Etymology
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moon-calf (n.)

also mooncalf, "abortive, shapeless, fleshy mass," 1560s, attributed to the influence of the moon; from moon (n.) + calf (n.1). In later 16c., "deformed creature, monster;" from 1620s as "congenital idiot."

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calf (n.1)
"young of a bovine animal," Old English cealf (Anglian cælf) "young cow," from Proto-Germanic *kalbam (source also of Middle Dutch calf, Old Norse kalfr, German Kalb, Gothic kalbo), perhaps from PIE *gelb(h)-, from root *gel- "to swell," hence, "womb, fetus, young of an animal."

Elliptical sense of "fine kind of leather made from the skin of a calf" is from 1727 (short for calf-skin, 1580s). Extended by 1725 to the young of marine mammals, the adults of which are called bulls and cows. Used of icebergs that break off from glaciers from 1818 (perhaps from Scandinavian use in reference to a small islet lying near a large one). Finnish kalpe is from Germanic. Golden calf "idol" is from Exodus.
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calf (n.2)
"thick, fleshy part of the back of the lower human leg," early 14c., from Old Norse kalfi, a word of unknown origin; possibly from the same Germanic root as calf (n.1). Relatively larger in man than in other mammals for the support of the body standing upright. Of garments, calf-length is from 1956.
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moon (n.)

"heavenly body which revolves about the earth monthly," Middle English mone, from Old English mona, from Proto-Germanic *menon- (source also of Old Saxon and Old High German mano, Old Frisian mona, Old Norse mani, Danish maane, Dutch maan, German Mond, Gothic mena "moon"), from PIE *me(n)ses- "moon, month" (source also of Sanskrit masah "moon, month;" Avestan ma, Persian mah, Armenian mis "month;" Greek mene "moon," men "month;" Latin mensis "month;" Old Church Slavonic meseci, Lithuanian mėnesis "moon, month;" Old Irish mi, Welsh mis, Breton miz "month"), from root *me- (2) "to measure" in reference to the moon's phases as an ancient and universal measure of time.

A masculine noun in Old English. In Greek, Italic, Celtic, and Armenian the cognate words now mean only "month." Greek selēnē (Lesbian selanna) is from selas "light, brightness (of heavenly bodies)." Old Norse also had tungl "moon," ("replacing mani in prose" - Buck), evidently an older Germanic word for "heavenly body," cognate with Gothic tuggl, Old English tungol "heavenly body, constellation," of unknown origin or connection. Hence Old Norse tunglfylling "lunation," tunglœrr "lunatic" (adj.).

Extended 1665 to satellites of other planets. Typical of a place impossible to reach or a thing impossible to obtain, by 1590s. Meaning "a month, the period of the revolution of the moon about the earth" is from late 14c.

To shoot the moon "leave without paying rent" is British slang from c. 1823 (see shoot (v.)); the card-playing sense perhaps was influenced by gambler's shoot the works (1922) "go for broke" in shooting dice. The moon race and the U.S. space program of the 1960s inspired a number of coinages, including, from those skeptical of the benefits to be gained, moondoggle (based on boondoggle). The man in the moon "fancied semblance of a man seen in the disk of the full moon" is mentioned since early 14c.; he carries a bundle of thorn-twigs and is accompanied by a dog. Some Japanese, however, see a rice-cake-making rabbit in the moon. The old moon in the new moon's arms (1727) is the appearance of the moon in the first quarter, in which the whole orb is faintly visible by earthshine.

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moon (v.)

c. 1600, "to expose to moonlight;" later "idle about, wander or gaze moodily" (1836), "move listlessly" (1848), probably on the notion also found in moonstruck. The meaning "to flash the buttocks" is recorded by 1968, U.S. student slang, from moon (n.) "buttocks" (1756), "probably from the idea of pale circularity" [Ayto]. See moon (n.). Related: Mooned; mooning.

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moon-face (n.)

"a full, round face," 1854, from moon (n.) + face (n.) . Related: Moon-faced.

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blue moon (n.)

"a long time," 1821, often in phrases indicating something rarely occurring. Compare at the Greek calends (from an ancient Roman phrase alluding to the fact that the Greeks had nothing corresponding to the Roman calends), and the native in the reign of Queen Dick and Saint Geoffrey's Day "Never, there being no saint of that name," reported in Grose (1788). Nevermass "date which never comes" is from 1540s. Blue moon is suggested earliest in this couplet from 1528:

Yf they say the mone is blewe,
We must beleve that it is true.

Though this might refer to calendrical calculations by the Church. Thus the general "rareness" sense of the term is difficult to disentangle from the specific calendrical one (commonly misinterpreted as "second full moon in a calendar month," but actually a quarterly calculation). In either case, the sense of blue here is obscure. Literal blue moons do sometimes occur under extreme atmospheric conditions.

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moon-up (n.)

"moonrise," U.S. dialectal, 1907, from moon (n.) probably based on sun-up (q.v.).

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moon-shot (n.)

"launching of a spacecraft toward the moon," 1958, from moon (n.) + shot (n.).

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