ECLISPE FACTS AND CONCEPTS
---------------------------
 John Pazmino 
 NYSkies Astronomy Inc
 www.nyskies.org
 nyskies@nyskies.org
 2014 July 11 initial
 2020 September 20 current 

Introduction
 ----------
 In 2013-2014  New York had several lunar and solar eclipses. By 
miserable luck all were totally or mostly clouded out. In preparation 
for each eclipse I wrote a feature article that also explained 
assorted concepts and facts about eclipses. 
     Much of this explanation was the same for all the eclipses and it 
made the articles a bit lengthy. I will no longer include this 
material in future eclipse preparation articles. 
    In the stead I gather it here in this one permanent piece that can 
be referred to on each occasion of an eclipse. 
    While I may revise this present article from time to time, I will 
not try to carry the revisions into the past eclipse articles. Those 
pieces are fixed, save for honest typographic and orthographic errors. 

Saros
 ---   
    A Saros interval contains 223 cycles of lunar phases, from new to 
new (solar eclipse) or full to full (lunar eclipse). These 223 cycles 
sum to 18y and 10-11 days, 8h. Most treatments of Saros make you count 
up the leapdays thru the whole 18 years. This is silly. Look for the 
FIRST leapday within the cycle. If it occurs within the first 24 
months, there are five leapdays in the cycle and he leftover days are 
10. If it occurs after then, n month 25 and beyond, there are only 
four and the leftover days are 11. That's all you have to do! 
    The Saros , and all other eclipse cycles, is not an integral 
number of days. It is 8h (rounded) more than full days. This means the 
Earth rotated about 1/3 more, making the eclipse take place father 
west  than the previous one in the Saros. After three Saros intervals, 
the 1/3 days accumulate to a full day and the eclipse then occurs in 
the same longitude belt as the initial one. 
    A solar eclipse occurs if the Moon crosses her nodal point at new 
Moon. This may be either the ascending or the descending node, so we 
have really two interleafed sets of eclipse operating simultaneously.  
    A Satos cycle begins when for the first time the Moon's shadow 
touches Earth at one of the poles, say the north one. Following 
eclipses in the cycle are laid down at from north to south, passing 
eventually over the equator. The after more eclipses are created 
toward the south pole. The cycle ends when the final eclipse misses 
the south pole. An other concurrent Saros starts at the south pole and 
deposits its eclipses toward the north pole. 
    Most readers forget that the Saros also contains 241 sidereal 
cycles of the Moon. The sidereal cycle is generally ignored because it 
does not contribute to the production of eclipses. 
   The Saros cycle does unravel after many rounds.. The slivers of 
inexactitude add up to drag the Moon and Sun out of line. No more 
eclipses are produced. A Saros begins when these slivers accumulate to 
push the Sun and Moon into alignment and start making eclipses. 
    Do mind that the Saros generates a series of eclipses spaced 18+ 
years apart. There are lots of other Saros cycles running during this 
interval, producing their own series of eclipses.  The number of 
concurrent cycles is found by counting the eclipses between two 
members of a given Saros. For example, for lunar eclipses, there are 
41 eclipses within the span 2000 Jan 21 and 2018 Jan 31. There are 41 
Saros series of lunar eclipses running at once. 
    There was a leapday within the first 24 months of this interval, 
on 2000 Feb 29, making five leapdays for this cycle.  The next eclipse 
in this cycle is 18y 10d (not 11d) 8h later, From the initial date we 
pace off 18 years, to 2018 Jan 21. Then 10 more days, to 2018 Jan 31 

Rule-of-19
 --------
    Many of us know the 'rule-of-19', by which a one eclipse is 
followed, or prreceded, by an other on the same calendar date but 19 
years later, or earlier. This works because 19 calendar years is quite 
235 lunations, 12 lunations longer than one Saros. 
the cycle producing  the rule-of-19 is the Metonic cycle, 19 solar 
years with 235 lunations. It just now is known more commonly by a 
modern name. After each round of the Metonic cycle the Moon is new 
again and stands in front of the Sun. Similar reasoning applies to a 
full Moon and lunar eclipses. 
    This rule applies also to lunar conjunctions and occultations of 
stars. It fails for planets due to the separate motion of planets 
along the ecliptic. Knowing when a specific one takes place, an other 
will occur 19 years later on the same date. By adding 13 sidereal 
periods to the 241 of a Saros, we have 254 cycles. This is almost 
exactly 19 calendar years of 365.25 days! 19 calendar years brings the 
Moon round to her initial location 
    The recurrence of an eclipse on the same calendar days works for 
the Gregorian calendar, which very well ties the calendar date to the 
Sun's ecliptic longitude. It bombs out for the Julian calendar and 
others not keeping pace with the solar year. 
    All of the above works for solar eclipses, but they occur in 
daytime when very few stars are seen in totality. It isn't easily 
noticed that eclipses in the rule-of-19 take place at the same 
location in the stars.
    The rule-of-19 is best demonstrated with a lunar eclipse. The 
eclipsed Moon stands in the same field of stars, seen at night. An 
other way is thru planetarium software that can turn off daylight. The 
Sun moves thru a dark sky with stars, like seen from an airless Earth. 

Mixed up rule 
 -----------
    When we were getting ready for the lunar eclipse of 2014 April 14, 
with its conjunction with Spica, some of us recalled a previous 
instance of a Spica-Moon eclipse. That one was on 1968 April 13. 
    This is NOT an even 19-year step back from 2014! Stepping back by 
9-years brings us to 1995, 1976, 1958, with no eclipse on or near 
April 15. What happened? 
    Like for the Saros, the rule-of-19 dissolves when the slivrs of 
error accumulate to shove the Moon, Sun, star out of line and produce 
no more eclipses. The 1968 Spica-Moon eclipse was one of a prior rule-
of-19 series and the 2014 one is tin the next series. The table here 
illustrates this transition  of series for the 20th and 21st century: 

    --------------
    LUNAR ECLIPSES 
    NEXT TO SPICA 
    -------------
    cyc1 | cyc2 | cyc3 
    -----+--- --+----- 
    1930 |  --  |  --
    1949 |  --  |  --
    1968 |  --  |  --
    1987 | 1995 |  --
     --  | 2014 |  --
     --  | 2033 |  --
     --  | 2052 | 2060 
     --         | 2079 
     --         | 2098 
    ------------------

    The tule-of-19 can work thru a single lifetime but not across 
generations. A similar analysis can be done for the Moon against any 
other fixed point on the zodiac, typicly a star or asterism. 

