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In Unfinished Tales, the Essay on the Istari
Aragorn claims to have penetrated the `far contries of Rhun and Harad where the stars are strange'.
and then links to the appendix, item #10:
The 'strange stars' apply strictly only to the Harad, and must mean that Aragorn travelled or voyaged some distance into the southern hemisphere.
So where is the equator in Middle-earth? Certainly it must be south of the Harnen river and be off the canonical map(s).
In Letter 294 Tolkien describes his world as follows:
The action of the story takes place in the North-west of 'Middle-earth', equivalent in latitude to the coastlands of Europe and the north shores of the Mediterranean. But this is not a purely 'Nordic' area in any sense. If Hobbiton and Rivendell are taken (as intended) to be at about the latitude of Oxford, then Minas Tirith, 600 miles south, is at about the latitude of Florence. The Mouths of Anduin and the ancient city of Pelargir are at about the latitude of ancient Troy.
Based on this we can overlay a map of Middle-earth on a map of our world and get something like the following:
(Image credit: http://gisninja.blogspot.com/2012/12/georeferening-middle-earth.html)
This only gets us about half the distance to the Equator, which is a good deal further off the map.
Obviously descriptions are relative: "Far Harad" may have seemed quite far indeed to a Hobbit map-maker, but there's a LOT of Harad beyond even that, and "Rhûn" barely even begins the journey East.
From "The Atlas of Middle Earth", which is probably the most accurate and complete mapping of Middle Earth, based entirely on Tolkien's writings and sketches.
The following map from Middle Earth Role Playing (the first role playing game based on Middle Earth, with permission of Tolkien Enterprises, 1984) show what is deemed as a complete map of Arda.
On it you can see how big Haradwaith is. The vegetation gives you clues: Haradwaith desert is like Sahara and under that, you get tropical vegetation like that of subsaharian Africa. Equator would be beyond the bottom side of the map.
Compare it with the actual Earth vegetation map.
If it is interpreted as journeying to where ALL the stars are strange, Aragorn would have to travel by land or sea far enough south that he couldn't see ANY of the stars he knew from home - if it was possible to go that far South.
Possibly Aragorn traveled far enough south that fifty percent, or twenty percent, or thirty five percent, or some other significant fraction of the stars he saw were below the horizon of his homeland and never seen from there.
Since we know the approximate latitude of Aragorn's home in Rivendell, and since we know when Aragorn was speaking (approximately 6,000 years ago according to one letter) it would be possible to do a computer simulation of the visible hemisphere at that time and place and deduce what latitudes Aragorn would have to reach for each percentage of unfamiliar stars there were in the sky.
One can decide for oneself what percentage of unfamiliar stars suffices, and thus what latitude Aragorn reached.
Or you can draw a circle and put Rivendell in at the approximate latitude of Oxford. Draw a line from the center of the Earth to Rivendell and out into space. That is the line to the zenith at Rivendell.
Since Oxford is at 51 degrees 45 minutes 7 seconds North we can make the latitude of Rivendell 52 degrees North, and the southernmost stars visible from Rivendell would be about 38 degrees South declination.
If Aragorn traveled to 38 degrees South latitude the stars which were on the southern horizon at Rivendell would now be at the zenith, and half the stars in the sky would be "new" stars not visible from Rivendell.
Aagorn was speaking more than 3,000 years after the world was changed from flat to spherical. However, it is not certain that the heavens were changed at the same time that the world was changed. If the stars were still very close to Earth and not at their modern and literally astronomical distances then the stars might drop below the horizon much more when going a specific distance south.
A limit to how close the stars might have been to Earth at that time can be determined by the southernmost stars and constellations seen from the Shire in The Fellowship of the Ring.
Technically, the equator isn't in Middle-earth at all. Middle-earth is actually a continent, not the whole planet. The name of the planet as a whole is "Arda", although it is sometimes referred to simply as "Earth".
Arda is, in fact, our own dearly beloved home, planet earth. Middle-earth eventually became the continent we know as Europe (as it happens, Tolkien once wrote, in a letter, that the destruction of the One Ring took place about 6,000 years ago). Obviously, the equator is several thousand miles south of the southernmost tip of Europe, and since Europe used to be Middle-earth, the equator of Arda was far to the south of it as well.
