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.