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Elsewhere online I keep reading that a supermoon is the situation when full moon coincides with moon perigee. But see this plot from wikipedia Lunar Distance entry

enter image description here

The perigee distance varies wildly across the year, so we could have "supermoons" closer than 360000 Km as well as "microsupermoons" as far as 370000. Not very super, if we consider the mean distance is 385000.

On the other hand, we can have perigee closest than 360000Km at any phase, and we have it a couple times each year. Is there a name for this "closest perigee", independently of moon phase? Perhaps some tidal wave name?

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    $\begingroup$ A cynical point of view: a supermoon is a super non-event, enabling lazy periodistas to paste pre-cooked material in place of real news. OTOH, as mentioned by Pierre, it's “good and free advertisement” for astronomy. $\endgroup$
    – gboffi
    May 31 at 8:31
  • $\begingroup$ @gboffi Well any complection of orbit is usually a non event, and people trends to make celebrations anyway. I would agree that coincidence of phase and perigee is not very interesting, but coincidence of phase and minimal perigee does not happen every year. $\endgroup$
    – arivero
    May 31 at 13:50
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    $\begingroup$ Was going to post relevant XKCD, apparently there's several: Superm*n, Every Major's Terrible, Lunar Cycles. This apparently annoys him quite a bit... $\endgroup$ Jun 1 at 15:05
  • $\begingroup$ @DarrelHoffman I'd say that xkcd.com/2172 is more angry about lunar models, or modelists, that about the concept. Note how it stops rationality at the point where he should draw the above picture with its peculiar, months long, period. $\endgroup$
    – arivero
    Jun 1 at 15:36
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To directly answer your question: There is no "precise" definition of the term "supermoon."

Term Origin: The origin of the term is generally attributed to the astrologer Richard Nolle in 1976. As Wikipedia notes, "In practice, there is no official or even consistent definition of how near perigee the full Moon must occur to receive the supermoon label, and new moons rarely receive a supermoon label."

Term in Practice: In practice, the term is usually used when perigee (moon's closest approach to Earth) and syzygy (alignment between three bodies -- in this case, Sun-Earth-Moon) occur within about a day of each other. Also often in media practice, the term will usually be applied when perigee and syzygy occur closest for the year, and/or when perigee is closest for the year and it's within a day or so of syzygy. An added qualifier is that the term is practically never applied to the new moon, only full moon, despite the new moon also being a syzygy point.

Meanwhile, at TimeAndDate.com, they use the definition of a supermoon being when "a full or new moon" happens when the moon is also less than 360,000 km from Earth, so they at least have tried to give a numerical definition though they don't define exactly what a new or full moon means, since a true new or full moon only happens during an eclipse.

How Much Bigger? The apparent size of the object in our sky is directly proportional to distance when angles are small (numbers from Wikipedia). The average perigee distance is 362,600 km, and average apogee is 405,400 km. Simple division indicates that the average perigee moon will be ≈12% larger than the average apogee moon. With a semi-major axis of 384,399 km, the perigee moon would only be ≈6% larger than an average full moon.

How Much Brighter? Here's where my answer varies from the other, which is incorrect. Brightness follows the inverse-square law, meaning that brightness falls off as the inverse-square of the distance. So, we have to square the result in the previous paragraph: (1.118...)2 ≈ +25% brighter. So, the perigee full moon will be roughly 25% brighter (not 5%) than an apogee full moon. It will be ≈12% brighter than an average full moon. At the extremes (perigee 356,400 km, apogee 406,700 km), the perigee moon will be ≈14% bigger in the sky and ≈30% brighter than the apogee. So, yes, this is quite noticeable, and is a problem for astronomers who rely on dark skies. Telescope time is usually apportioned factoring in the lunar phase, and it is especially an issue when perigee and full moons align.

Other Names: To answer your last question, so far as I know, there is no term for a "closest perigee," and there are no special tide names for it. We do have spring and neap tides, but those refer to when the sun-earth-moon are aligned vs at right angles.

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    $\begingroup$ Your brightness estimation is wrong. It would be correct it the Moon was bright due to the Earth, but no: its brightness is due to the Sun, from which the distance changes negligibly between Moon perigee and apogee. For a fixed illuminance of the Moon, its brightness will remain the same regardless of distance to the observer (Earth). What will change between perigee and apogee is the size of the lunar disk, and thus illuminance of Earth's surface by the Moon. The amount of this change is proportional to the change of lunar disk area, i.e. $\approx1.06^2-1$. $\endgroup$
    – Ruslan
    May 31 at 8:42
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    $\begingroup$ +1 for quantifying. Is 12% bigger radius or diameter or surface area? $\endgroup$
    – stevec
    May 31 at 10:19
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    $\begingroup$ @steve average=384,399, super < 360,000, so diameter scales by atan(1737/360)/atan(1737/384) = 1.066, as said by Ruslan The 12-14% figure is for area, then $\endgroup$
    – arivero
    May 31 at 14:06
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    $\begingroup$ @Ruslan - Every single source I have found for this says that my math is correct, including NASA (moon.nasa.gov/news/29/…), Space.com (space.com/22025-supermoon-2013-full-moon-myths.html), and TimeAndDate (timeanddate.com/astronomy/moon/super-full-moon.html). I looked there before I wrote it because I also wasn't entirely sure on that one. $\endgroup$ May 31 at 19:46
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    $\begingroup$ These sites seem to confuse brightness and illuminance due to the object. They might be applying the non-photometric sense of "brightness" (that's related to apparent magnitude) that's commonly used for point-like objects like stars. But it's misleading when used for non-point objects like the lunar disk, since you'll still see the same surface brightness while apparent magnitude will decrease. $\endgroup$
    – Ruslan
    May 31 at 21:05
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No, there is no special name for the closest supermoon.

Besides, the very name “supermoon” was coined by an astrologer, NOT an astronomer, and it is basically all just media hype. During a so-called “supermoon,” our satellite is on average 15% larger and 5% brighter than during a regular full moon. Since the previous full moon dates from a month before (the etymology of “month” is the same as that of “moon”), it is impossible to remember precisely how bright and big the lunar disk then was. So anyone and everyone who claims that they noticed the Moon as “bigger and brighter than usual” during a “supermoon” is actually just being influenced by the media.

Astronomers see nothing special with a “supermoon”—the only “advantage” I see is that the media then talk more about astronomy, so it’s some “good and free advertisement.”

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    $\begingroup$ Comments are not for extended discussion; this conversation has been moved to chat. $\endgroup$
    – Connor Garcia
    Jun 1 at 18:02

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