So on the first day of fall and spring, night and day are 12 hours each everywhere on earth.
But does the sun take the same path through the sky if the observer is on the North Pole vs the Equator?
Also, is there any day / location where the sun rises directly in the east, goes directly overhead, and then sets directly in the west?
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> But does the sun take the same path through the sky if the observer is on the North Pole vs the Equator?
No: if you’re on the equator the sun will be directly overhead, if you’re at the north pole the sun will always be in the southern part of the sky.
> Also, is there any day / location where the sun rises directly in the east, goes directly overhead, and then sets directly in the west?
The closest you could get to this is being exactly on the equator during an equinox. It’s still not perfect, the tilt of the earth makes what you’re describing impossible, but it’s pretty close.
Not even remotely. The sun should follow an almost exactly the same path per latitude, but the path is different at every latitude. At the equator, the sun goes directly overhead on the equinox. The further from the equator you go, the lower the angle the sun rises from the horizon. The path is similar on the opposing latitude, but reversed from south and north horizons.
An interesting side point is that the tropic lines (tropic of Cancer and Tropic of Capricorn) are the lines where the sun goes directly overhead on the solstices. Outside of these lines, the sun never gets directly straight up. The opposite are the Arctic and Antarctic Circles. Those are the lines where the sun never sets around the summer solstice and never rises around the winter solstice. These lines of latitude move slightly every year to account for the irregular wobble of the earth and slight elliptical orbit.
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