Lunar caution 
 ----------- 
    Please be extra careful when compiling timetables for the Moon. If 
For events spanning midnight your ephemeris generator may fold over 
the time sequence of lunar activity. Do a sanity check with a 
planetarium. 
    As an example the Moon rises on 2014 April 15 at 20:14 EDST. This 
is in the night of the 15-16, some 18 hours AFTER the lunar eclipse of 
the 14-15! The Moon rise you need is that on the 14th BEFORE the 
eclipse. That's at 19:10.  
    The error comes from our embedded thinking of solar time. The Sun 
rises, transits, sets within the same block of 24 clock hours. The 
Moon advances thru the zodiac 13ish degrees per solar day.  Her 
circumstances migrate some 52 minutes later on average. 
    If the ephemeris calculates events within a one given solar day, 
you could pick up a lunar event that's too early or too late in the 
sequence of activity you're assembling. 
    An other source of error is the shift of daylight and standard 
time near midnight. You could take information for a full day earlier 
or later. Midnight of April 14-15 in daylight savings time is 23h on 
April 14 in standard time. 

Lunar contacts 
 ------
    The 'contacts' listed in a timetable for a lunar eclipse are the 
various tangencies of the umbra with the lunar disc. Recall that the 
umbra is the very shadow of Earth projected directly behind the Sun. 
It is not seen be\cause normally there is nothing for it to fall onto. 
It blocks sunlight from the Moon when the Moon passes thru it and 
causes the lunar eclipse. 
    Surrounding the umbra is a less dark zone where sunlight is only 
partly blocked by Earth. This ts the paenumbra. It shades from full 
sunlight at its outer edge to quite deep darkness at its inner edge 
against the umbra. 
    For a total lunar eclipse there are four contacts. 

    --------------------------------------------------
    1st contact | 1st exterior tangency | partial phase begins 
    2nd contact | 1st interior tangency | total phase begins 
    3rd contact | 2ns interior tangency | total phase ends
    4th contact | 2nd exterior tangenvy | partial phase ends 
    --------------------------------------------------------
    In a partial eclipse we have only the 1st and 4th contacts because 
there is no totality. The Moon always shows part of her lighted disc. 
    -----------------------------------------------------------------
    1st contact | 1st exterior tangency | partial phase begins 
    4th contact | 2nd exterior tangenvy | partial phase ends 
    --------------------------------------------------------

    The paenumbra gradually shades darker inward toward the umbra. 
About 20 minutes before 1st contact, and for the same span after 4th 
contact, there is usually a brownish stain of the Moon at the contact 
points. For 1st contact this warns of the coming of partial phase. 
After 4th contact we get a last lingering shading of the Moon to 
finish the viewing session. 
    The graduation of shading in the paenumbra differs among eclipses 
and can not be reliably foretold. I always use a nominal 20-minute 
limit, based on the many lunar eclipses I've observed since the 1960s. 
    For eclipses where the umbra misses the Moon and she passes only 
thru the paenumbra we generally do not bother with viewing. We note 
the geometric moment when the outer limb of the paenumbra does 
exterior tangency with the lunar disc, as the 0th and 5th contacts,. 
These moments have no visible indication on the Moon.  

Solar contacts 
 ------ 
    As the Moon crosses the Sun in a solar  eclipse she touches the 
solar disc at several points of tangency, where the two discs meet at 
a point. From New York there is in the 2013 eclipse only one visible 
tangency of the two orbs. This is the 'fourth contact' mentioned a 
couple times above. 
    In an eclipse seen for its full duration there is a set of 
contacts for each kind of eclipse. For a total eclipse they are: 

        ---------------------------------------------
        1st - first exterior tangency, eclipse begins 
        2nd - first interior tangency, totality begins 
        3rd - second interior tangency, totality ends 
        4th - second exterior tangency, eclipse ends 
        --------------------------------------------

    Interior tangency hs the two orbs overlapping, the one nested 
within the other. Exterior tangency hs the two orbs touched next to 
each other. The Moon is invisible in the daylight around the Sun. 
    In a partial eclipse there are no 2nd and 3rd contacts because 
there is no total phase: 

        ---------------------------------------------
        1st - first exterior tangency, eclipse begins 
        4th - second exterior tangency, eclipse ends 
        --------------------------------------------
    For an annular eclipse the order of the contacts is shuffled 
because the Moon does not completely cover the Sun. The trailing edge 
of the Moon breaks onto the solar disc before the leading edge does. 
        ---------------------------------------------
        1st - first exterior tangency, eclipse begins 
        3rd - second interior tangency, annularity begins 
        2nd - first interior tangency, annularity ends 
        4th - second exterior tangency, eclipse ends 
        --------------------------------------------
 
Lunar  magnitude 
 -----=-
    One figure of merit for a lunar eclipse is its 'magnitude'. The 
greater this number, the more total is the eclipse. A value less than 
1.00 indicates a partial eclipse.  A negative value points to a 
paeumbral eclipse. The Moon misses te umbra and only the paenumbra 
lies over her disc. Such magnitudes are rarely cited because paenumral 
eclipses are generally neglected. 
     Sadly as it does happen, the explanation of this figure can be 
loused up badly. The usual statement is that the magnitude of an 
eclipse is the fraction of the lunar diameter overlapped by the 
umbra. By this rule all total eclipses have magnitude 1.00 because the 
entire diameter is obscured by the umbra. Yet total eclipses have 
magnitudes greater than one. 
    An other description says that the magnitude is the ratio of umbra 
to Moon diameter. This makes a fixed magnitude thruout the eclipse, 
ignoring phase. Here's the proper way to calculate an eclipse 
magnitude. 

    (ecl magn) = (Mrad + Urad - sep) / (2 * Mrad) 

    Mrad and Urad are the angular radius of the Moon and umbra. When 
diameter is given, take one half of it. Sep is the angular separation 
of Moon's and umbra's centers. 
    The magnitude of a lunar eclipse is the same for all observers. 
The eclipse takes place on a plane faceon to the observer, where any 
change in angular dimension is called equally for any remoteness of 
the observer on Earth's surface. 
    The magnitude is virtually always stated for the moment of maximum 
eclipse, when the separation of Moon and umbra is the least. As the 
Moon moves thru the umbra the center-center separation varies to yield 
a continuous gradation of the magnitude number. 
    The largest value of magnitude for a set of radii is a center-
over-center crossing of Moon thru umbra. The separation is zero and 
the formula reduces to (Mrad + Urad) / (2 * Mrad). This gives the most 
overrun of the umbra on the Moon. 
    It's possible to have zero and negative magnitude. A zero value 
indicates a grazing partial eclipse. The Moon just kisses the Sun at 
one exterior contact on the north or south lunar limb. A negative 
value, which I hardly ever hear of, means the Moon misses the umbra 
and does a normal Full Moon phase. There is no eclipse, except perhaps 
an overlay of only the paenumbra. 
    The table here gives the various scenarios of eclipse magnitude 

    ----------------
    magn    | scenarios 
    --------+---------- 
      < 0.00 | no eclipse, normal Full Moon 
        0.00 | graze partial eclipse 
      < 1.00 | prtial eclipse, Moon excentric from umbra 
      < 1.00 | deep partial eclipse 
        1.00 | graze total eclipse
      > 1.00 | normal total eclipse 
      ----------------------------                     

    A related figure is the obscuration of an eclipse. This is the 
fractional area of the lunar disc covered by the umbra.This is common 
for a solar eclipse but only occasionally cited for lunar ones, and 
then only for partial eclipses. 
    It is sometimes found by squaring the magnitude but this is not 
the way of computing it. You must go thru geometry of two overlapping 
discs of different diameters, for umbra and Moon, based on the data 
used for the magnitude. 
    Once the Moon is fully in the umbra, in a total eclipse, the value 
of obscuration remains constant at 1.00. It decreases when the Moon 
starts to quit the umbra exposing more of her disc. 

