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i see this and wonder the same! a few weeks ago the moon was humungous and moved so fast rising! i couldn’t stop looking at it. it’s so mysterious.
Because the Moon is not right above the horizon but upper and a bit closest to the zenith , and the sun is still above the horizon, as we can see on 0:22 to 0:25. For the Moon to be “full” to our point of view, **in the globe mode**l, it must be radically opposite to the Sun; it means, the angle Moon-Observer-Sun, where the observer is the vertex, must be close to 180°. The farthest the angle is from 180°, the less illuminated area you’ll see from the Moon.
There are cases which are truly inexplicable, though. The *”gibbous moon at morning” (I’ve seen it myself)*, where both “bodies” (Sun and Moon) are behind the zenith, or both bodies are beyond it, exists and are impossible on a globe model (*Moon could not be gibbous on that condition, no more than half Moon should be illuminated for that positions; except if the Sun is about the size of Moon and about the same distance from us than Moon, it means: only if Sun is “inside” the system Earth-Moon, which already breaks all the globe model*). Those discard the globe model, but I think this is not one of these.