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If we look at orbital mechanics, we can find great tables like these, demonstrating the name of the periapsis and apoapsis around various celestial bodies:

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

(table from How do apsides of celestial bodies get their names?)

My question is why? Why have so many composite names? Are there a few standard justifications for why such naming is useful?

I ask my question from a linguistic perspective. Obviously the real reason why it is done this way is because this is the way it is done. However, often in linguistics, we can come up with "reasons" for why things are done. For example, in mountain climbing, we see vocal calls between two climbers like "on belay" "climbing" "climb." One of the justifications for these terms is that they have different numbers of syllables: 3-2-1. Obviously it is very bad news if, in bad windy conditions, you mistake one instruction for another, and it may be that the number of syllables you hear is all the information you get! We see similar in the military, where language forms patterns that can withstand the din of combat.

Is there a reasonably accepted justification (or a few common justifications) for why we have so many terms for the periapsis and apoapsis? Or is it just the way it is done?

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    $\begingroup$ ...or History of Science and Mathematics SE, or English SE, or even Linguistics SE. This is basically "Why are there so many words?" or "Why did people choose to name every instance of a thing with a different name?" and so is more about language and human behavior than anything about science and technology. It's like asking "Why are there so many names for Geological time periods?" (There are over 100 ages) $\endgroup$ – uhoh Feb 13 '18 at 23:24
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    $\begingroup$ @uhoh A geologist might be able to answer "There are N geological time periods because we found there were N-1 really substantial shifts in what happened, which would be useful." Or they might answer "There's so many names because the universities were fighting for glory at the time, so everyone wanted to name a geologic time period." Either way, the geologists are most likely to know best. $\endgroup$ – Cort Ammon Feb 13 '18 at 23:28
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    $\begingroup$ @uhoh And the bodies are sufficiently important enough to warrant these terms why? Is it that it's hard to figure out from context what the body is? Is it because we got the names from several strands of research? Is it because someone sold the community on AR efforts to bulk up their textbooks? $\endgroup$ – Cort Ammon Feb 13 '18 at 23:31
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    $\begingroup$ @uhoh Yeah, that's definitely related. It's where I copied the table from. $\endgroup$ – Cort Ammon Feb 13 '18 at 23:38
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    $\begingroup$ And what happens with regards to apside names as it becomes relevant to describe orbits of objects around other named stars or extrasolar planets... Sirius, Betelgeuse, Dimidium, Amateru, ... $\endgroup$ – Anthony X Feb 14 '18 at 0:19
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Although this question might be ported it seems, I'll give it my two cents.

The answer is, as often in astronomy, twofold:

  1. It's a historical artifact: Astronomy is probably the oldest science [citation needed], and it was already remarked that the apo/peri naming scheme dates back to the Greeks. We sometimes work with very old data (admittedly, as the amount of data becomes exponentially more due to modern instruments, probably not all of us), but at least reference it sometimes. It is good to understand what you reference.
    Additional to that, as scientists, we like clarity. This also implies that we become a bit conservative about naming conventions, as changing things means confusion when reading older texts.
  2. It's also so goddamn useful, convenient and brief: As I said, clarity is important. You wouldn't ask why medical doctors have so many names for every muscle, fiber, tissue, state of the body, would you?
    In the same way that an MD can save time and effort talking to their colleagues, astronomers can as well using the language of the trade.
    It's use stems from the need to describe the positions of celestial bodies relative to each other. The need for that can arise whenever in astronomy, be it someone discussing orbital dynamics, storms on the moon Titan, the magnetosphere of Uranus or theoretical calculations of planets forming around binary stars.

Referring to the last part: How would you describe the positions of celestial bodies, when you want to discuss data about Saturn's moon Titan, just before it disappears behind the sun, as viewn from Earth, just when it's at it's largest distance from Saturn?
Simple: "During Saturns opposition while Titan is at apokronium."

How to describe the fact that the vector pointing from the Sun towards Mercury's closest point of approach rotates? Answer: "Mercury's perihelion shift"

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    $\begingroup$ It could be argued that "Titan is at apokronium" is still redundant in that example, and "Titan is at apoapsis" would work fine; nobody would suggest that it means that it's farthest from the Sun or the Earth using "Titan is at apoapsis", it would be assumed to apply to the body to which it is gravitationally bound. However, a spacecraft or an asteroid in an orbit associated with a Lagrangian point might be a horse of a different color. A Jovian Trojan asteroid could be at apozene or aphelion, and apoapsis might be ambiguous. $\endgroup$ – uhoh Feb 14 '18 at 1:18
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    $\begingroup$ @uhoh: That's the point. 'Would be assumed that' doesn't work in science. You have and want to be on point. $\endgroup$ – AtmosphericPrisonEscape Feb 14 '18 at 1:40
  • $\begingroup$ And when we discuss exoplanets, what terms will we use then? Why not use those terms within our own solar system for consistency? $\endgroup$ – Sir Adelaide Feb 14 '18 at 1:46
  • $\begingroup$ @SirAdelaide: So far, there's no need to go beyond 'periastron' and 'apoastron' for exoplanets, as we didn't discover any exomoons yet. I don't know what you mean, where do you think their usage is inconsistent with what? $\endgroup$ – AtmosphericPrisonEscape Feb 14 '18 at 1:59
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    $\begingroup$ @uhoh That asteroid one is interesting to me. That's the first orbit I've heard of where I wouldn't consider the body being orbited to be immediately obvious. ones like "Mercury's perihelion" seem like they could easily be just called "Mercury's periapsis," without loss of comprehension, but an asteroid might have situations that are less clear. Thanks! $\endgroup$ – Cort Ammon Feb 14 '18 at 15:32

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