Solar magnitude 
 -----=-
    One figure of merit for a solar eclipse is its 'magnitude'. The 
greater this number, the more total is the eclipse. A value less than 
1.00 indicates a partial or annular eclipse. Sadly as it does happen, 
the explanation of this figure can be loused up badly. 
    The usual statement is that the magnitude of an eclipse is the 
fraction of the solar diameter overlapped by the Moon. By this rule 
all total eclipses have magnitude 1.00 because the entire diameter is 
obscured by the Moon. Yet total eclipses have magnitudes greater than 
one. An other says it's the ratio of Moon to Sun diameter. This makes 
a fixed magnitude thruout the eclipse, ignoring phase and parallax 
    Here's the proper way to calculate an eclipse magnitude. 

    (ecl magn) = (Srad + Mrad - sep) / (2 * Srad) 

    Srad and Mrad are the angular radius of the Sun and Moon. When 
diameter is given, take one half of it. Sep is the angular separation 
of Sun's and Moon's centers. 
    The magnitude in general tables of eclipses is stated for the 
geocentric observer. The figure given for a specific location on the 
Earth should consider the angularly larger Moon and the separation as 
modulated by parallax. 
    The magnitude is virtually always stated for the moment of maximum 
eclipse, when the separation of Sun and Moon is the least. As the Moon 
moves across the Sun the center-center separation varies to yield a 
continuous gradation of the magnitude number. 
    The largest value of magnitude for a set of radii is a center-
over-center crossing of Moon over Sun. The separation is zero and the 
formula reduces to (Srad + Mrad) / (2 * Srad). This gives the most 
overrun of the Moon on the Sun. 
    It's possible to have zero and negative magnitude. A zero value 
indicates a grazing partial eclipse. The Moon just kisses the Sun at 
one exterior contact on the north or south solar limb. A negative 
value, which I hardly ever hear of, means the Moon misses the Sun and 
does a normal New Moon phase. There is no eclipse, 
    The table here gives the various scenarios of eclipse magnitude 

    ----------------
    magn    | scenarios 
    --------+---------- 
     < 0.00 | no eclipse, normal New Moon 
       0.00 | graze partial eclipse 
    << 1.00 | partial eclipse, Moon excentric from Sun 
     < 1.00 | deep partial or annular eclipse
       1.00 | graze total eclipse 
     > 1.00 | normal total eclipse 

      ----------------------------

    A related figure is the obscuration of an eclipse. This is the 
fractional area of the solar disc covered by the Moon. It is sometimes 
found by squaring the magnitude but this is not the way of computing 
it.  You must go thru geometry of two overlapping discs of different 
diameters, for Sun and Moon, based on the data used for the magnitude. 
    Once the Moon is fully on the Sun, in an annular or total eclipse, 
the value of obscuration remains constant. It decreases when the Moon 
starts to quit the Sun, exposing more of his disc. 

Selenehelion
 ----------
    A selenehelion (seh-leh-neh-HEH-lee-yonn) is the simultaneous view 
of a lunar eclipse AND the Sun together in the sky. This sight can 
occur only near sunset or sunrise, with the Moon near the opposite 
horizon. There are many varieties of selenehelion, from requiring the 
Moon to be fully immersed in the umbra to allowing only part of the 
Moon to be covered by the umbra. The latter can be either for a 
partial eclipse, the moon never sinking completely into the umbra, or 
the partial phase of a total lunar eclipse. 
    Seeing the shadowed Moon, for a total covering, in a bright dawn 
sky is not an easy task! When considering that the umbra may be a dark 
one, where in a night sky the Moon is almost completely oblitterated, 
will surely make the Moon just about impossible to spot. A light 
umbra, making the disc a bright orange hue, offers a fighting chance 
to catch a selenehelion.
    A textbook selenehelion in New York City was on 2014 October 8. 
The Moon just about passed second contact when the Sun came up. As 
fate fell, the sky was hazy and partly cloudy, masking the scene for 
most observers in the City. Other selenehelia were in 1963 (sunrise) 
and 1976 (sunset). 
    A relaxed definition is that any full Moon, not only that in 
eclipse, is seen with the Sun. This is the tighter application of the 
loose fact that the full Moon rises at sunset and sets at sunrise. 
    Because the Moon looks quite round nd full a up to two days from 
geometric full phase, a tolerance, usually a number of hours, is part 
of the selenehelion definition.
    Full-Moon selenehelia occur a couple times per year. A good 
selenehelion occurred on 31 July 2015 at sunrise. It attracted 
substantial public notice in the newscasts of that morning. Full Moon 
was within an hour from sunrise and3 -1/2 de north of the ecliptic. 
    A spectacular full-Moon event occurred on 11 July 2014 DURING 
MANHATTANHENGE! Viewers favored by sightline both east and west along 
a manhattan street were thrilled to see the rising full Moon balancing 
against the setting Sun. 
    For New York, a full-Moon selenehelion requires that the Moon be 
north of the ecliptic, else it is still under the horizon at 
sunrise/sunset. 
    Casual observers may not wit for the full Moon but take in the 
sight of a large, nearly full, Moon at sunrise or sunset. This event 
akes place every lunar month, 12 or 13 times per year. 

lunar eclipse experiments 
 ---------    ----------
    The next total solar eclipse over New York is long off in the 
future. Total lunar eclipses come a couple per decade, offering 
chances to conduct simple experiments during totality. The next 
several sections describe some of them, all producing useful 
information that would be lost if there was only the normal full Mon. 

Umbral darkness 
 ------ ------
    The overall darkness of the umbra ranges widely across eclipses. 
    It may be a bright cherry red to dense charcoal gray. The former 
limit 
has a Moon that still outshines the planets and brightest stars. At 
the latter limit the Moon quite vanishes from view to the eye and is 
hard to recover in binoculars. 
    Some hint of the darkness can be foretold by volcanic activity on 
Earth. Excess high-elevation dust expelled from volcanos may block 
light from filtering thru the atmosphere. It doesn't reach tot he 
Moon. Yet for the most part, we merely let the Moon surprise us. 
    Over the decades various methods were tried to assess the darkness 
of the umbra. One was to see which of a set of lunar craters is 
visible under a specified telescopic magnification. 
    An other was to opticly shrink the Moon to a point and then 
compare it with stars seen by direct sight. One way to shrink the 
Moon, at least to a small size, is to look at her thru the wrong end 
of binoculars. 
    One older method was the Danjon scale, described from time to time 
in astronomy media prior to major lunar eclipses. It assigns a number 
to the umbra according as its color and texture. 
    No one method was generally accepted and the litterature on umbral 
darkness is spotty. 

