FACTORS FOR FIRST CRESCENT
------------------------
John Pazmino
NYSkies Astronomy Inc
www.nyskies.org
nyskies*nyskies.org
2020 April 14
Introduction
----------
In the past several years NYSkiers took up interest in the
astronomical ways of regulating calendars. In particular they started
anew observing project, spotting the first Crescent that begins
certain important months.
Many early peoples marked time by the motion of the Moon thru the
zodiac. The period of one round of the zodiac is 29-1/2 days for a
Sun-to-sun lap. For a star-to-star lap it's 27-1/6 days.This period is
close to 1/12 of a solar year, making it a convenient timespan to
govern society's chores and mind the seasons.
The month began cy actually seeing the Moon first come around into
the evening sky after her New phase. This is 'First crescent' and is
usually seen on the day after New Moon. The month then after is
clocked off by the position of the Moon among the stars and her phase.
the month ends with Last Crescent just before the next new Moon. This
is seen in the morning sky before sunrise.
For astronomers in New York there are two First Crescent of
interest, induced by the social composition of the City
. One is the one beginning of Nisan, the Hebrew month that leads
into passover and Easter. This occurs in early spring each year,
forced there by adjustments in the hebrew calendar to match the lunar
month with the solar year.
The other begins Ramaadan in the Moslem calendar. In 2020 it occurs
in April. The Moslem calendar ignores the solar cycle and counts of
twelve lunar month to the year. Ramadan, and other Moslem months,
carousel thru the solar year.
There is an other First Crescent of potential interest for New
York but there is so far little motive, yet?, to witness it. This is
as associated with Chinese New Year, It came in January for 2020 with
the parades and festivals in the City's Chinese districts..
I give here the physical, natural, principles of first Crescent.
All First Crescent observances are modified by other rules specific to
each culture.
First Crescent
------------
The Moon from the beginning of sky awareness was an easy,
reliable, continuous marker of time. She runs thru the zodiac in a
convenient manageable period, which is some 12-1/3 rounds per solar
year. Nota bene that this is not a whole number of months.
While it takes some skill to follow the motion of the Sun, even
tho it correlates to the seasons, the Moon is seen against the stars
and goes thru changes of shape, the phases. Against the stars the Moon
takes 27-1/3 day to round the zodiac for one sideteal period. The
synodic period, one cycle of phases against the Sun, is 29-1/2 dasy.
This is the usual meaning of 'lunar month'.
The month in many early calendar schemes starts when the Moon
first emerges out of the Sun's glare soonest after sunset. This can
happen on the day after or maybe the second day after New Moon. This
sighting of the Moon to initiate a new month is First Crescent.
From the evening of First Crescent. day #1 of the month, other
important dates are set. These could be keyed toother lunar phases,
most commonly Full Moon. It is from this means of declaring the start
of a new month that some calendars still begin the day at sunset, not
midnight. The day then runs to the next sunset.
The watch for First Crescent wasn't a reckless hunt night after
night. The skywatchers saw the Moon al during the previous month,
until she was a waning crescent in the east before sunrise. They knew
that after the final sight of the Moon, she passes New Moon phase and
emerges in the evening sky was a waxing crescent.
from the last view of the Moon they figured to start looking for
First Crescent two days later. This gave the Moon time to round New
Moon and recede eastward fro the Sun.
Since under bare-eye observation it is impossible to tell just
when the moon is geometricly full, Full Moon was often set by rule. In
the Hebrew calendar it is day #15 of the month, 14 days after First
Crescent.
It was always a struggle for early calendar schemes to mesh the
solar year with the lunar months. About 12-1/3 lunar months fit into a
solar year. Some calendars like the Moslem one, let go of the solar
year, probably because it was established in desert regions with no
strong seasons. It Its year is 12 lunar months, with no adjustment to
keep up with the solar year.
The Hebrews have a base lunar year of 12 lunar months. when the
shortfall approaches one more lunar month, roughly every three years,
an additional 13th month is inserted. A schedule of years with and
without the added month is part of the cultural rules of the calendar
system.
