John Pazmino
 NYSkies Astronomy Inc
 2017 December 5

    Over the past 10 or so years the general and astronomy news media 
alerted the public to the coming 'supermoon' event. The story is that 
the next Full Moon is is larger and brighter than nromally in the sky. 
Occasionally the further detail is noted that the Moon is ner her 
perigee, being then closest to Earth iun her orbit.  
    Altho there is nothing special about a supermoon, it could promote 
a sky awareness among the public, like Manhattanhenge does for people 
on Manhattan. 
    Longtime astronomers treat this event as a erun of the 1980s when 
the Full Moon rounded suzygy (SIH-zih-jee). Syzugy is the opposite 
ends of the orbit mjor axis. The perigee is the end nearer to Earth; 
apogee, farther. The maor axis is simethimescalled the line of 
syzygies or line of apsides (PP-sih-deez). 
    Only the suzygy at perigee is newsworthy; the apogee is almost 
never noticed. 

    'Supermoon', sometimes with a hyphen, is the current, 2010s, name 
for the larger Full Moon. I see others like 'maximoon' and 
'macromoon'. 'Syzygy' fell againstthe boards by 2000. These contrast 
the Moon when she is fathest from Earth near apogee. The names are 
'minimoon' and 'micromoon'. The variety of names,in English at least, 
comes from the informal definiton of the event and its minimal 
astronomical significance. 

Apprciating Supermoon 
    The problem  with appreciating a supermoon is that no one -- not 
even seasoned lunar observers -- routinely measures the Full Moon to 
angular size, and much less her distance from us. It is impossible to 
appreciate a supermoon by casually looking at it with no context for 
other Full Moons. The Full Moon atperigee is about 13$ karger ub 
duaneter tgab at aoigee but this is utterly beyond detection without 
direct comparison or careful measurements. 
    To the layman all Full Moons lok humongous, like the one in the 
'Honeymooners' splash scene, no mattter where she is in her orbit. 
Whent he admires the Full Moon during a supermoon he's satisfied that 
she somehow is bigger than other Full Moons. 
    A large factor in this mistaken impression is the 'Moon illusion'. 
We usually catch sight of the Full Moon in dusk or nightfall, when she 
is low on the skyline. The Moon illusion, with today still no firm 
explanation, is an apparent enlargement of the Moon at low altitude 
due to some peculiar physioloy of human vision. 
   With a pair of pictures, actual phorographs or simulations from a 
planerarium software, you can illustrate the supermoon. The software 
must display thr Moon with  her reaL SIZE, NOT A STOCK PICTURE. tHE 
TYPICLY WITHIN THE SAME YEAR. Compare the pictures side-by-side or 
overlapping. There is a clear difference in angular size, some 13%. 

Ancient Supermoon! 
    Supermoon refers to the ncreased angular size of the Moon when 
near her perigee. The Moon near periee also is the angularly fastest 
Moon, moving more degress per day than else where in the orbit. It may 
sound bizarre that this variation of speed was recognized, and 
exploited, thousands of years ago! 
    Astronomers in Babylonia maintained careful records of the Moon's 
position among thee stars. They found that in each cycle of phases 
there was one segment of zodiac where the Moon moved fastest. In the 
opposite zodiacal place she moved slowest. They, in spite of hiligence 
and attention, have no record of noticing the change of angular siize 
of the Moon. 
    The two places are around the perigee and apogee. Babylonians 
discovered that these points migrated thru the zodiac with an 8.85 
year period. The astronomers used these findings to calibrate their 
calendars and track the Moon for catching First Crescent. If a 
sighting was missed for clouds, they looked up in prepared tables fo 
the expected location of the Moon, taking into account her speed 
suring the span of missed observations. 
    I don't know the Babylonian terms for the fast and slow zones. I 
made up the words 'celerilune' and tardilune' for my presentations 
about ancient lunar astronomy. 

Defining a supermoon
    There are many ways to qualify a supermoon. Often they derive from 
the tools to hand to calculate a supermoon. 
    Some authors track the Full Moon  distance and qualify a supermoon 
when this is less than so-many kilometers. 
    Others may require the Full Moon to be within a certain angular 
displacement from the perigee. Othrs may call for a maximum difference 
of time when the Moon rounds perigee and Full phase. Other factors may 
be maxium angular size and maximum angular speed. The latter derives 
from the Kepler motion of the Moon, being fastest around perigee and 
slowest around apogee. 
    Because the Moon moves so rapidly thru the stars, almost any 
reasonable qualification for a supermoon yields the same date. I 
haven't come across a discrepancy of date eithin a given timezone. 
    Probably no author cites a sprcific hour for a supermoon since the 
event requires two points of attainment, which can almost never happen 
simultaneously. As long as people oohs and aahs at the gigantic Moon 
in some hour on the night of supermoon, eery one is happy. 
    Every thing in this piece is homed on New York, more generally the 
territory of NYSkies. A date shift can occur for timezones else where 
in the world that upsets the discussion of supermoons here. 