Umbral size
 ---------
    By the late 1600s, after many lunar eclipses were studied with the 
newly developed telescope, we found that the umbral diameter is 
consistently a bit larger than the geometricly calculated one. The 
usual explanation since the early 20th century is that the sunlight 
passing around the Earth on its way to the Moon is refracted a bit 
outward to enlarge the shadow. But atmospheric optics should reduce 
slightly the umbra's size. 
    The effect is sometimes assigned to human physiology in the vision 
, yet it shows up in photographs. Continued efforts to measure the 
size of the umbra are still needed.
    The easiest way is to time when the umbra crosses various lunar 
topographic landmarks. Because the umbra moves slowly and has a 
diffuse edge, the timing can be taken to only a ten-second fineness at 
best. This is quite enough to define the actual umbra against the 
geometric one.
    The Moon is full for a lunar eclipse so the craters and other 
relief have no shadow. Pick in the stead bright and dark patches  over 
the disc. In many instances these coincide with craters, like Plato, 
Grimaldi, Tycho, Proclus. Choose the smaller ones to better fix a 
crossing point. When selecting features, refer to photographs of the 
full Moon, not just a lunar map or composite picture. You could by 
mistake pick a feature that under real full Moon conditions is 
oblitterated for lack of light-&-shade.
    Note the time, from a well-synchronized clock, when the umbra 
first touches, is midway over, and completely over the feature. Same 
process in reverse is done for the crater when it leaves the umbra. 
    By geometry or graphics you can work out the circle that best fits 
your timings and compare its diameter to the calculated one for the 
eclipse. It will almost always be a couple percent larger, the reason 
and cause still being unknown. 

Umbral texture 
 ------------
    The umbra is very unevenly shaded, making lighter and darker 
patches over the lunar disc. It's hard to depict the umbra shading 
because the lunar disc has its own light and dark patches in the maria 
and terrae. 
    Digital cameras offer an amazing faculty to remove the Moon's own 
irregular shadings and leave just those of the umbra. Take a picture 
of the Moon a few minutes before first contact before the eclipse. 
Then take pictures during the partial and total phases. 
    In the image processor do a 'subtract' of the fully lighted Moon 
from the eclipses Moon. The resulting image has only the dark-light 
pattern of the umbra. A sequence of these subtractions over the 
eclipse span shows the movement of the Moon thru the umbra.
 
Lunar heat 
 --------
    If you have CCD imagers, you could try measuring the sudden and 
drastic drop of temperature on a lunar crater as the umbra covers and 
uncovers it. A lot of interpretation of the measured brightness of the 
crater is called for, depending on the properties and behavior of your 
peculiar imaging system. Technical help from the system's manufacturer 
may be needed, plus filters for certain wavebands.
    If all goes well, you'll be astounded at the fall of heat in an 
eclipse. Within minutes after the umbra crosses a crater, the 
temperature drops from around +100C to -100C!! When the umbra clears 
the crater the temperature rapidly climbs back to +100C.
    During totality you may search for hotspots of internal lunar 
heat, places where heat is emitted in spite of the lack of sunlight. 
As I recall the findings are inconsistent over eclipses, which could 
be due to erratic action of the hotspots.

Occultations
 ----------
    There is a severe lack of detailed observations in the days 
surrounding full Moon. The Moon smothers fainter stars from view. Look 
up occultations occurring during the eclipse and try to time them. The 
Moon doesn't have to be fully umbrated. As long as the area around the 
contact point of the star is in umbra, you can get good timing. 
    The better lunar occultation trackers alert you to possible events 
during a lunar eclipse, even if you set the the program to exclude 
full Moon periods. 
    Occultation timings are still valuable in this day of precise -- 
to one meter resolution! -- tracking of the Moon by spaceprobes and 
laser ranging. Home astronomy work continues to supplement and cross-
check that of the spacecraft.
    Some occultation software don't recognize the dark lunar disc 
during an eclipse. They may see only that the Moon is full and skip 
over  occultations deemed too difficult to observe against a bright 
lunar disc. You may have to force the software to leave out the effect 
of phase. 

Variable stars
 ------------
    Every month the large Moon interferes with monitoring variable 
stars. In eclipse the Moon is faint enough to allow about as dark a 
sky as possible for your observing location. This sky lets you inspect  
k stars most affected by the Moon-gap. 
    A collateral project is nova search. The Moon gap reduces the 
ability to detect novae, or supernovae in other galaxies, as faint as 
when the Moon is absent or very small. Because the Moon is large for 
several days around full phase, a nova could erupt and start to fade 
without detection. The lunar eclipse gives at lest a hour or so of 
dark sky to do a quick look at your nova areas or galaxies. 
    Prepare for your work with all the needed charts, cut from the 
AAVSO website. Lay them out in an itinerary around the Moon. know well 
how to find the star's field quickly and confidently. For supernovae 
in other galaxies, be thoroly practiced to quickly find the targets in 
your scope. 
    Have in had arrangements to phone or email suspected nova or 
supernova to an astronomer who can confirm your report and assist in 
entering it with the appropriate clearing house of discoveries. Lunar 
eclipses take place at local night, when most astronomy resources may 
be out of reach.. make sure your partner knows about your 
nova/supernova watch. 
    Variable star times are cited in Julian Day Number. Be very 
careful to properly account for your timezone and midnight crossing 
when converting the calendar and clock to Julian Day Number. 

Meteor showers
 ------------
    A meteor shower may run during the large Moon span surrounding the 
lunar eclipse. With no eclipse the shower is usually passed over by 
observers for bring smothered by bright moonlight.. A total lunar 
eclipse gives the rare chance to fill in meteor information when it 
would else wise be lost. 
    For a long totality you can take breaks to inspect the Moon/ 
Meteor watches are done in spells of a half hour or more to accumulate 
a useful record of shooting stars. 

GLOBE at Night 
 ------------
    The nights selected for the GLOBE at Night campaign avoid large 
Moon. On the occasion of a total lunar eclipse you may capture 
additional sky measurements, if the GaN target constellation is also 
in the sky. qA clllateral opportunity comes with the eclipse for other 
sky transparency assessment exercises. 