Societies with solar calendars often divided them into 12 more or
less equal parts, some 30 days long, as months. Our modern civil
calendar os of this kind. The months remain as a handy right-size
division of the year, recalling the synodic period of the Moon.
Egyptians
-------
The Egyptian society had two calendars. The civil calendar was
solar based with 365 days. The leftover 1/4 day was ignored with no
leapday feature. It served for business, government, civil affairs.
The cultural calendar was lunar based, used for keeping track of
festivals and celebrations. It banked off of Last Crescent, not First
Crescent.
Last Crescent is the final sighting of the Moon before vanishing
near the Sin near sunrise. The Egyptian day began at sunrise, not
sunset. Calendars based on First Crescent, like the Hebrew's, the day
begins at sunset.
The use of last Crescent to mark months derived from the geography
of Egypt. 1The Egyptians lived along the Nile river, which flows south
to north. The right bank was convenient to hills, woods, and the Red
Sea. These provided game, relief from hot, lumber, fruit, water
transport to the Mid East and African coast. In fact, they built a
canal from the Nile, downstream from modern Cairo, to the Red Sea. Is
remanents are now a tourrist attraction.
The left bank fronts the Sahara desert, of indefinite extent and
offering little resources. There were no other substantial peoples for
interaction..Egyptians traveling without proper provision and
protection into it faced almost certain death.
The society reserved the east side of the Nile for human activity.
This gave easy access to the resources there and avoided countless
trips back and forth across the river.
The west bank was reserved for the dead, with cemeteries, tombs,
pyramids, necrpppolites. No one frequented the west bank except for
visits, burials, property maintenance..
It seemed reasonable that the rising Sun, in the east over the
land of the living, begins the day. It cleared the sky of darkness,
gave light and warmth to the land, revived human activity after sleep.
this was the time to watch the waning Moon in her last appearance
ahead of sunrise, the Last Crescent.
The Egyptians treated the setting Sun, in the west over the land
of the dead, as the end of life, shutting off light and warmth,
suspending human activity, inducing sleep.
Directions
--------
For this article I use the astronomical directions of east-west on
the Moon. In this method, used by astronomers until the 1970s, treats
the Moon as a disc attached to the celestial sphere. When the Moon is
a waxing crescent the side of the Moon lighted by the Sun, the very
crescent itself, faces toward the west in the sky and is the west
limb, edge, margin.
The opposite side, on the night side of the Moon, is the east
limb.
The west edge is also the trailing or following edge because
against the stars it trails, follows, the Moon in her motion. An
occulted star emerges from the west limb.
The east limb is also the leading, preceding, edge. A star
immerges into it when occulted.
Noeth and south are the directions toward teh north and south
celestial pole. This is distinct from north and south on the lunar
surface, which are tied to the Moon's own poles.
The astronomical east-west is distinguished from the astrnautical
directions. In this scheme the Moon is a globe in space. The edge
lighted for First Crescent is the east edge and the opposite one is
the west limb.
Astronautical directions were introduced in the 1970s by the space
projects. They sent probes to the Moon and, with no Earth sky to
provide directions, had to consider the Moon as a whole other world
like Earth. a collateral shift was the flip of lunar maps ad
pictures. Traditional astronomy oriented these with south at top,
matching the classical inverted view in telescopes. Astronautical maps
and pictures have north at top like for views of Earth.
Picture Earth with North America facing us. Atlantic Ocean is on the
east side of Earth; Pacific Ocean. west. We continue with the
astronomical scheme in this article.
The sketch here may keep things right way round
A B
N N
N - -
| / \ / \
R -+--W E |Moon| W W |Moon| E
| \ / \ /
S - -
S S
Scene a shows a compass rose on the celestial sphere near the
Moon. the Moon is a flat disc on the sphere and takes on its
directions. This is the astronomical direction system.