supermoon Every Month 
    In hr cvourse of cycling thru her phases The Moon in each lap of 
her orbit passes perigee. She then is at some phaw, from new thru full 
and back. Ahe is a supermoon in every month, altho not always when she 
is full.
    I never hear of a swupermoon for any other phase then full and 
new. The New Moon instances are associated with solar eclipses. AS 
larger Moon, maybe a supermoon, usually results in a longer span of 
totality. A New Moon near apoee may actually be too small to cover the 
Sun, making this instance an annular eclipse.
    When the Full Moon isa near apogee it is sometimes called a 
minimoon or micromoon. Little public noticve is taken for this event 
an most astronomers pass it up. 

Freuency of Supermoons 
    Supermoon has no definitive rule to qualify it as such.  We can 
obtain a frequency of supermoon by asking how often the perigee and 
Full Moon pass each other around the zodiac. The Moon rounds full 
phase in 29.53 days; this is the synodic month .She rounds perigee in 
27.55 days for an apsidal month. Both are mean values. 
    The interval between passes of the perigee with Full Moon is found 
by the same formula used for finding intervals for lunar eclipses at 
one of the orbit nodes. In place of the draconic, or nodal, month for 
eclipses, we insert the apsidal (anomalar, syzygy, anomalistic) month: 
    (interval of supermoon) = (yunodic month) * (apsidal month) 
                            / ((sunodic month)  - (apsidal month)) 

                            = (29.53 * 27.55) / (29.53 - 27.55) 
                           = 410.88 daus 
                          -> ~13-1/2 months 

Only the absolute value, without its signum, is needed, in case the 
subtraction is done in reverse. 
    This interval is for one end of the apsidal line, the perigee. The 
halfway interval applies for the apogee end for a minimoon. 
    Why isn't this formula the official rule for supermoon? The 
perigee, anf lineo f apsides, has a variable migration, progression, 
speed.  The supermoon could happen on the previous or following Full 
Moon. This interval is best treated as a filter to look for possible 
    Mind that in some instances, two or three adjacent Full Moons 
around each interval could qualigy as supermoons. This happens in 
December 2017-January 2018. 
    This 13-1/2 month inteerval applies to ANY lunar phase, age, 
elongation. not only for full phase. If a cultural or emotional 
calling attaches significance to the 10-day-old Moon when she is extra 
large, these instances occur, on average, 13-1/2 months apart. 

 The rule here 
    Many astronomy softwares can compute tables of assorted parameters 
or events. These save immense amounts of time and labor to hnt up 
supermoons. In my case I could develop a table of lunar passings thru 
key points around her orbit. Thesse include the quarter phases and 
apogee/perigee. The table was saved in text form, whence I shivved out 
extraneous events. I keeped all Full Moons and the perigees close to a 
Full Moon. 
    I also include the percent illumination, which for a Full Moon is 
100%. For me it was simplest to scan the initial tabular output for 
instances when a perigee occurred when the Moon was 100% lighted. To 
catch outlier events I keeped perigees with a 99% Moon, which in fact 
is indistinguishable from a true Full Moon. 
    The resulting table is here, where the supermoons are set apart 
from the normal Full Moons. I skipped the minimoon events for being of 
almost no public notice. 

 UT date & hour    EST   Moon       %Ill DisrKm Diam 
 ---------------- ------ ---------- ---- ------ ----
 24/01/ 2016 01:46 20:46 Full Moon  100- 387709 30.8'
 22/02/ 2016 18:20 13:20 Full Moon  100- 397959 30.0'
 23/03/ 2016 12:02 07:02 Full Moon  100- 404630 29.5'
 22/04/ 2016 05:24 00:24 Full Moon  100+ 406242 29.4' 
 21/05/ 2016 21:15 16:15 Full Moon  100+ 402675 29.7' 
 20/06/ 2016 11:03 06:04 Full Moon  100+ 394977 30.3'
 19/07/ 2016 22:58 17:58 Full Moon  100+ 384818 31.1'
 18/08/ 2016 09:28 04:28 Full Moon  100+ 374104 31.9'
 16/09/ 2016 19:06 14:06 Full Moon  100+ 364755 32.8'

