Stack, hear where I'm at and correct me if I'm wrong. The Himawari 8 satellite is so high in the sky that it can take an entire shot of the Eastern Hemisphere in one shot.
Correct.
And if the world is round, that's all you can ever ask a satellite to do.
I don't think so. As you could have a non-geostationary satellite, at that distance, orbiting around an entire sphere, and/or capturing the entire sphere revolving.
But if the Earth is flat, then is it not conceivable that the Himawari isn't high enough to capture both the Eastern and Western Hemispheres in one shot?
I don't understand what you're trying to say.
As for the "other side" we have a NOAA geostationary imaging satellite over the Western Hemisphere, the GOES 16. It too captures a full disc image just like Japan's Himawari 8, "
The default scan mode concurrently takes a full disk (Western Hemisphere) image every 15 minutes, an image of the Continental U.S. every five minutes, and two smaller, more detailed images of areas where storm activity is present, every 60 seconds (or one every 30 seconds). Alternatively, ABI can operate in full disk mode, continuously imaging the full disk every five minutes."
The GOES 16 maintains a similar altitude as the Himawari 8, 35,780.2 km (22,232.8 mi). From GOES 16:
So now we have both "sides", the Eastern & Western Hemispheres.