The astronomical convention of showing the Moon with south at top
is imitated by turning the page to put the text upside down.
Scene B is the Moon in space, as seen by an approaching
spaceprobe. It's directions are laid on a globe, not a flat disc, like
for Earth. this is the astronautical system.
There seems to be no trend to invert an astronautical picture of
the Moon with south at top.
Age and phase
-----------
The elongation of Moon from Sun is counted continuously from zero
at New Moon round to 360 degrees at the next New Moon. Since it takes
29-1/2 days for a cycle of phases, the synodic period, the 'age' of
the Moon is clocked off by 12.2 deg/day. a three-day old Moon is some
37 degrees elongation from the Sun,.
In general the age of the Moon is
age = elongation / 12.2deg/day.
This is at average lunar speed, ignoring variations around her orbit.
The concept of age comes from a common ancient belief that the
Moon actually dies when she enters New Moon phase. A whole new Moon is
created after that new Moon. This concept carries into home astronomy
because most observe the Moon at daily intervals. The Moon seems to
notch forward day by day. Smooth flowing motion comes into play for
special occasions like eclipses and occultations.
New Moon can occur at any hour within its day, not only at sunset.
The elongation thenafter generally does not equal an integral number
of days. A 'three-day' Moon may be any age from 2.5 to 3.4 days, by
elongation, for a New Moon in the early and late part of its own day.
This is why such a Moon can look quite different, thicker or thinner
crescent, than an exact 3.0 day Moon.
Mind well that the terminator, the dividing line between the day
and night side of the Moon, is the sunrise line for the Moon from New
to Full phase. Craters and other details on the disc abutting the
terminator are more fully revealed as the Sun rises over them.
After Full Moon, thru the next New Moon, the terminator then on
the disc is the sunset line. Surface features abutting it are covered
up into the night side.
On the lunar ground the terminator migrates 1/2 deg/day or quite
30km.. Within a hour or so watch of a small crater on the terminator
shows dramatic change of light & shadow around it. Such observations
are a favorite for home astronomers.
The phase is sometimes expressed as the fraction of the moon's
disc lighted by the Sun, sometimes as percent lighted. The illuminated
fraction is
(lighted fraction) = (1 - cos(elongation)) / 2
This works ONLY for the Moon. It gives silly answers for Venus and
Mercury because they orbit the Sun, not Earth.
Some lunar observing references have a crosswalk table of
elongation age, lighted fraction. Else a calculette will work the
above formula .
Elongation
--------
The Moon moves each day 13.2 degrees downrange in the zodiac,
spending 2-1/2 days to cross thru each sign. The Sun moves one degree
each day, spending some 30 days in each sign.
For this section let the Moon run in the ecliptic, with zero
deviation north or south from it.
The net movement of the Moon relative to the Sun is 12 .2 deg/day.
y either the 12 or 13 deg/day lunar motion, the Moon mover 1/2
deg/hour, or quite her own 1/2 deg diameter per hour. Occultation of
stars last an hour when the star passes head-on behind the Moon.
From the moment of New Moon the Moon pulls ahead of Sun 1/2
deg/hour. At New Moon and many hours thenafter the Moon is utterly
too thin a crescent and in utterly too brilliant twilight to discern
in the sky.
Eventually she acquire enough distance and thickness of crescent
and darkness of twilight to be seen by eye in the sky. This is First
Crescent and a new month is called.
How far downrange must the Moon stand to come within range of
first Crescent? There geometric, photometric, cultural factors, all
with heavy conditions. One sometimes applied is the Danjon limit of
some 8-1/2 deg, when the crescent should be thick enough to be
recognized as a distinct feature in the sky against bright twilight.
it was devised separately from First Crescent.
In any case the sighting of First Crescent applies only to the
first instance after new Moon. Looking for it on the following dusk
doesn't count. The Moon is then 12 degrees farther from Sun, in darker
twilight and higher altitude, well within range of bare-eye sight. In
fact, few observers casually notice the Moon within the first full
day, 24 hours, after new Moon, yet most observers clearly recall
seeing a two-day old Moon.