 16/10/ 2016 04:24 23:24 Full Moon  100+ 358485 33.3' 
 16/10/ 2016 23:46 18:46 Perigee     99- 357865 33.4' 

 14/11/ 2016 11:21 06:21 Perigee    100+ 356536 33.5'
 14/11/ 2016 13:53 08:53 Full Moon  100- 356546 33.5'
 14/12/ 2016 00:06 19:06 Full Moon  100- 359470 33.2'
 12/01/ 2017 11:34 06:34 Full Moon  100- 366887 32.6' 
 11/02/ 2017 00:33 19:34 Full Moon  100- 377424 31.7'
 12/03/ 2017 14:55 09:55 Full Moon  100- 388866 30.7'
 11/04/ 2017 06:09 01:09 Full Moon  100- 398719 30.0'
 10/05/ 2017 21:44 16:44 Full Moon  100- 404906 29.5'
 09/06/ 2017 13:10 08:11 Full Moon  100+ 406241 29.4'
 09/07/ 2017 04:08 23:08 Full Moon  100+ 402592 29.7'
 07/08/ 2017 18:12 13:12 Full Moon  100+ 394787 30.3'
 06/09/ 2017 07:03 02:03 Full Moon  100+ 384388 31.1'
 05/10/ 2017 18:40 13:40 Full Moon  100+ 373418 32.0'
 04/11/ 2017 05:23 00:23 Full Moon  100+ 364009 32.8'
 03/12/ 2017 15:47 10:47 Full Moon  100+ 358002 33.4'
 04/12/ 2017 09:03 04:03 Perigee     99- 357505 33.4'

 01/01/ 2018 21:33 16:33 Perigee    1000+ 356584 33.5'
 02/01/ 2018 02:24 21:24 Full Moon  100- 356621 33.5'

 31/01/ 2018 13:27 08:27 Full Moon  100- 360201 33.2' 
 02/03/ 2018 00:52 19:52 Full Moon  100- 368033 32.5' 
 31/03/ 2018 12:38 07:38 Full Moon  100- 378494 31.6'
 30/04/ 2018 00:59 19:59 Full Moon  100- 389471 30.7'
 29/05/ 2018 14:21 09:21 Full Moon  100- 398830 30.0'
 28/06/ 2018 04:54 23:54 Full Moon  100- 404764 29.5'
27/07/ 2018 20:21 15:21 Full Moon   100+ 406071 29.4'
26/08/ 2018 11:57 06:57 Full Moon   100+ 402412 29.7'
25/09/ 2018 02:53 21:53 Full Moon   100+ 394471 30.3'
24/10/ 2018 16:46 11:46 Full Moon   100+ 383847 31.1'
23/11/ 2018 05:40 00:40 Full Moon   100+ 372711 32.1'
22/12/ 2018 17:49 12:49 Full Moon   100+ 363363 32.9'

21/01/ 2019 05:16 00:16 Full Moon   100+ 357722 33.4'
21/01/ 2019 19:49 14:49 Perigee      99- 357354 33.4'

19/02/ 2019 08:39 03:39 Perigee     100+ 356772 33.5'
19/02/ 2019 15:54 10:54 Full Moon   100- 356859 33.5'

    Astronomers generally calculate celestial events in UT,lo called 
GMT, and let the reader worry about a timezone shift. Look out for a 
UT/EST wrap around 00:00. The EST date is notched back one day from 
the UT date. 
    In the %Ill column a '+' means a waxing Moon; '-', waning. 
    In the Diam column the size is in archminutes. 

Other features of the table 
    For the three years 2016 thru 2018 the Full Moon angular size 
ranges from 29.4 to 33.5 arcminute. It may seem fossible to remember 
how big the Moon looked and now for the supermoon see how much bigger 
she is.  A 4-minute differnce should be obvious to ordinary vision. it 
would be in a side-by-side comparison. In a view of one without the 
other, as is the actual situation, the change of size is just not 
    Another confusion in judging angular size is the 'Moon illusion'. 
The Moon, een when not full, simply looiks large near the horizon than 
when she is in high sky. Since we usually noticee the Full Moon in 
early eveningm when she is still low in the skyline, she looks huge. 
This is how the public experiences the supermoon. 
    The table lists all Full Moons in the three years. See how the 
distance and diameter vary month by month as the Moon is near or far 
from perigee. The distance ranges from about 356,000 kilometers to 
about 406,000 kilometers. The spread of 50,000 ilometers is over 3-1/2 
times the Earth's diameter! 
    When the UT and EST hour wrap around 00:00 the local, in New York, 
date is notched back by one. This ro..over thru midnight is sometimes 
missed by experienced astronomers, causing their calcs to be off by 
one day. 