The fine folks at the LotR wiki have produced a map showing how the old continent of Middle-earth probably would have aligned with modern-day Europe:
Moving on to where the equator would have been on Arda:
In Tolkien's works, the equator is referred to as the "Girdle of Arda" or the "Girdle of Earth". The only references to it, as far as I can recall, are in The Silmarillion. In this book, I have come across two mentions of the Girdle of Arda.
The first reference isn't very helpful; it merely says that the sun and moon followed the Girdle as they traversed the heavens. The other reference is only slightly more useful: it says:
Now Fëanor led the Noldor northward, because his first purpose was to follow Morgoth. Moreover Túna beneath Taniquetil was set nigh to the girdle of Arda, and there the Great Sea was immeasurably wide, whereas ever northward the sundering seas grew narrower, as the wasteland of Araman and the coasts of Middle-earth drew together.
- The Silmarillion, Chapter 9: "Of the Flight of the Noldor"
Túna is the hill housing the city in which the Elves lived in Valinor, and Taniquetil is the tallest mountain in Valinor. From this passage, we can see that the hill of Túna is near (nigh) to the equator of Arda (i.e., the earth).
This isn't especially helpful, however, because as far as I know, there are no canonical maps of Valinor, so there aren't any maps that show Valinor's position in relation to the position of Middle-earth. Therefore, we can't really say where the Girdle of Arda would have crossed the planet in relation to the area we are most familiar with (i.e., Middle-earth).
I'm not sure if this map is canonical, but it was drawn by Tolkien himself, so it must be close to canon status. It is known as "Ambarkanta Map V". The word "Taniquetil is visible on the far left, near the middle of the drawing, which gives us some idea of where the equator (or Girdle of Arda) would be; Middle-earth is far to the north of it.
We can, on the other hand, say that the Girdle of Arda did not cross Middle-earth itself, since we never hear anything about it; the climate of Middle-earth is also far too temperate for it to be anywhere near the equator. Furthermore, I don't have the quote handy right now, but Tolkien did say that The Shire is at roughly the same longitude and latitude as the British Isles in the real world. The canonical maps of Middle-earth focus on a relatively small area which is far to the north of the equator.
I would assume that the Girdle of Arda is somewhere to the distant south of Middle-earth, possibly in Harad.
When the world changed from flat to spherical, Imbar, the planet, may have ripped from its home within Eru's vision and cast into a universe. the Sun and Moon became celestial bodies, and the stars would have changed drastically. People there may have mistaken a Venus-like planet for Eärendil.
Also, in Tolkien's maps that deal with earlier ages, the areas not occupied by Ekkaia form a circle. When the world became spherical, the described distances would have created a much smaller world with only those lands, plus the 'new lands' that Belegaer 'washed up.' Also, a circle does not become a sphere. From this, we can conclude that tracts of land were added to far eastern Middle-earth. Thus, Orocarni would correspond to the Ural mountains. Harad probably had some lands added, and the Lands of the Sun were either taken from the world along with Aman, forged into these added lands, became the New Lands, or became a land south of the New Lands, while Belegaer did create some new lands (Belegaer's lands corresponding to North America, The Lands of the Sun corresponding to South America,) or any number of possibilities. As for the Fourth Age/Fifth age transition, no, the lands could not have changed that much in 6,000 years. The Fourth Age probably ended about 1,000 years after it began, with a cataclysm (Morgoth almost re-entering the world, a potential time for Dagor Dagorath, many others,) and the Fifth Age began with the Children being moved to Earth. The reason for Earth's choosing was that its lands resembled strongly those of Imbar, and peoples were relocated based on their latitude and longitude. The 'downside' of Earth's choosing was it being a low magic area, with magic almost undetectable. The 'upside' of this 'downside' is that the holes that magic filled now had to be filled with technological advancements, causing the rapid rise in human technology. Potential human ethnic lines:
Rohirrim - Mix with Dúnedain peoples to become PIE and Caucasus peoples, some ethnic Rohirrim mix with Easterlings to form Mongoloid groups and steppe-people. Easterlings - Various groups, from native americans to Asians to Siberians Haradrim - Various groups, from Arabs to subsaharans to Mesopotamians Forodwaith - Uralic and Inuit peoples
Of course this is hypothetical, and no one but a nut would actually believe that the world evolved from Arda in 6,000 years, or that elves and dwarves are real, and stuff like that. But it's fun to create these types of fanfictions.
P.S. I'm not being mean to those of you that I have descended from Easterlings or Haradrim. In Tolkien's legendarium, they were probably forced to fight for the Enemy or just didn't know who they were fighting for. Plus, they geographically align.