Twilight
------
To see First Crescent skywatchers stood duty just after sunset to
maxmize the Moon's altitude above the horizon. Waiting too late lets
the Moon descend lower, into horizon haze and be lost to view.
The sky just after sunset is still as bright as daylight. Waiting
a bit longer lets the sky darken into twilight. This increases the
contrast between Moon and sky.
In general twilight is a gradient of darkness upward from the
horizon with some radial gradient left and right of sunset. The zone
closest to the sunset is the brightest with the least chance of seeing
the Moon in it.
When is the optimal time between sky darkness and lunar altitude
can not be confidently forecast, or retrodicted. Twilight is a
meteorplogical effect that is far too complex to model observing
conditions for a particular first Crescent.
In addition, there can be local influences like desert dust
storms, volcano dust (even if blown off in remote places), clouds of
pollen and insects, and ordinary haze and thin cloud cloud
Calendar keepers relied on past observed First Crescents and
matched their circumstances to the instant ones. They figured that in
spite of losing actual sighting, First Crescent should have been seen
on the instant evening. While twilight can not be reliably modeled to
examine particular First Crescent events, schematic models are built
into some planetarium softwares. They tint the sky near the horizon to
make a pleasing 'typical' twilight.
Ecliptic
------
The Sun and Moon travel eastward thru the zodiac. The Sun takes
365-1/4 days for one lap while the Moon takes 27-1/3 days. This is
the sidereal period, also the orbital period.
Measured against the Sun, after one lap of the zodiac the Moon
must chase the Sun, which moved farther downrange, to complete a phase
or synodic round in 29-1/2 days.
The Sun's motion repeats each year over the same path, the mirror
of Earth's orbit around the Sun. This path is stable enough over a
couple millennia to delineate it on starmaps. This is the ecliptic.
At sunset in a given geographic latitude the ecliptic slopes
upward from the horizon by an angle of
slope = colatitude +/- 23.5 degrees
For New York latitude of +40.7 deg the colatitude is (90)-
(+40.7) = 49.3 deg. The maximum and minimum inclination of the
ecliptic for New York is
slope(nax) = (49.3) + (23.5)
= 72.8 deg
slope(min) = (49.3) - (23.5)
= 25.8 deg
A steep ecliptic puts the Moon higher in the sky for a given
distance she stands downrange from the Sun. A shallow ecliptic keeps
the Moon at low altitude for the same distance.
A B
\ \
\ \
M M
\ \
\ \
--------------\=------ ---------------\----
O O
Scene A shows the Sun 'O' just after sunset. The Moon 'M' is
on the ecliptic. The steep ecliptic holds the Moon high in the sky,
the altitude being most of her downrange distance from the Sun. She is
also in a darker zone of twilight. First Crescent would be easier to
observe by greater altitude and lower sky brightness.
Scene B shows the a shallow ecliptic. The Moon at the same
distance from Sun as in scene A is lower in altitude and is in
brighter sky. First Crescent would be harder to discern.
The slope anglE for a given sunset is a function of date or,
equivalently, the place of the Sun along the ecliptic. In New York the
slope is greater in spring and less in autumn.
for far north latitudes, the slope can be negative,.The ecliptic
extends under the horizon at sunset. Durning months when this happens
The Moon sets before the Sun and there is no First Crescent. Cultures
in these regions have other means of regulating their calendars.
Longitude
-------
The Moon's rapid motion causes her aspect in the sky to be radicly
different across geographic longitude. If, for example, New Moon
occurred at sunset in one longitude zone, it would be would stand east
of New Moon in longitudes father west. The angular advance of the Moon
is the 1/2 deg/hour for every fifteen degrees of longitude, or,
roughly, each hour of timezone. e When the early followers of a
calendar were close to hand, the month was called by an audible
signal, or at times a visible one like a flag or smoke plume. As the
followers dispersed around the world, longitude separation could pull
the call of the month out of synch from a historical home base.
