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If you look at this site, it shows some of our common bodies' apsidal names, as shown below:

Objects     Periapsis       Apoapsis

Galaxy      Perigalacticon  Apogalacticon
Black hole  Perimélasma     Apomelasma
Star        Periastron      Apoastron
Sun         Perihelion      Aphelion
Mercury     Perihermion     Apohermion
Venus       Pericytherion   Apocytherion
Earth       Perigée         Apogee
Moon        Periselene      Aposelene
Mars        Periareion      Apoareion
Jupiter     Perizene        Apozene
Saturn      Perikrone       Apokrone
Uranus      Periuranion     Apouranion
Neptune     Periposeidion   Apoposeidion 
Pluto       Perihadion      Apohadion

My question is, how do scientists, astronomers or whoever, come up with these names?
Is there a list waiting for discovered bodies? Do they make them up as they go?

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There is no generally agreed upon naming convention that I'd know of. Since the prefixes for the closest (peri-) and farthest (apo-) orbital point to the parent body are of ancient Greek origins, most commonly found forms use ancient Greek names for celestial bodies. Either ancient Greek gods that are equivalent to Roman gods that the celestial bodies were named after (e.g. for Latin / Roman Mars, ancient Greek equivalent is Ares, both gods of war), any objects, places and so on that they were associated with, or even their alternative names. Similar goes for adjectives. But the names used both for apsides as well as adjectives can also come from Latin, for example, for the Moon:

  • Adjectives: lunar (from Latin Luna), selenic / selenian (from Greek Selene) or alternative cynthean (from Greek Cynthia, epithet of the Greek goddess of the moon Artemis)
  • Apisides: (peri-/apo-) lune, selene, cynthion

Forms from Artemis are missing, perhaps because it would make such named apsides sound like a bad medical condition. Some of the remaining forms are more commonly used for artificial satellites (e.g. -cynthion), others for natural satellites (e.g. -selene) and so on. But their use might depend on something as simple as which one sounds better or catches on in scientific and popular literature. And yes, such naming can get pretty inventive, like for example for black holes (-melasma/-bothra/-nigricon) or Venus (-cytherion/-cytherean/-krition).

Wikipedia used to have a table of most common names of apsides, but that's sadly gone with new revisions:

Body        Closest approach                            Farthest approach
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General     Periapsis/Pericenter                        Apoapsis/Apocenter
Galaxy      Perigalacticon                              Apogalacticon
Star        Periastron                                  Apastron
Black hole  Perimelasma/Peribothra/Perinigricon         Apomelasma/Apobothra/Aponigricon
Sun         Perihelion                                  Aphelion
Mercury     Perihermion                                 Aphermion
Venus       Pericytherion/Pericytherean/Perikrition     Apocytherion/Apocytherean/Apokrition
Earth       Perigee                                     Apogee
Moon        Periselene/Pericynthion/Perilune            Aposelene/Apocynthion/Apolune
Mars        Periareion                                  Apoareion
Jupiter     Perizene/Perijove                           Apozene/Apojove
Saturn      Perikrone/Perisaturnium                     Apokrone/Aposaturnium
Uranus      Periuranion                                 Apouranion
Neptune     Periposeidion                               Apoposeidion
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    $\begingroup$ Ah-hah. So that's where the revision went. I was looking back a bit and was like, "wheres the table I saw earlier!?". $\endgroup$
    – user7078
    Dec 31, 2014 at 5:44
  • $\begingroup$ On a side note, thanks. Your answer seems valid and makes perfect sense. I just wanted to know how they did it, which you explained well... $\endgroup$
    – user7078
    Dec 31, 2014 at 5:45
  • $\begingroup$ That table was deleted just recently, apparently on the basis of being "personal research". Perizene, for example, appears to be a completely made up word, on the basis that "perijove" is bad form. Google ngrams finds zero references to perizene in books, and google scholar finds zero references to perizene in scholarly articles. But then again, that same concept of not mixing Greek and Latin would mean periapsis and perifocus are bad form. Apsis and focus come from the Latin, not Greek. $\endgroup$
    – David Hammen
    Dec 31, 2014 at 16:20
  • $\begingroup$ @DavidHammen But then that makes all of them made up? Correct? $\endgroup$
    – user7078
    Jan 1, 2015 at 0:28
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    $\begingroup$ @FinnRayment Well, technically, all names are made up. That makes all adjectives of names, if we agree on naming convention and which names will we use to form adjectives or not, at last equally if not even more made up. Wolves for example call a full moon like this. They all know what that means. None of them would recognize what that means if I told them that's called howling in some odd use of vocal cords that's apparently called English by English. Actually, they might fail to understand me so badly I could end up being their dinner. :) $\endgroup$
    – TildalWave
    Dec 11, 2015 at 23:42
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They are generally composed by using the adjectival form of the Greek god name:
Star = Asteria
Sun = Helios
Mecury = Hermes
Venus = Cytherea
Earth = Gaia
Moon = Selene
Mars = Ares
Jupiter = Zeus
Saturn = Kronos
Neptune = Poseidon
Pluto = Hades

Uranus was never known by its Latin equivalent, Caelus, as it was not a planet known to the ancients. Uranus was the Greek "Father Sky," the consort of "Mother Earth," or Gaia.

"Galacticon" is a (rather awkward) back formation from "galaxy."

Which leaves "melasma," which has nothing to do with the skin condition. It is Greek for "black spot."

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