Comets & aurorae
 ---------------
    If there be a nighttime comet, it'll show up better during the 
eclipse. I recall several instances when a comet could have been 
visible but for the large Moon in the sky. By the time the Moon moves 
along and shrinks in phase, the comet is fading away. 
    By spring 2014 solar activity may stay moderate or weak. There 
likely is little chance of catching an aurora during totality. Look 
around anyway! Scan around the northern quadrant for suspicious glows 
and patches, those not normal for you site. Then look again a couple 
minutes later because auroral features shift aspect quickly. 
    If by chance there is a lunar halo, the colors fade away to leave 
mostly red. Same for parselenia. 
    Like for nova searches, have a definite plan to phone or email a 
suspected comet to an astronomer who can confirm your find. 
 
Lunar meteors
 -----------
    This is a very long shot experiment. There is already a home 
astronomy program to look for the flash of a meteor colliding with the 
Moon. The observing is done on the dark side of the lunar disc during 
the regular cycle of phases. Meteor hunting quits when the Moon gets 
near full because there 
is then too little dark surface to monitor. This leaves each month a 
hole in the records for captured crashes of meteors and biases 
statistics about them.
    A lunar eclipse offers the chance to collect meteor crashes when 
otherwise they are utterly nonobservable. The search is done on the 
part of the Moon within the umbra. A given spot on the Moon can be 
watched for the whole span of totality at that spot, which will in 
general be different from the overall totality duration. 
    If you are planning videography for the Regulus occultation of 
2014 March 20,use that gear for this eclipse. Your rig must record 
stars of 6th to 8th magnitude, the typical brightness of a meteor 
flash on the dark side of the Moon. 
    Hook up the video device to a telescope to show the whole or major 
portion of the lunar disc in the field. A meteor can hit any where, so 
a wider area of lunar surface has a better chance of getting a strike. 
    Take videos within the umbra, keeping the lighted part of the disc 
out of the camera field. Start and stop the shoot at known moments, 
within a few seconds by a synchronized clock. 
    Examine the movie in slow motion to see if you got any meteor 
flashes. Overwhelmingly the odds are that you didn't. Yet, in spite of 
the long odds, home astronomers persevere and they did catch many 
meteor strikes. NASA has an office at the Marshall Space Flight Center 
to collect and coordinate such observations. 
    The time of the collision is taken from the frame rate and count 
of frames from the start moment of your video shoot. Depending on the 
capacity of your camera's memory you may have to do several runs each 
on a fresh memory device. 
    It is not really feasible to watch by eye at the telescope. The 
stress is much too great and you can very easily miss a flash, that 
lasts only a second or two. You do need the videography rig.

Nature studies
 ------------
    If you view from a place with interests in wildlife, you may try 
to monitor the actions of small animal s and insects during the 
eclipse. I don't know what to expect but I suppose that ants use the 
Moon to guide them at night. When the Moon is covered up how do the 
ants react? Do birds come to ground and wait out the eclipse? Do 
burrowing animals come out, thinking it's dark enough for safety? So 
crickets change their chirping? 

Solar protection
 -------------- 
    All future solar eclipses in New York are partial for the next 
couple decades. All requires full protection of the kind used for 
regular solar viewing. If you watched the 2004 and 2012 Venus transits 
with proper solar filters, they are the ones for solar eclipse.
    If you don't have eclipse-rated filters, GET THEM NOW!! Do NOT 
defer until the next solar eclipse rolls around. it. Supplies of 
filters may run out quickly when a solar eclipse approaches. 
    You need only low power to capture the full solar disc in the 
telescope field. There's nothing much more to see under high power. In 
case the Moon uncovers a sunspot or has a jagged limb, have a high 
power eyepiece to hand. 

Eclipse limits
 ------------
    Eclipse limits was a topic we older astronomers learned about but 
which today is more or less neglected. Probably no modern astronomy 
education purposely discuss it. The subject relates to the amount of 
off-line position of Sun, Moon, Earth, umbra that can still produce an 
eclipse. If these bodies (treating the umbra as a phantom body) were 
all points, we would never have eclipses. It is plain impossible to 
expect a perfect alignment of points. 
    The four bodies do have linear extent and, as seen from Earth, the 
other three have substantial angular diameter. Doe a lunar eclipse, as 
example, the Moon and umbra can stand a bit off of the lunar node yet 
still overlap. We still see a lunar eclipse, altho it is not a headon 
centered one. The eclipse limit is the distance off from the node for 
the bodies to produce eclipses. Beyond that distance the bodies miss, 
passing apart from each other, and there is no eclipse. 
    here I use typical diameters for the bodies to illustrate the 
concept. other treaties elaborate the calculations for the range of 
sizes the bodies can have. In fact, the limits are unique for each 
eclipse based on the instant diameters. 
    Qw use the parameters below as typical values. They are rounded 
somewhat to simplicity sake.

     ------------------------------------
    PARAMETERS FOR TYPICAL ECLIPSE LIMITS 
    -------------------------------------
   radius of Sun - - - - - 15 min 
    radius of Moon - - - - 15 min 
    radius of umbra  - - - 40 min 
    parallax of Moon - - - 60 min 
    inclination of orbit - 5.1 deg 
    --------------------------------

   NOTE WELL THAT THESE ARE NOT 'average' or 'mean' values but those 
that we eclipse observers use for quick calculations. If we find a 
result to be critical, we then look up and employ refined values. 
There are two situations for eclipse limits. For a lunar eclipse the 
aspect of the Moon is virtually the same for all observers who see the 
Moon during the eclipse. The difference in lunar and umbra size due to 
the exact distance of the observer ,on Earth's surface, to the Moon is 
negligible. 
    The aspect of a solar eclipse ranges from a complete miss of Moon 
past the Sun to full total or annular phase, as a function of the 
observer's location on Earth.  Due to the large diameter of the 
paenumbra of a solar eclipse, some eclipses have no total or annular 
phase. The umbra,  where the Moon is centered on the Sun, misses Earth 
over one or the other pole but the paenumbra drapes over the Earth. We 
handle this situation by looking at the extreme displacement of the 
Moon in the sky due to her parallax across the  radius of Earth. 
    Because we work on the inner surface of the celestial sphere we 
should bone up on spherical geometry.  We do well with plane geometry 
here because the Moon moves thru a narrow belt of the zodiac that can 
be unrolled into a flat strip. The error between calculations with  
the two geometries is too small to matter. 

Lunar limits
 ---------- 
    In the diagram below M is Moon,; N, ascending node; U, umbra; MN, 
Moon's orbit; MNU, orbit inclination; MU, ecliptic. In all scenarios 
here the umbra or Sun are centered on the ecliptic while Moon travels 
obliquely across them. I here work only with the downrange scene, 
where the Moon passed her node, but symmetry across the node gives the 
same result for the Moon approaching her Node. Similar symmetry logic 
applies to scenarios at the lunar descending node. 
    The Moon is so far downrange, east being to the left, that she 
just fits internally tangent within the umbra as her orbit diverges 
from the ecliptic.  This is a tangential total lunar eclipse. For 
distances nearer to the node, the Moon is well within the umbra for 
deeper total eclipse. 