In general a First Crescent can be missed at one longitude for
being too close to the Sun. In farther west timezones must wait until
their own local sunset, coming hours later. The Moon is then a bit
farther from Sun, being a bit easier to see.. It can happen that a
month is not called in some parts of the world but is so called in
others.
To keep all followers on the same date, cultural rules, like
naming a home station for the one official caller of the month, are
employed. With today's Internet services the official call of the
month can be sent to all followers at once.
A B C
\ \ M
\ M \
M \ \
--------------\--- --------------\- --- ------------\---
O O O ----
Scene A is the view from a given longitude with the Sun ' O' just
after local sunset. The Moon 'M' is near the Sun, too close to discern
as first Crescent. Location a does not call a month but must wait for
the next evening for a second attempt.
Scene B is a place a couple timezones west of place A. At its own
local sunset the Moon moved farther from Sun at the rate of 1/2 degree
of elongation per hour of timezone. Location B has a better chance of
calling the month.
Scene C is a location still farther west fy a couple more
timezones. The here may have advanced far enough for observers at C to
claim sighting of First Crescent. For them the new month begins while
the locations in longitudes a and B are still in the previous month.
On a world map the age of the Moon when spotted at first Crescent
increases westward in longitude. Many First Crescent softwares plot
the age, amount to the chance, of First Crescent on a world map.
Schematicly it look like
| |
-----+----------------------------+----------------------------
IDL <---W lpm--- 0 ---E 1on--->
| | |
-+---------+------------------+---------------+----------+--
next | present day | resent | next day
| | | | | New Moon
|30-32|26-29|22-25|18-21| Moon too close
The upper row is a skeleton scale of longitude. 'IDL' is the
International Date Line and '0' is the Greenwich meridian.
The second tow is a time scale for a First Crescent day. The Sun
sets several hours before midnight. Note carefully that the date jumps
at the IDL to prevent wrapping the same date round and round the
world, like running a tight circle around the north pole or riding a
satellite around Earth.
The third row shows the age, in bands of hours, when First
Crescent could be spotted as sunset migrates westward around the
world.. These is a zone from New Moon sunset to the very youngest e,
age of the Moon for a fighting chance to see it. This age, or
elongation, is set by each calendar system. Observers in this zone of
longitude do not see First Crescent. The Moon is too young, too close
to the Sun.
Farther west longitudes may catch First Crescent for ages at their
local sunset. the youngest is in the east end; oldest, west. The age
bands are established by the rules built into the software. Some
programs stop computations at age 36h because there had to a sighting
already in a farther east longitude.
The plot cuts off at the IDL. Observers west of IDL are in the
next day, when a full day beyond reasonable First Crescent sighting..
By then the month is already called.
It could seem that observer C 'waited too long' to catch First
Crescent because the Moon was well within the zone to see it earlier.
Could location C see First Crescent with the Moon closer to the
Sun? No, because the very prior chance to spot First Crescent was in
the previous evening. The Moon then would have been far too close to
the Sun.
In the diagram above it may seem that observer C 'waited too
late'. Couldn't he look for the Moon earlier? He would be hunting her
up in a daytime sky with the Sun not yet set. A Telescope can darken
the background sky and increase contrast for the Moon. Such a sighting
would not be a First Crescent. All First Crescent calendars require
that the Moon be seen by bare-eye right after sunset.
Latitude
-------
The Moon runs in an orbit inclined 5-1/2 degrees from the
ecliptic, which accounts for the infrequent occurrence of solar and
lunar eclipses. The Moon at New and Full phase is usually too far
north or south of the ecliptic to produce an eclipse. The deviation
is the ecliptic latitude of the Moon, from +5-4/2 deg to -5-1/2 deg
and back month by month..
The Moon's ecliptic latitude alters the altitude of the Moon for a
given elongation. A northern Moon is higher in the sky than when on
the ecliptic, zero latitude. First Crescent is easier to pick out
A southern Moon is lower in altitude, harder to discern.
