Stars

The  Stars:

    Alcarinquë "The Glorious" is one of the bright new stars created by Varda for the Firstborn.

Reference: "Of the Coming of the Elves", Silmarillion

Borgil

    (Aldebaran or Betelgeuse?)
    Borgil is a star described as red, glowing like a jewel of fire. It rose after full dark, after the Remmirath constellation (Pleiades) had arisen and before the Menelvagor constellation (Orion).

    In astronomy, Betelgeuse is a first magnitude giant red star near one shoulder of the constellation of Orion. If "Borgil" arose before Orion, then it could not be in Orion.

    Aldeberan is a first magnitude red star, the brightest in the constellation Taurus where it is positioned as the eye of the bull..  Aldebaran is called "the follower" in Arabic, because it appears to follow the Pleiades except in extremely southern latitudes.

Reference for Borgil: "Three is Company",  Fellowship of the Ring: Lord of the Rings

Carnil

    Carnil is a red star, one of the bright new stars created for the Firstborn.

Reference: Silmarillion 

Eärendil

    "The star of Eärendil shone bright in the West as a token that all was made ready, and as a guide over the sea; and Men marvelled to see that silver flame in the paths of the Sun.
    "Then the Edain set sail upon the deep waters, following the Star; and the Valar laid a peace upon the sea for many days, and sent sunlight and a sailing wind....But so bright was Rothinzil that even at morning Men could see it glimmering in the West, and in the cloudless night it shone alone, for no other star could stand beside it. And setting their course towards it the Edain came at last over leagues of sea and saw afar the land that was prepared for them, Andor, the Land of Gift..."

    Rothinzil was the Númenorean Adûnaic name for Vingilot, the ship of Eärendil.
    Andor was also called Númenor.

Reference: "Akallabêth", Silmarillion
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Elemmírë

Reference:Silmarillion
see also Elves: Elemmírë

Helluin/Nielluin

    (Sirius)
    In astronomy, Sirius is the brightest star in the heavens, found in the Canis Major constellation and therefore called the Dog Star.
This dog follows Orion.

    In the Silmarillion, Helluin is a bright star of blue fire. It is one of the bright new stars created for the Firstborn.
    The Book of Lost Tales I includes the earlier name of Nielluin, the "Blue Bee" or "Bee of Azure", and plainly states that it is Sirius in "Commentary on 'The Tale of the Sun and Moon'".
    In the text of "The Tale of the Sun and the Moon", the time Nielluin is seen is during "autumn or in winter burning nigh the foot of Telimektar son of Tulkas", Orion.
    In the same text, some stars, perhaps including Nielluin which is in the same long paragraph, are said to be steady, translucent lamps instead of the more normal traveling ships.
    Also called Niellúnë;, Nierninwa in BoLT.
    In BoLT, Nielluin was originally Ingil, the son of Inwe (Ingwë in the Sil). This made him heir to the throne of the elves in Valinor.
Other names for Ingil are in BoLT's Appendix as Gilweth, Githilma.
Gil is the star Sirius, Gil being the new name of Gilweth after he went into the heavens in the form of a great bee bearing honey of flame, following Orion (here called Daimord and Telimektar). Gil means "gleam" according to the commentary.
Gil in Sindarin means "star" in the Silmarillion.

Reference: "Of the Coming of the Elves",  "Of Fëanor", "Index of Names", Silmarillion
"The Tale of the Sun and Moon", Book of Lost Tales I
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Luinil

    Luinil is a blue star, one of the bright new stars created for the Firstborn.

Reference: "Of the Coming of the Elves", Silmarillion

Lumbar

    Lumbar is one of the bright new stars created for the Firstborn.

Reference: "Of the Coming of the Elves", Silmarillion

Morwinyon

    (Arcturus)
    In both of JRRT's word lists of Quenya and "Gnomish", Morwinyon is defined as Arcturus, according to Christopher Tolkien's commentary on "The Tale of the Sun and Moon" in BoLT 1.
    Morwinyon is the Quenya word for Arcturus, according to the Lore Book.
    In the text of BoLT 1's "The Tale of the Sun and Moon", Morwinyon is said to mean "the glint at dusk".
    In the very early story, "The Coming of the Elves", Morwinyon was a star accidentally dropped by Varda as she hastened back to Valinor, inspired to make more stars by Aulë's accidental making of the Seven Stars/Valacirca at her news of the coming of the Eldar, so she carried perhaps overmuch of the radiance of Telimpë from Aule's basin/bason. This left Morwinyon unmoving, blazing low in the west. Movement for it had to come at a later time after being refound. The story of Valacirca was changed several times, leaving Morwinyon's story a bit lost.
    In "The Tale of the Sun and the Moon", we have another reason why Morwinyon held still in the western sky. Instead of one of the stars that travelled in ships manned by the spirits of the Manir and Suruli, Morwinyon may be one of those that was a lamp, since it is in the same paragraph. These lamps were translucent, set in Ilwë or the edge of Vilna and Middle-earth's breathable air. They flickered and waned in the upper winds.

References:
"The Coming of the Elves", "The Tale of the Sun and the Moon", Book of Lost Tales I
English to Quenya wordlist of the Lore Book of the High Elven Tongue by Beren-(Valar)

Nénar

Reference: Silmarillion

The  Constellations:

Anarríma

    Anarríma is the name of a constellation formed by Varda by gathering old stars together to increase their brightness for the benefit of the coming of the Elves.

