjusts for voltage.
Read his thread
Albin Owners Group • View topic - Solar Panels
It's on the Albin forums. You should not need to sign up just to read the post.
Your useage may be different so YOU need to find out how much power the fridge uses for real, allow for ~ 90% only inverter efficiency, and how much other power the rest of the equipment you need to run uses. The SOC meter and if needed the K a W meter. He did this after the first years use so he had a good idea what was going on + he had that SOC meter as a big help.
Then decide how many days you want to be able or need to go without running the boat or a gen. You must take into account those cloudy days. That can be done by adding another panel to whatever you think is needed, extra battery capacity or both. Both would be better of course but I realize cost is also a factor. Initially batts. I think if you have the space and purchase a controller that can take extra panels over the initial purchase. Of course you must have the space for both batts and panels.
He used 135W panels but there is no reason a different capacity panel could not do the same. He had the area to cover atop his Bimini cover and the 135 were perfect and covered all available space. If you have more space then even better. You can go longer if the SYSTEM is thought out and put together correctly.
Your specific fridge will have a huge amount to do with this. Poor insulation, typically house fridges are not as electrically efficient ,total watts used, as dedicated boat fridges, poor ventiation to get rid of heat where the fridge is mounted but it can be done.
For the system overall though one of the best things to do is reduce electrical load. LED lighting will help a lot. A small muffin type fan to evacuate the fridge cavity cast off heat. Set it up so it runs only when the fridge runs. If the fridge can't get rid of that heat it can't cool the interior and it will run and run and run.