There is another instance of the ‘red dawn’ being a portent of doom:
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Arise, arise, Riders of Theoden!
Fell deeds awake: fire and slaughter!
spear shall be shaken, shield be splintered,
a sword-day, a red day, ere the sun rises!
Ride now, ride now! Ride to Gondor!
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The red sky in the morning folklore does have some scientific basis in meteorology, I’m happy to say, though I would have to look this up to say exactly why this phenomenon happens - it's something to do with particles.
On the nature of Elven sleep, I’m sure that this is strongly linked to the nature of Elven time. If an immortal has a wholly different perception of the passing of time,
surely they should have a different need for sleep? I would like to think that they need to sleep less often than mortals, yet in proportion to their infinite lives, it would be equivalent to the sleep that mortals take.
To work out why Legolas can see so far will need some very ‘out there’ physics to begin to explain, but I shall attempt it, at the risk of the men in white coats coming out again, and possibly they will be having to round up anyone who attempts to read this.

This goes back to the concept of Light, though in a purely (or
is it?) scientific sense.
Light travels one foot in one billionth of a second, and the Light from the Sun takes 8 minutes to reach us. If the Sun exploded (presuming its constituent parts would travel at no faster a velocity than the speed of light), then we would not know this for 8 minutes; we would experience the past in the present. So in effect, all the Light we receive is the past, it is something which has already happened;
our Light (and our present) is the
Sun‘s history. As for Time, it exists at several levels, including psychological time, and our psychological time by necessity moves forwards. Here is what Hawking says of this:
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Suppose, however, that God decided that the universe should finish up in a state of high order but that it didn’t matter what state it started in. At early times the universe would probably be in a disordered state. This would mean that disorder would decrease with time. You would see broken cups gathering themselves together and jumping back onto the table. However, any human beings who were observing the cups would be living in a universe in which disorder decreased with time. I shall argue that such beings would have a psychological arrow of time that was backward. That is, they would remember events in the future, and not remember events in their past. When the cup was broken, they would remember it being on the table, but when it was on the table, they would not remember it being on the floor.
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If you consider an immortal, maybe their time moves forward at a different velocity, hence their light, and thus what they can see, and how far they can see, also is different.
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Is the 'other' world still the original flat earth - which would perhaps explain why they can still find the Straight Road into the West? Do Elves like Legolas walk on both a straight & a 'curved' world? Maybe Legolas can see the Rohirrim at such a great distance & calculate their number instantly because the physics of the Other World are different to the physics of this world?
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Now this
is important. There is a possibility that the universe is round, but there is also the possibility that it is flat, that it even has
walls; it is most likely fairly flat, with a slight shape. I won’t go too far into this as I think I’ve meddled with cosmology enough for one post, but in terms of Tolkien’s universe, it could indeed be that for Elves, with their different perceptions of Time, and hence Light, exist in a perfectly flat universe. I have thought this is a possibility for a long time, and often think of the search for the straight road as akin to the search for the secret of time itself.