The range of altitude shift from a farthest north latitude of Moon
to farthest south, for New York, averages+ /- 3-1/2 degree from a zero
latitude Moon.
A B C
\ \ \ M
M \ \
\ M \ \
--------------\--- --------------\- --- ------------\---
O O O ----
Scene A shows the Moon on the ecliptic near First Crescent. She
may or may not be observed as such due to altitude.
Scene B has a southern Moon of same elongation as A. She is lower
in altitude, also in brighter twilight, and possibly missed as First
Crescent.
Scene C has a northern Moon, same elongation as A. At her higher
altitude she is in darker sky and more likely to be caught for First
Crescent.
In back-of-envelope calculation of candidate evenings for First
Crescent latitude is ignored. The Moon is placed on the ecliptic. Such
candidate day can be a day off.
Latitude has greater effect for a shallow ecliptic. The
displacement of the Moon is then more vertical, raising or lowering
the lunar altitude by about 4 dg for New York. A steep ecliptic puts
the latitude deviation more horizontal, with less shift of altitude.
it's about 3 deg for New York.
Refraction
--------
The atmosphere has a vertical density gradient that refracts light
passing thru it. The effect is to raise the apparent altitude of
celestial objects above their geometrical positions. Refraction is
strongest at the horizon, some 1/2 degree, a lunar diameter. It
weakens rapidly with altitude to a couple arcminues at about 15
degrees. This is negligible for home astronomy purposes but celestial
navigation must account for it.
The refraction is so severe against the horizon that the Sun and
Moon suffer a gradient of altitude lift over their discs. The disc is
squashed into a ovoid shape, the lower part being lifted more than the
upper.
In New York's latitude refraction delays sunset and moonset by two
minutes.
A surprisingly good estimate of refraction is found from the local
temperature and pressure at the observer. This is apparently valid
even tho refraction is processed all along the lightpath from the
horizon. This can be many kilometers long. Celestial navigation texts
give temperature-pressure formulae for refraction.
First Crescent software usually include refraction in computing
the altitude of the Moon. . The program configuration asks for the
local temperature and pressure. I suspect this is routinely skipped,
unless they are substantially off from the default values, like for an
observer at high elevation.
Altho the refraction at altitudes of First Crescent are only many
arcminutes, it could make or break a First Crescent sighting. Without
refraction the Moon could be a bit too low to spot, specially in hazy
or brighter twilight.
Mechanical planetaria, like astrolabes, do not have refraction
functions.In most cases the devices are too small to read out
altitude better than a degree or two. Computer planetaria commonly
offer refraction as an option to produce more realistic sky scenes and
simulate horizon events.
Related to refraction is looming. This is an apparent enlargement
of the scene along the horizon that causes remote features to seem
closer. I hear about looming from desert stories where a traveler sees
a town ahead. it seems to be a few more hours away but ends up taking
many more hours away. As the traveler approaches the scene it evolves
into its proper angular size.
If the Moon near the horizon on a candidate day for first
Crescent is inflated in angular size by looming, she is more likely to
be noticed. I know of no accounts of a First Crescent observed under
looming. I do come across other sightings of the Moon refracted larger
by looming. In any case there is no good model for looming and it can
not be reconstructed for a past First Crescent.
Disc size
-------
As the Moon rounds perigee and apogee in her orbit she accedes and
recedes with Earth. Near perigee she is larger angularly; apogee,
smaller. A larger thin crescent would be easier to discern then a
small one.
Bare-eye astronomers didn't know about the disc size changes, they
being beyond casual notice. They did know about the variable speed of
the Moon. Their model of lunar motion, with an excentric circular path
around Earth, had a faster angular speed near perigee; slower,
apogee.
The variable speed was well known by the Babylonians. They
compiled tables of the lunar motion to anticipate First Crescent and
to fill in records on cloudy evenings. This knowledge mapped into
later cultures in Asia Minor and Mid East.
