You know you’re not supposed to capitalize sun, right? Well, guess what that means about capitalizing moon…
Either capitalize all of Southern Hemisphere (as the name of a region — fully half, as it happens — of the Earth) or don’t capitalize either word. Ditto for Northern (Hemisphere).
“This is because we’re on a spherical planet.” D’uh! What other kind is there? If you want to keep that sentence at all, change to This is because the Earth is a sphere.
Up is up; the explanation for why the moon looks different, depending on where on Earth the observer is located, is somehow both logical and nonsensical in how it’s expressed here, and that takes some doing! I recommend just deleting all that about standing with the head up, because of course your head is up when you’re standing, unless specifically stated otherwise.
The moon appears upside-down in the Southern Hemisphere, compared to how it looks in the Northern Hemisphere. This is because the Earth is spherical, so observers on each side of the planet are viewing the moon from opposite directions.
That’s better, at least.