            - /-\ 
          /  |M |\  ----- \ 
        /    \-/  \         \-----\ 
       |          |           -----\ N 
       |     U    | ----------------\-----
        \         /                  \ 
         \---- -/                     \-----

    In the triangle MNU, side MU is the radius of umbra minus radius 
of Moon, or 40 min - 15 min = 25 min. Angle MNU is 5.1 deg. Angle UMN 
is 90 deg. Side NU is 

    NU = MU / tan(MNS)  
       = 25 min / tan(5.1 deg) 
       = 25min / 0.0893 
      = 280.1195 min 
     =  4.6687 deg 

    Doubling this to include the symmetrical case on the other side of 
the node, we have that the Moon can create a total eclipse within a 
zone 9.3373 4deg centered on the node. 
    We do the same analysis for the Moon just grazing the umbra for a 
tangential partial eclipse. 

              /-\ 
             |M |   ----- \ 
        /   -\  /           \----- \           
          /      \                   \-----\ 
        /         \                        \  -----\ 
       |          |                                 \   N 
       |     U    | --------------------------------- -\---- 
        \         /                                     \ 
         \---- -/                             

    The distance MU is now the umbra radius plus the Moon radius or 35 
+ 15 = 50min. The rest of triangle MNU are the same as for the 
tangential total eclipse. The downrange distance NU is 

    NU = MU / tan(MNU)  
       = 55 min / tan*5.1 deg) 
       = 55 min / 0.0893 
       = 615.9015 min 
       = 10.2650 deg. 

    Doubling this for symmetry, the limit for partial lunar eclipse is 
1s  20.5300deg 

Solar limits
 ----------
    The limits for a soar eclipse are complicated by the large 
parallax of the Moon for observers over the Earth's daytime face. With 
the Sun and Moon of just about the same angular size, 15 min for this 
work, the leeway for a headon total solar eclipse is essentially zero. 
Moon must sit accurately on her node to fit snugly over the Sun. 
    If the Moon is off of the node, she could still cover the Sun for 
an observer away from the headon center of Earth, toward the polar 
regions. The limiting case is when the Moon is displaced from the 
ecliptic by its full parallax, causing a total eclipse at the very 
pole of Earth. I do neglect the small but finite size of the Moon's 
shadow on the ground, yypicly 100-200 km. 
    In the diagram below S is Sun; M and N, Moon and node. MS is 60m 
in, the parallax of Moon displaced to the north, in this scenario, 
pole. An observer there sees the Moon  shoved back south to sit on the 
Sun for a total eclipse. 

              /-\ 
             |M |   ----- \ 
            -\  /           \----- \           
                                     \-----\ 
                                           \  -----\ 
              /-\                                                 \   N 
              |S | --------------------------------- -\---- 
             -\  /                                            \ 

    For most stargazing we ignore parallax. We see the Moon in the sky 
and aim our scope to her directly with no concern that for a remote 
observer the Moon is shifted among the stars. We must factor in 
parallax for occultations and close conjunctions as well as for solar 
eclipses. 
    The downrange distance NS is

    NS = MS / tan(MNS)  
       = 60 min / tan*5.1 deg) 
       = 60 min / 0.0893 
       = 671.8925 min 
       = 11.1982 deg 

    Including the west side of the node to double this distance the 
total solar eclipse limit is 22.3964 deg 
    For a partial eclipse the Sun and Moon are externally tangent, 30 
min apart for the headon case. We could now compute the limit for a 
headon partial eclipse but this has little significance. We go recta 
mente to the extreme with parallax. 
    Except for scale the diagram above will serve us. Distance MS is 
now 75min, the 15min to get the headon tangential partial eclipse plus 
the 60min for parallax.

    NS = MS / tan(MNS)  
       =90 min / tan*5.1 deg) 
       = 90 min / 0.0893 
       = 1007.8387 min 
       = 16.7973 deg 

    Taking both sides of the node we have the partial solar eclipse 
limit is 33.5946 deg 

    The table here summaries our results. Values are rounded to the 
  tenth degree. 

        -------------------------------
        TYPICAL VALUES FOR ECLIPSE LIMITS 
       distance on each side of node 
        ---------------------------------
        total lunar eclipse - - - -  4.7 deg 
        partial lunar eclipse   - - 10.3 deg 
        total solar eclipse - - - - 11.2 deg 
        partial solar eclipse   - - 16.8 deg 
       ----------------------------------------
       
Frequency of eclipses
 -------------------- 
        --------------------------------------
    The size of the limits determines the likelihood of having lunar 
or solar eclipses each year. As an example I stepped thru a made up 
year where the first full or new Moon occurs just after the east limit 
for partial eclipses.  This has the larger limit than for total 
eclipses and allows for having an eclipse of any kind during the year.
The year starts on March 20 with ecliptic longitude 0deg and runs the 
the next March 20. 

Interaction of Moon and nodes 
 ---------------------------
    The eclipse limits and seasons produce eclipses usually four per 
year. The maximum number is seven, two in January, three in June-July, 
two in December. 
    The conventional guidance says that there a year could have no 
lunar eclipses. This neglects paenumbral eclipses, which are hardly 
observable due to the weak shading of the Moon by the paenumbra. 
Paenumbral eclipses have a much larger distance of Moon from a node to 
to generate eclipses. This is because the paenumbra is much larger 
than the umbra and presents a larger target for the Moon to hit when 
near a node. As a result, there are lunar eclipses probably in every 
year, even if all for a given year are paenumbral. 
    On the other hand there must be at least two solar eclipses in a 
year. The limit for solar eclipses covers the whole Earth, pole to 
pole, with the Moon's parallax factored in. 
    The table here give the relation of the Moon to her nodes and 
eclipses for year 2010. Column 'lon' is the ecliptic longitude (round 
degree) where the Moon passes thru the event.      wHen the new/full 
moon is close to a node, an eclipse occurs. The proximity of node and 
phase at an eclipse is flagged by 'L' for lunar; 'S', solar. 

