The answer will depend heavily on the efficiency of your inverter. Looking at the DirecTV receivers, the most power drain I see is around 20 watts. But it burns almost as much when it is off. I suspect your TV draws more than that, so it is probably that adding the satellite receiver will have a negligible effect on your total power budget. My H-24 is specified to draw around 12 watts, so at 12 volts that is one amp, but it will be more depending on the efficiency of your inverter. Even if the inverter is only 50% efficient, that would be 2 amps for 2 hours or only about 4 amp-hours per day. Your 200 watt array should be capable of delivering 50-60 amp hours on a good day.
Full disclosure - back of the envelope estimates, I have no direct experience with satellite on solar.
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