Reference: "Of the Coming of the Elves", Silmarillion

Menelvagor/Menelmacar

    (Orion)
    In the Fellowship of the Ring, Menelvagor rises after the Remmirath and after Borgil. It is described as "the Swordsman of the Sky, Menelvagor with his shining belt". As it rose, Gildor and the other elves who were escorting the hobbits burst into song, lit a fire, and said it was time for speech and merriment.
    In the Silmarillion, Menelmacar is called the Swordsman of the Sky "with his shining belt, that forebodes the Last Battle that shall be at the end of days."
    Menel in Quenya elvish means "heaven" or "heavens" or "sky". In Quenya, mak- means slay, makil means sword. Makar was the Warrior Vala in the Book of Lost Tales. Thus it could suggest a warrior Vala in the heavens complete with sword belt, a threat to Melkor. The letter k in Quenya elvish was generally changed to a c in later work, but the c is pronounced as a k as in Celebrimbor.
    Even earlier names found in the Book of Lost Tales were Telumehtar, "warrior of the sky", and Telimektar, the son of Tulkas. Quenya has Telimektar, Telimbektar, Taimondo, Taimordo, Taimavar.
Sindarin Gnomish has Telumaithar and Daimord.

References:
"Three is Company",  Fellowship of the Ring: Lord of the Rings
"Of the Coming of the Elves", Silmarillion. Book of Lost Tales 1.
"The Tale of the Sun and the Moon", Book of Lost Tales 1
Lorebook of the High Elven Tongue by Beren-(Valar).
Quenya to English wordlist by Beren-(Valar)

Menelmacar

    In an old story, Menelmacar was the son of Tulkas.

Reference: Book of Lost Tales #1

Remmirath

    (Pleiades)
    The Remmirath is a constellation mentioned in the Fellowship of the Ring created by a gathering of old stars by Varda. The Remmirath and the red star Borgil rose before Menelvagor/Menelmacar/Orion.

References: Fellowship of the Ring, Silmarillion

Soronúmë

    Soronúmë is the name of a constellation formed by Varda by gathering old stars together to increase their brightness for the benefit of the coming of the Elves.

Telumendil

    Telumendil is the name of a constellation formed by Varda by gathering old stars together to increase their brightness for the benefit of the coming of the Elves.

Valacirca

    (The Big Dipper, The Great Bear)
    Also called the Seven Stars, Sickle of the Valar, Sign of Doom, the Seven Butterflies in "The Coming of the Elves", BoLT I.
Called the Plough in BoLT 2.
    The Quenya elvish word, circa, means sickle.

"And high in the north as a challenge to Melkor she set the crown of seven mighty stars to swing, Valacirca, the Sickle of the Valar and sign of doom."

    Beren, almost dreaming, sang a song heard by Lúthien that let her know where he was imprisoned by Sauron, and he made up the song as a challenge. The subject was "in praise of the Seven Stars, the Sickle of the Valar that Varda hung above the North as a sign for the fall of Morgoth".

References:
"The Coming of the Elves", Book of Lost Tales I
"Of the Coming of the Elves", "Index of Names", "Of Beren and Lúthien", Silmarillion

Valacirca

    The Seven Butterflies: That name is from the old tale of the coming of the Elves, here it was Aulë who made them but it is a beautiful name for Valacirca I think.
  Aulë was making a silver sickle when Melkor told Aulë a lie about Yavanna and he got so angry he broke the sickle with a blow and seven sparks leapt up and winged into the heavens. There Varda caught them and gave them a place as a sign of Yavanna`s honour.

Reference: Book of Lost Tales #1

Wilwarin

Reference:
Origin: "Of the Coming of the Elves", Silmarillion
Name in Quenya and modern: "Index of Names", Silmarillion

The Creation of the Stars for the Firstborn

The Prophecy:

   "But at the bidding of Manwë Mandos spoke, and he said: 'In this age the Children of Ilúvatar shall come indeed, but they come not yet. Moreover it is doom that the Firstborn come in the darkness, and shall look first upon the stars. Great light shall be for their waning. To Varda ever shall they call at need.'

--"Of the Coming of the Elves", Quenta Silmarillion, The Silmarillion

The Creation:

    "Then Varda went forth from the council, and she looked out from the height of Taniquetil, and beheld the darkness of Middle-earth beneath the innumerable stars, faint and far.
    Then she began a great labour, greatest of all the works of the Valar since their coming into Arda. She took the silver dews from the vats of Telperion, and therewith she made new stars and brighter against the coming of the Firstborn; wherefore she whose name out of the deeps of time and the labours of Eä was Tintallë, the Kindler, was called after by the elves Elentári, Queen of the Stars."

    Varda made new stars, brighter than her old ones. Then she gathered many of the old, faint stars into constellations to increase their brightness and to use as signs in the heavens.
    When she ended her long labors, the light awakened the Firstborn of Ilúvatar, the elves, by the mere of Cuiviénen, "Water of Awakening". Their first sight was the field of stars, so that they loved the starlight and revered Varda above all the other Valar. The light of the stars shone ever after from their eyes.

Reference: "Of the Coming of the Elves", Silmarillion

Link:
Link to an intriguing page "The Astronomy of Middle-earth" by Dr. Kristine Larsen, Professor of Physics and Astronomy, Central Connecticut State University.
It includes yet more links to her work, available from this list.