    -----------------------------
    MOON, NODES, ECLIPSES IN 2010 
    -----------------------------
   UT day & hr | lon | event
1--------------+-----+------
    Jan 01 12h | 110 | dscending node 
  S Jan 14 23h | 291 | ascending node 
  S Jan 15 07h | 295 | new moon 
  S Jan 15 07h | 295 | SOLAR ECLOPSE 
    Jan 29 00h | 111 | descending node 
    Jan 30 06h  1262 | full moon 
    Feb 11 05h | 291 | ascending node 
    Feb 14 02h | 325 | new moon 
    Feb 25 09h | 110 | descending node 
    Feb 28 17h | 160 | full moon 
    Mar 10 08h | 289 | ascending node 
    Mar 15 21h | 355 | new moon 
    Mar 24 13h | 107 | descending node 
    Mar 30 02h | 189 | full moon 
    Apr 06 10h | 287 | ascending node 
    Apr 14 13h |  25 | new moon 
    Apr 20 14h | 105 | descending nodew 
    Apr 28 12h | 218 | full moon 
    May 03 13h   286 | ascending node 
    May 14 01h |  53 | new moon 
    May 17 16h | 104 | descending node 
    May 27 23h | 249 | full moon 
    May 30 18h | 285 | ascending node 
    Jun 12 11h |  84 | new moon 
    Jun 13 22h | 102 | descending node 
  L Jun 26 12h | 275 | full moon 
  L Jun 26 12h | 275 | LUNAR ECLIPSE 
  L Jun 27 01h | 282 | ascending node 
  S Jul 11 07h | 102 | descendingg node 
  S Jul 11 20h | 104 | new mooon 
  S Jul 11 20h | 104 | SOLAR ECLIPSE 
    Jul 24 07h   281 | ascending node 
    Jul 26 02h | 303 | full moon 
    Aug 07 17h | 101 | descending node 
    Aug 10 03h | 137 | new moon 
    Aug 20 12h | 281 | ascending node 
    Aug 24 17h | 331 | full moon 
    Sep 04 00h |  99 | descending node  
    Sep 08 11h | 166 | new moon 
    Sep 16 14h | 279 | ascending node 
    Sep 23 09h |   0 | full moon 
    Oct 01 03h |  97 | descending node 
    Oct 07 19h | 195 | new moon 
    Oct 13 16h | 276 | ascending node 
    Oct 23 02h |  30 | full moon 
    Oct 28 03h |  94 | descending node 
    Nov 06 05h | 224 | new moon 
    Nov 09 20h | 273 | ascending node 
    Nov 21 12h |  56 | full moon 
    Nov 24 06h |  93 | descending node 
    Dec 05 18h | 254 | new moon 
    Dec 07 01h | 271 | ascending node 
  L Dec 21 08h |  88 | full moon 
  L Dec 21 08h |  88 | LUNAR ECLIPSE 
  L Dec 21 14h |  93 | descending node 
  -----------------------------------   

    The descending node retrogress from longitude 110 to 88 degree; 
ascending, 291 to 271. A complete lap of a node around the ecliptic 
takes some 18 years. 

Eclipse seasons
 -------------
    The eclipse limits allow the Moon to be some distance from the 
node at new or full phase and still create an eclipse. It turns out 
that there are usually two eclipses in a given lunation, a solar and 
lunar, or vice versa, spaced about 15 days apart. Some times there are 
three eclipses, bridging two lunations, solar-lunar-solar or lunar-
solar-lunar. After the last eclipse the Moon comes to the node too far 
to produce eclipses. The set of two or three is an eclipse season. 
This does not mean all the eclipses a re visible from a given 
observer's location. some may occur in other parts of the world. 
    The continues thru new or full phase in following lunations but 
too far north or south. We see ordinary nw and full moons. After  
five lunations the Moon approaches the opposite node and can start 
producing eclipses again. We can get a new set of two or three 
eclipses before the Moon once more recedes too far away from the node.
    She does this in turn passing the one node in one season and the 
other in the next season. Within a season the solar eclipses occur at 
one node; lunar, the other. The nodes are swopped season by season. 
    The interval between  seasons is a bit irregular from the chance 
of having two or three eclipses. It averages out to 346.58 days, 
between eclipses at the same node, in alternate seasons. This interval 
is called the the eclipse year, spanning two consecutive eclipse 
seasons. On the calendar seasons are spaced about 5-2/3 months 
apart, 11-1/3 months for the full eclipse year. 
    The month is 30-31 days (neglecting February for now) while a 
lunation is 29-1/2 days. The eclipse seasons, year to year, slide 
backward on the calendar, taking place earlier by 1/3 month. 
    The longer calendar moth can hold all three eclipses of a season. 
The two lunar, or solar, eclipses are at the ends of the month. The 
other type is in the middle of the month. Usually a season overlaps 
into the next or previous month. 
    There are normally two seasons in a year. Occasionally three will 
fit. The ones in January and December extend into the adjacent year, 
with only one or two of the eclipses inside the instant year. The 
third season is in June-July. In such years there can be the maximum 
seven number of eclipses, taken from all three seasons. 
    The timeline here for years 2000-2009 shows the layout of eclipse 
seasons. To better bring out the seasonal pattern I included 
paenumbrallunar eclipses.

 -----------------------------------------------------
       Jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dec 
 2000 |--l|S--|---|---|---|---|SLS|---|---|---|---|--S| 
 2001 |L--|---|---|---|---|-LS|---|---|---|---|---|-SL| 
 2002 |---|---|---|---|--L|-SL|---|---|---|---|--L|S--| 
 2003 |---|---|---|---|-LS|---|---|---|---|---|L-S|---| 
 2004 |---|---|---|-S-|L--|---|---|---|---|-SL|---|---| 
 2005 |---|---|---|S-L|---|---|---|---|---|SL-|---|---| 
 2006 |---|---|-LS|---|---|---|---|---|L-S|---|---|---| 
 2007 |---|---|LS-----|---|---|---|--L|-S-|---|---|---| 
 2008 |---|S-L|-------|---|---|---|SL-|---|---|---|---| 
 2009 |--S|L--|-------|---|---|L-S|-L-|---|---|---|--L| 
 ------------------------------------------------------

    In this range years 2000. 2001. 2009 have whole or part of three 
seasons. The other years have two seasons.A season can run in a give 
month for two or three consecutive years, then the next running in 
that month is about 9-10 years later. This is half of a Metonic cycle, 
or half of the rule-of-19. Both of these apply to one of the two nodes 
of the Moon's orbit. Taking both nodes, we have the half-cycles. 

