OK I will just answer and let you be the judge. It depends on your location but using national averages of solar insolation about 30 to 40 minutes per day. In Summer up to 45 minutes, and about 20 minutes in winter. If you live in Phoenix a little longer, in Seattle a whole lot less.

One warning here if you discharge your battery down to 11 volts below 0% capacity, it will only last a few cycles (about a month before you destroy it). You should never go below 50% capacity of 12.2 volts. Also note if you do go to 0% capacity it will take your solar panels 15 days to recharge them, and 8 days if you go down to 50% capacity. Your battery is way to large for your solar panels.

and your loads are too large for your PV array. The easy way to size what your needs are:

1) total up your loads into KWh. 200W tv for 3 hrs = 600wh [ .6kwh ]

2) what is the number of good charging hours for your location - usually 10am - 3pm, only 4 or 5 hours. (I don't know what your location is, I don't know how sunking got 30-40 minutes)

3) Take your load kwh and multiply by 2 [1.2 KWh x 2 =2.4kwh ]

4) Divide your line 3 number, by hours of usable sun [ 2.4 /4 =0.6 KW ] This is the size of your required array. (600W in this case, .6KW)

5) Your battery should be 10x the charge current your array puts out, depending on your chosen voltage. Say 12.5V @ 600W = 48A, so you need a 480ah battery. (or several batteries, since most big box store batteries are about 90ah capacity.)

You lost me on line 3....your example load was .6 kwh x 2 = 1.2 kwh not 2.4?
1.2/6.5 (sun 10:00 am to 4:30 pm)= .18 kw or 180 w array? Is that correct?

I just used the national yearly average of 4.2 Hours

K2yi, let's run an example using a little of the info you gave us which is not much.

Only thing we know is you have a load of 75 watts + 50 watts = 125 watts operated for an unknown amount in time in an unknown location.

So first we need to know how many watt hours you will use in a day. I will assume you will run your TV and SATV receiver 4 hours per day, 125 watts x 4 hours = 500 wh or .5 Kwh. For a battery system the overall efficiency is 50% so we need to adjust your daily load by multiplying by 2, so 2 x 500 wh = 1000 wh or 1 Kwh per day minimum is what the solar panels will need to generate each day.

To find the solar panel wattage we need the location to look up your winter insolation. You did not give that information, so I will use Kansas City which has a winter insolation of 1.9 Hours. So the solar panel wattage needed is 1000 wh / 1.9 h = 526 watts.

For the battery size you first need to know the battery voltage which we know is 12 volts. So to determine the battery Amp Hour capacity [5 x 1000 wh]/ 12 volts = 416 AH

So if you live in an area like KCY and want to wath TV for 4 hours each day you would need a 500 watt solar panel and a 400 AH battery. With what you have now you are not even in the ball park. With your solar panel wattage you may get 15 to 30 minutes in summer, and just a few minutes in winter depending on where you live. Your 125 AH battery is you had the panel wattage to support it would give you about 1 hours and 45 minute per day.

But the problem is nothing was designed to do what you want it to do, so everything is a mismatch. The only thing you have that you can use is just the battery and inverter, and you need 2 to 3 more batteries with the above example. I did not do the math for the charge controller, but I can tell you the one you have is useless.

So if you really want to know what takes either tell us what we need to know or DIY

Just an example I wasn't trying to actually DO a site caculation

Well, I live 50 miles north of Albany, NY, and yesterday, I watched just the TV on solar for 4 hours, in full sun, and ended with 12.2 volts on the battery after I switched back to comm power....so it's working somewhat, but I do appreciate the math...
Thanks

OK you used 50% of your battery capacity. It will take several days for you to recover back to 100% as long as you do not watch TV. Come winter a week or more.

Please be patient, I am trying to absorb all this....
Referencing 50% of your battery capacity and 100% of your battery capacity, are we talking volts or amps?
Is 12 vdc 50% capacity and 14 vdc 100% capacity? or is it dependent on the amperage reserve in the battery at a specific voltage? And that said, what is the maximum voltage a 12 vdc battery will/should charge to? And I'm assuming the controller should sense an overcharge scenario and disallow it, if the controller is worth it's weight....
Also, I'm assuming that the battery(s) should not drop below 12 vdc, assuming dropping below that level may harm the battery?
Sorry for all the dumb questions....these Q's just come into my mind, and I have to ask....
By the way, Sunking, thanks for all the help...