For sure they had no inkling of the size correlation with speed or
of 'orbit' as a spatial path. It happens that when the Moon is near
perigee she moves faster and also presents a larger disc. A perigee
First Crescent should be more frequently spotted than an apogee First
Crescent.
The faster Moon near perigee also moved her farther along from the
Sun than average to get her into higher altitude and darker sky than a
Moon of average speed. This, too, enhanced chance of catching First
Crescent. Conversely an apogee Moon, moving slower, didn't reach so
far from the Sun, sitting at lowar altitude in brighter sky.
The size of the lunar disc in modern times makes for the
'supermoon' and 'minimoon'. These are Full Moons occurring near
perigee and apogee, being than larger or smaller than average. a
casual observer, and the public, will not notice the altered size in a
single look. Changes in size are appreciated by comparing photographs
or telescope views of Full Moon around the orbit.
Eartthshine
---------
When the Moon to us is a thin crescent, an observer on the Moon
sees a nearly full Earth. The phases of one body as seen from the
other are inverse. The daytime fraction of one is the nighttime side
of the other.
The lunar ground is lighted by sunlight reflected from Earth. We
sometimes see this lighted ground as a soft glow, called 'earthshine'.
This glow can be bright enough to bring out the maria and a few other
surface details in binoculars. On other occasions it barely outlines
the lunar disc against the sky. The brighter apparitions of earthsine
is known as 'new Moon in ol Moon's arms'.
Earthshine is much brighter than moonlight on Earth from the
larger disc of Earth in the lunar sky and the higher reflectance of
that disc. The angular area of Earth's disc averages 13.7 times the
lunar disc in our own sky. Earth reflects light from its clouds while
the Moon reflects off of rock. The
The geometry of earthshine is shown here. S, M, E are Sun., Moon,
Earth. I moved the Moon away from her First Crescent place to avoid
overlapping lightpaths.
A
S-----------------------------E
/ /
B/ /C
/ /
M
A is the path of sunlight from S to E. Some sunlight is reflected
off of Earth to Moon, path B. Moon reflects some of B's light back to
Earth,path C, appearing as the gray glow on the Moon's night side.
The minimum illumination by Earth on the Moon is the ratio of
disc area. This assumes the reflectance, albedo, is the same for both
Earth and Moon. This ratio is 13.7 to 1. With the greater albedo of
Earth's clouds, the actual illlumination ratio is more like 40 to 1.
Earthshine can occur with large elongation, it's just a lot
dimmer. The Earth is less than full and the Moon's lighted part causes
glare. I can't recall seeing earthshine farther from the Sun than
degrees, or age greater than 6 days.
Earthshine, being a weather-generated effect, can not be reliably
predicted for the future or reconstructed for the past. its brightness
ranges widely from crescent to crescent. Earthshine also occurs on a
waning crescent before sunrise, but i found only the egyptian culture
banked their calendar off of the last Crescent.
With strong earthshine the First Crescent would be far more easily
spotted. The Moon is a disc in the sky with a brighter edge facing the
Sun. A dark or no earthsine leaves only the thin crescent to look for.
I could not find reference to earthshine in any litterature about
First Crescent. Not even a report of an earlier visibility of First
Crescent because of earthshine.
Libration
-------
Libration is the periodic rocking or balancing of the Moon during
the month. The word comes from 'libra', a two-pan weighing scale. it
rocks, blances, as it settles down for a reading.
The Moon librates both east-west and north-soth. The east-west
libration is libration in logitude. This altrnately expose a bit of
the Moon's far side around the west and east edge of the lunar disc.
An equal bit is rolled off of the disc into the far side at the
opposite limb.
Libration in latitude rocks the Moon noeth-south to reveal far
side details in turnrm along the north or south limb. This effect for
First Crescent is small and neglected here.