Tetrad 
 ----
    Lunar or solar eclipses occur at either node during the year. 
Usually one node is missed, reducing the number of eclipses for that 
year. In 2014-2015 we a treated with a series of four total lunar 
eclipses at sequential nodes, spaced 5-6 months apart. The series 
started with the lunar eclipse of 2014 April 15 and ends with that of 
2015 September 28.  A run of four total lunar eclipses, one at each 
node intercept in sequence, is a tetrad. The four eclipses must be 
total, with no intervening partials. 
    There is no special astronomy significance, other than a more 
frequent chance to see en eclipse, four times, neglecting timezone 
effects, in two years.  As it happened, the 2015 Apr 4 eclipse was 
missed in New York by timezone. Bad fate clouded out the other three 
eclipses in the City. 
    In addition, for this particular series, the eclipses were at full 
Moons defining Hebrew major holidays. Recall that the Hebrew calendar 
starts each month at first Moon, the thin crescent immediately after 
new Moon. The full Moon is the 15th day of that month by convenience 
sake because it was really rough to fix by bare eye the actual day 
when the Moon was geometricly full.
        A lunar eclipse on a Hebrew holiday is sometimes called a 
'Blood Moon', altho thee is no extra cautions or prparations for the 
holidays. Sometimes dire claims of disaster are issued both in favor 
of and disgavor to the Jews. All such prediction are duds. 
    The four eclipse of the 2014-2015 tetrad are

    --------------------------------
    date        | Hebrew holiday 
    ------------+-------------
    2014 Apr 15 | Passover
    2014 Oct  8 | Sukkoth 
    2015 Mar 20 | solar eclipse on Nisan new moon 
    2015 Apr  4 | Passover 
    2015 Sep 28 | Sukkoth 
    ---------------------

    This tetrad was quite rare because in the middle, between the 
lunar eclipses of 2014 and of 2015, there was a total solar eclipse. 
It occurred at the Nw Moon of Hebrew month Nisan. Some extra troubles 
for the world were foretelled for that eclipse! 
    Tetrads are rare without connection to Hebrew holidays. They also 
occur at irregular intervals. There were NO tetrads in the 17th thru 
19th centuries.  then we enjoyed FIVE in the 20th. We are excedingly 
blessed to have in this 21st century EIGHT tetrads! 
    The eclipse of 2015 April 4. flagged by '*', is a borderline total 
of magnitude a tick greater than 1. Some  computations show this 
eclipse as a partial  with magnitude a hair-width less than 1. 
    The table here shows all the tetrqads of the 16th-21st centuries. 

    ----------------------------------------------
    TETRADS IN 16TH-21ST CENTURIES 
    ----------------------------------------------
    last tetrad of 16th century 
    1580 Jan 31, 1580 Jul 26, 1581 Jan 19, 1581 Jul 16 
    ----------------------------------------------
    no tetrads from 1582 thru 1908 
    -----------------------------------------------
    1909 Jun 04, 1909 Nov 27, 1910 May 24, 1910 Nov 17
    1927 Jun 15, 1927 Dec 08, 1928 Jun 03, 1928 Nov 27
    1949 Apr 13, 1949 Oct 07, 1950 Apr 02, 1950 Sep 26
    1967 Apr 24, 1967 Oct 18, 1968 Apr 13, 1968 Oct 06
    1985 May 04, 1985 Oct 28, 1986 Apr 24, 1986 Oct 17 
    -------------------------------------------------
    2003 May 01, 2003 Nov 09, 2004 May 04, 2004 Oct 28 
    2014 Apr 15, 2014 Oct 08, 2015*Apr*04, 2015 Sep 28 
    2032 Apr 25, 2032 Oct 18, 2033 Apr 14, 2033 Oct 08 
    2043 Mar 25, 2043 Sep 19, 2044 Mar 13, 2044 Sep 07 
    2050 May 06, 2050 Oct 30, 2051 Apr 26, 2051 Oct 19  
    2061 Apr 04, 2061 Sep 29, 2062 Mar 25, 2062 Sep 18 
    2072 Mar 04, 2072 Aug 28, 2073 Feb ,22 2073 Aug 17 
    2090 Mar 15, 2090 Sep 08, 2091 Mar 05, 2091 Aug 29 
    --------------------------------------------------

    I recall the tetrads of 1967, 1985, and 2003. Many of their 
eclipses were clouded out or were under the horizon at New York. I do 
not recall anything special claimed for them like for the 2014-2015 
tetrad. The sequence of four total lunar eclipses was treated as a 
curious result of general eclipse mechanics. 

No more total solar eclipses 
 --------------------------
    The phaenomenon of a total solar eclipse on Earth is unique in 
this solar system. Other planets have moons that cover the Sun but 
they are angularly either much larger or much smaller than the Sun.The 
effect of a surrounding aura, there is no corona, with prominences and 
chromosphere that shine for a few minutes over the observer. 
    It is only be a freak accident Sun and Moon are almost the same 
size to create the apparition of a total solar eclipse. In fact, the 
size of the Moon is gradually decreasing due to her recession from 
Earth. The angular size of Sun is gradually increasing as he continues 
to evolve in his stellar life cycle. 
    There is a time way in the future 
when the Moon will always to small to completely hide the Sun and we 
have no more total solar eclipses. All central solar eclipses will be 
annular with a ring of the solar disc surrounding the Moon. Thee's no 
cause for short term concern. All plausible future generations of 
astronomer will continue to enjoy total eclipses of the Sun. 
    I here give a simplified method to guesstimate when total eclipses 
end, based on the measured recession of the Moon by the laser 
reflectors left there by various lunar spaceprobes. We allow that the 
current rate prevails into the indefiinite future, which may be 
stretching the trend a bit. 
    The Moon is creeping away at about 22 millimeters per year[!] by 
the exchange of angular momentum between her and Earth. Already we 
have a good mix of annular and hybrid eclipses because frequently the 
Moon's shadow does ot quite reach to the ground. The portion of totals 
will decline as the angular diameter of Moon shrinks by her recession. 
    I take the critical case of the eclipse occurring in the local 
zenith when the Moon is closest to the observer, some 377,600km. This 
is the mean distance of Moon from Earth's center minus the 6,400km  
radius of Earth at the observer. 
    In all of this piece I assumed Moon and Sun to be exactly the same 
angular size. If we keep this premise we should lose our total 
eclipses on the day after I send this article into the NYSkies web.
    I here allow that the Moon is 31min diameter against Sun's 30min 
to force totals for a while while still having substantially the same 
size for both bodies.  I also could not find consistent estimates of 
the solar expansion rate from, say, 30min to 31min. I read some 
estimates that the Sun may reach 33min diameter before it shifts 
energy production away from the Main Sequence. I leave the Sun alone 
for now at 30min on the hope that the Moon will kill off totals by her 
recession long before the Sun swells out.
    A shrinkage from 31mi to 30min is 0.9677 ratio. With the angles 
hee so small this ratio is the reciprocal of the distance increase, 1 
/ 0.9677 = 4.033. The Moon must slid  e outward some 3.33% farther 
than she orbits now.  This is some 12,586km. It is only by coincidence 
that this is so nearly the diameter of Earth. 
    The time to move away is then 12,586km / 22mm/yr = 572.0909 
million years[!], With the simplifications cranked into this 
calculation, we should state this as 572 million years.
    Amazingly, this is within the range of other estimates I come 
across computed by far fancier methods. The point is that it will be a 
long while before far future peoples will know of total solar eclipses 
only from legend and song. 
    
Conclusion
 --------
    The material here is more or less permanent across eclipses and is 
not repeated for future articles for specific eclipses. The last 
article with this material in it was for the lunar eclipse of 2014 
April 15.