Triple Supermoon? 
    Normally for a given supermoon the adjacent Full Moons are too 
ar from perigee to be suepermoons. The killer phrase is 'too far from 
the perigee' because there is no generally accepted rule for assessing 
this condition. As a result some authors can claim that we have in a 
certain span two or three supermoons in succession. 
    One instance so claimed is in Dec 2017-Jan 2018 when we have  
three supermoons! Coming down the track is some news media hype as a 
rare triple supermoon. 
    These Full Moons by certain supermoon rules come 'close to 
perigee' to qualify as supermoons. They are on 2017 December 3, 2018 
January 1, 2018 January 31. There is no astronomy importance but the 
three do make for a winter of pleasing stargazing. 
    In my inquiry I find only a double suprmoon in Dec-Jan. The one to 
make a triple on 31 January misses because it is not 'full'. It's only 
98% lighted. This shows that we can not take an author's word without 
knowing how he selected his supermoons.  

2018 January 31 
    The Full Moon of 31 January 2018 has FOUR features in her! 
Accepting for now that she's a supermoon by a this or that rule, 
this Moon is eclipsed, makes a selenehelion, and is a blue Moon!  
The eclipse, a total, misses NYSkies land by beginning just before 
moonset. She sets with only a small segment of her upper limb obscured 
by the umbra. At the same time the Sun rises. 
    Observers in the Central timezone and farther west see most or 
all of the eclipse in darker dawn or full night. The see the Full 
Moon, restored after the eclipse, setting with the rising Sun.
    Here is the timetable of activity for the eclipse in New 
    ------------------------------------- -----
     EST  | event            | alt-az | remarks 
    05:51 | zeroth contact  | 12 282 | Moon enters paenumbra 
    06:04 | nautical dawn   | 10 284 | full night ends in New York 
    06:38 | first paenumbra  | 10 284 | first paenumbra shading 
    06:38 | civil dawn      | 04 288 | daytime work begins 
    06:48 | first contact   | 02 290 | partial phase begins 
    07:06 | Sun rises       | 00 292 | daylight begins 
    07:07 | Moon sets       | 00 293 | eclipse viewing ends 

    After moonset the eclipse continues under the horizon thru totality 
and beyond   Observers farther west of the City see more of the eclipse 
before their local moonset;. 
    'First paenumbra' is a nominal moment when the darker inner zone 
of paenumbra is first discernible on the Moon. It is a smoky or 
nebulous shading next to the point of first contact. I allow ten 
minutes before first contact, based on previous eclipses.

    This is a tough eclipse to observe due to strong dawn and low 
altitude. It could also be smothered in horizon haze or cloud. Mind 
that January 31st is in mid winter. Temperature can be 0C or below 
with strong wind chill factor, 
    We have a a true selenehelion, when a lunar eclipse occurs at 
sunrise/sunset. The soft rule is an uneclipsed Full Moon rising ar 
sunset or setting at sunrise. To apply this rule we must state the 
deviation from 100% full phase allowed at sunset/sunrise. Else we end 
up with the common case of a 'large moon' at these two times. 
    Like for any selenehelion you need an open view of the horizon, in 
the northeast for this one.
    NYSkies enjoyed a really rare selenehelion on 2014  July 11. This 
was during Manhattanhenge outside our Seminar room in 14th Street. We  
urged Manhattanhenge viewers to turn around and see the rising Full 
Moon! For a couple minutes as the Sun was setting in line of 14th St, 
the Moon was lifting out of the street in the east! 
    We have a blue Moon, the second Full Moon in January 2018. This is 
by the soft definition, not the hard one relating to the Full Moons 
per seasonal quarter of the year. 

    We miss most of te lunar eclipse on January 31st. We do catch the 
Moon on that date as a supermoon, selenehelion, and blue Moon. We also 
get the other two supermoons in the triple-play of Full Moons in 
    Play with your astronomy software to learn what compilations it 
can generate, like the table of Full Moons above. Not all programs can 
do this. Please cruise the software webs for your computer system to 
collect softwares that can let you exercise problems like supermoon, 
blue Moon, and selenehelioon 
    Please look at astrology software! Astrologers keep careful track 
of the Moon. For example, they mark on their horoscope  Lilith 
creature, the lunar apogee. Perigee is merely six signs away on the 
opposite side of the zodiac. Some astrology softwares have a search 
function to look for celestial events. You code the event, according 
to the program's instructions. The program output  a table of 
instances doe the event