This is an overview of the cosmology of J. R. R. Tolkien's Middle-earthlegendarium. Each entry is followed by any alternative names, any roughly corresponding primary world name in parentheses, and a brief description. A question mark after the primary world name indicates that the identification may be partially speculative or disputed.
Timeless Halls (Heaven) — The home of Eru (God) outside of Time. They are similar to Heaven in that they exist outside the boundaries of the universe and in that they do not have a physical form. Some hypothesize they are the final destination of the souls of Men; however, it is a greater possibility they may be only a temporary, intermediate dwelling before the restoration of Arda. In fact, it is confirmed in the tale of Adanel that Men return to Eru, but it is doubtful if that tale can be considered canon, although Christopher Tolkien once considered putting it in the appendices of The Silmarillion.
Eä (the Universe) — Eä (Quenya: [ea]) is the Quenya name for the universe, as a realization of the vision of the Ainur. The word comes from the Quenya word for to be. Thus, Eä is the World that Is, as distinguished from the World that Is Not. It may thus be assumed that everything outside Eä, including the Timeless Halls, has no material form. The Ainur, angelic beings from the Timeless Halls beyond Eä, refer to it as "the Little Kingdom", because all creation that humans can perceive is tiny in comparison to the mind of Eru Ilúvatar (God). Eä was the word spoken by Eru Ilúvatar by which he brought the universe into actuality.
The Void, Avakúma, Kúma, the Outer Dark, the Eldest Dark, the Everlasting Dark — An uninhabited region of nothingness described as existing outside Arda, and reached through the Doors of Night. Nothing of any power or strength can be used within the Void. Melkor was cast into The Void after the War of Wrath, but legend predicts his return to the world before the end. There is some confusion between this concept of the Void, as the vast spaces that surround Arda but that are a part of Eä, and the Void that predated the creation of Eä, as a state of Not-being.
Arda, Ilu — See Arda. The world, including everything in the skies around it.
Vaiya, Ekkaia, the Enfolding Ocean, the Encircling Sea (Outer space) — A dark sea that surrounds the world before the cataclysm at the end of the Second Age. Vaiya flows completely around the world, forming a sea below it and a form of air above it. Arda is described as floating on Vaiya, like a ship on a sea. Ulmo the Lord of Waters dwells in Vaiya, below the roots of Arda. Vaiya is described as extremely cold: where its waters meet the waters of Belegaer in the northwest of Middle-earth a chasm of ice is formed, the Helcaraxë. Vaiya cannot support any ships except the boats of Ulmo: the ships of the Númenóreans that tried to sail on it sank, drowning the sailors. The Sun passes through Vaiya on its way around the world, warming it as it passes. After Arda was made round Vaiya apparently disappeared, although it may have been changed into the upper atmosphere of the world.
Ilmen (the Solar system) — A region of clean air pervaded by light, before the cataclysm at the end of the Second Age. The stars and other celestial bodies are found in this region. Tolkien likely derived its name from ilma, the Finnish word for air. The Moon passes through Ilmen on its way around the world, plunging down the Chasm of Ilmen on its way back.
Eärendil’s Star, "Gil-Amdir", "Gil-Estel", "Gil-Oresetel", and "Gil-Orrain"  - The light of the Silmaril set on Eärendil's ship Vingilot, which represents the planet Venus.
Menelvagor, Daimord, Menelmacar, Mordo, Swordsman of the Sky, Taimavar, Taimondo, Telimbektar, Telimektar, Telumehtar (Orion) — A constellation meant to represent Túrin Turambar and his eventual return to defeat Melkor in The Last Battle. Menelmacar superseded the older form, Telumehtar (which nonetheless continued in use), and was itself adopted into Sindarin as Menelvagor.
Valacirca, the Sickle of the Valar, Burning Briar, Durin’s Crown, Edegil, Otselen, the Plough, Seven Stars, Seven Butterflies, Silver Sickle, Timbridhil, (Ursa Major / Big Dipper) — An important constellation of seven stars set in the sky by Varda as an enduring warning to Melkor and his servants, and which precipitated the Awakening of the Elves. It also formed the symbol of Durin, seen on the doors of Moria, and inspired a song of defiance from Beren. According to the Silmarillion it was set in the Northern Sky as a sign of doom for Melkor and a sign of hope for the Elves. The Valacirca is one of the few constellations named in the book, another significant one being Menelmacar.
^ abcdeTolkien, J. R. R. (1984), Christopher Tolkien, ed., The Book of Lost Tales1, Boston: Houghton Mifflin, Appendix, ISBN 0-395-35439-0 — Concurrent with early versions of the mythology Tolkien developed a list of names and meanings called the Qenya Lexicon. Christopher Tolkien included extracts from this in an appendix to The Book of Lost Tales, including mentions of specific stars, planets, and constellations in the entries: Gong, Ingil, Mornië, Morwinyon, Nielluin, Silindrin, and Telimektar.
^Larsen, Kristine (2005). "A Definitive Identification of Tolkien's 'Borgil': An Astronomical and Literary Approach". Tolkien Studies (West Virginia University Press) 2: 161–170. doi:10.1353/tks.2005.0023. In The Fellowship of the Ring, 'Three is Company' Tolkien indicates that Borgil is a red star which appears over the horizon after Remmirath (Pleiades) and before Menelvagor (Orion). Larsen and others note that Aldebaran is known as 'the follower' of the Pleiades and is the only major red star to fit the description.
^ abcd"Qenya Lexicon". Parma Eldalamberon12. The twelfth volume of the linguistic journal Parma Eldalamberon published the complete text of Tolkien's Qenya Lexicon, including star names listed in entries that were not included in the Book of Lost Tales appendix. These additional entries can be found on pages 35, 43, 63, and 82