Both librations are purely a mechanical phaenomenon due to the
Moon's variable orbital speed and constant rotational speed. . The
Moon does not physicly rock in her orbit. They were first described by
Hevelois in mid 1600s.
The thin crescent has a mix of dark and light details, the maria
and terrae, along it. The combined reflected sunlight form these
details blend, with bare-eue inspection, into a certain brightness.
The resulting crescent brightness factors into discerning First
Crescent.
The scenes here, a slice of the crescent,show three steps of
libration. The mumbered aras are maria; blank areas, terrae. The
smooth right edge is the lunar limb; jagged left, the terminator or
inner edge of the crescent.
A B C
>-----| >-----| >-----|
<111 | <1111 | <11 |
>111 | >1111 | >11 |
<111 | <111 | <11 |
> 1 2| > 1 | >1 22|
< 2| < | < |
> 3 | > 3 | > 3 |
<-----| <-----| <-----|
In scene A a large mare sits on the terminator with two small ones
nere the limb.
In scene B the Moon rolled details toward and over the limb. More
of the crescent is occupied by dark areas. The crescent reflects less
sunlight. The Moon is a bit dimmer and harder to spot for First
Crescent.
In scene C libration rolled some far side details onto the disc
Some other features on the disc are pulled into the night side beyond
the terminator. The crescent has more light areas, reflecting a bit
more sunlight and being easier to spot for First Cresecent.
Because the rules for First Crescent were developed under bare-eye
observations, account for libration mis missing from calculation of
First Crescent. I found no reference for an uppdate method that
factors in libration.
Software to calculate first Crescent often offers reqadings of
libration and some plots a moonmap that includes it. i don't know if
libration is also actually cranked into the First Crescent
computation.
Aniticipating First Crescent
--------------------------
Early skywatchers selected a coming First Crescent by tracking the
waning crescent before New Moon. When the last sight of this Moon was
recorded, First Crescent should come two days later.
The interveing ay is New Moon. They inspected the dusk sky for any
sign of the Moon and usually they got it right. Once in a while they
were sure there was no Moon, not just obscured by weather,. They went
out on the next evening, with a positive sighting..
A mechincal planetarIum, an astrolabe, was in early times used to
find Fiest Crescent. This function was one strong factor in its
perfection in the Ioslem world. The Sun on the day of New Moon is
placed a few degrees under the horizon, amount varied with local
practice. The ecliptic was marked 12 degrees downtaaange from the Sun
to represent a one-day old Moon. If this Moon is at OR BAOVE a
prescribed altitude, the associated date is a candidate for First
Crescent. Else the Moon is marked 12 more degrees farther and a second
assessment is done.
In midern times home astronomers like to play with first Crescent
with computer planetaria. They set the program to, say, twenty mnutes
after sunset on the day of local New Moon. The date is bumped forward
one day to put the Moon ffarther from the Sun at the same clock hour.
Some sky wiseliness is applied to judge if the Moon could be a
First Crescent. Software that sinulates twilight and horizon mist
gives a more confident assessment than one that has a simple all-sky
dimming after sunset.
Dedicated First Crescent software embdedSd some cultural factors
besides the natural ones. Some plot Zones on a woeld map FOR chances
of seeing the First Crescent. Fancier programs allow selection of the
cultural factors to account the variety of calendars banking off of
first CCrescent.
The home astronomer can use these programs to plan a watch for
first Crescent, according as the calendar scheme he follows. Be
mindful that the official call of the month may be a day off of the
one predicted by the program due to local application of cultural
rules.
Conclusion
--------
This article considers only the natural, mostly celestial, fators
that produce a first Crescent. To these factors must be added the
cultural ones peculiar to the calendar scheme you follow.
Home astronomers in the 2010s picked up a higher fascination with
First Crescent. Such interest can enlarge the sphere of engagement
with the circumstant society and lead to exploration of other
calendar culture.
In a district with several followers of a particular calendar, an
astrdocial event can be staged for a joint watch for First Crescent.
Iy van start with a late afternoon picnic and followed by starviewing.