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THE STONEHENGE EFFECT IN NEW YORK CITY
====================================
John Pazmino
NYSkies Astronomy Inc
nyskies@nyskies.org
www.nyskies.org
2003 May 24 initial
2015 July 3 current
Introduction
----------
On the Salisbury Plains in the southern part of England is a
stone-age structure unique so far on Earth. It is Stonehenge, a
multiring of stones and holes which supposedly served as a calendar
and calculator of celestial events.
What makes this structure unique is that it has several post-&-
lintel bays, which were once complete all around the ring, about 30
meters in diameter. There are many other circles of stones thruout
England, but they never had lintels, only posts.
Regardless of the actual use of Stonehenge, which is still under
debate, it is true that on the first day of summer, near June 20th of
each year, the Sun does rise along the axis of the stone ring. Beyond
the ring were two stones, placed so the Sun rose between them. Today
only one remains, called the Heel Stone. The Sun rises alongside of
it, throwing off earlier attempts to explain the purpose of the Heel
tone and leading to speculation that the ecliptic suffered major
shifts of inclination.
The sunrise on the first day of summer, erroneously called
'midsummer's day' is today a festival occasion at Stonehenge. It is
thronged by tourists and presided by local members of the druid
group. With the dismal weather of England, we can wonder just how
useful Stonehenge was for monitoring any sunrise!
New York's Stonehenge
-------------------
Stonehenge was reproduced all over the world. Sometimes the
alignment matches the original, with due consideration for differences
in latitude. Other models were haphazardly set and are not at all
aligned with anything celestial.
New York does not have a specific Stonehenge model but in fact it
does after all by fortuitous accident. The axis is the east-west
streets on Manhattan and the stones are the very towers that so
dramaticly characterize the City.
Geography lesson
--------------
Manhattan is an island about 20 kilometers long and barely 2-1/2
kilometers at the widest. The gridiron of streets etched onto
Manhattan aligns with the island, a long skinny spar of bedrock. The
east-west streets, the 'streets', run along the short dimension of the
island. The longest continuous east-west street is 14th Street. The
north-south streets, the 'avenues', are orthogonal to the streets and
run along the long dimension of the island.
The direction of movement along the avenues to the north is called
'uptown'. That heading south in the avenues is 'downtown'. These words
are directions and not placenames. There is no such a place on
Manhattan called 'downtown'.
Now Manhattan is inclined from the lat-lon grid such that its
streets run 29-1/2 degrees right of the due east-west points on the
horizon. That is, their bearing is 119-1/2 degree to 299-1/2 degree of
celestial azimuth.
A little history
--------------
The City began as a Dutch settlement at the southern end of
Manhattan, near present South Ferry. The public commons was at the
foot of Broadway and was a field for playing the game of bowls. This
game in time developed into our modern bowling. This is now Bowling
Green, an urban greenspot.
The main arterial road out of the City was Broadway. It ran on a
ridge along the central axis of Manhattan to the northern barrier
wall. The wall was merely a dirt berm cribbed with logs. It deterred
indigenous natives from intruding but would be easily overrunned by a
European attacker. This line is now Wall Street.
As the City grew, Broadway was the main road leading north. It
exited the City thru a gate in the wall, and continued on the median
spine of the island. Today, in numerous places, despite land shaping
over the centuries, you can see the terrain sloping downward away from
Broadway.
Broadway was linearly extended northward and most other new
streets in the growing City were laid out parallel and perpendicular
to it. By the 1810s, it was obvious that eventually Manhattan would be
completely covered by New York City and a formal plan of new streets
was enacted. The existing streets, mainly those in the older Dutch
part of the City and in Greenwich Village -- a separate town back then
-- were left alone. The new streets would parallel Broadway or be
orthogonal to it right up to the Harlem River on the northern flank of
the island.
It just so happens that this pattern is skewed on the lat-lon grid
by that 29-1/2 degrees.
Some astronomy
------------
The Sun cycles thru declination -23.5 degree to +23.5 degree over
the year. The Sun's declination is zero as he crosses the celestial
equator on the vernal and autumnal equinoxes. His declination is +23.5
degrees on the summer solstice; -23.5 degree, winter solstice.
In consequence, the sunset point wanders from due west over the
year. From the vernal equinox, thru the summer solstice, to the
autumnal equinox he sets to the right (toward the north) of due west.
His maximum departure from due west is at the summer solstice, when he
also has the maximum northern declination.
The swing of the sunset point is the Sun's amplitude. Astronomers
differ whether it is the full spread from farthest left to farthest
right or just the span from due west to either farthest right or left.
In any case, this amplitude is a function of latitude, being least for
the Earth's equator and most for the arctic and antarctic circles.
In New York at latitude 40.7 degrees north, the amplitude,
counting from due west to the solstice sunset point, is 31.7 degrees.
This is surprisingly close to the 29.5 degree skew of the streets!
A compromise
----------
If the streets were aligned to 31.7 degrees the Sun would set
along them on the summer solstice. I neglect the effect of the
atmosphere, which would raise the Sun as much as a half degree when he
is geometricly on the horizon. The Sun would appear to set later and
farther to the right than without an atmosphere. However, the extent
of this lifting is highly variable and can not be predicted in
advance.
In the absence of the atmosphere, I note that the Sun would set
along Manhattan's streets when his declination is not +23.5 degrees at
the solstice, but at 21.9 degrees. This occurs on the 22nd day before
and after the actual summer solstice, on May 30 and July 12 in 2002.
The solstice was on June 21st.
OK, New York does not have a perfect Stonehenge effect, but one
that's amazingly close given the purely terrestrial accident of its
street grid! I would allow a couple days of window to hedge against
clouds and summer shmutz. Also, the solstice floats on the calendar.
Let the window be May 29-31 and July 11-13.
Note that the lifting of the Sun by atmospheric refraction
actually enhances the effect. When the Sun should be just disappearing
below the horizon on, say May 30th, it is in fact sitting on the
horizon centered along the street!
A little leeway
-------------
The geometric dates for Manhattan's Stonehenge are 30 May and 12
July. Because the Sun is a disc, not a point, a street has some
wideth, and the refraction of the atmosphere is so erratic, there is
some leeway around these dates. You can experience a good Stonehenge
effect between 28 May and 1 June and between 10 and 14 July.
The range of dates allows for adverse weather, schedule conflicts,
remoteness from the viewing site, flubbed viewing attempts, and other
contingencies. Yes, you can avail of the range of dates togo out and
see the Stonehenge sunset more than once,
Manhattanhenge
------------
In the first couple years that the Stonehenge effect was seriously
anticipated there was no special name for it. It was the Manhattan
Stonehenge sunset. The routine association of 'Manhattan' with
'Stonehenge' soon merged the words into 'Manhattanhenge', It was a
madeup word that had good currency among New Yorkers starting with the
2006 pair of sunset events.
Manhattanhenge took off since 2006 to become the definitive term
for the peculiar sunset show on Manhattan. It was adopted thruout the
world and appeared in both astronomy and cultural litterature.
It is capitalized, after the name of the island and as the proper
name for this specific astronomy phaenomenon. On 2013 June 1 the
Oxford English Dictionary 'officiated' Manhattanhenge as a new valid
word! Its definition was very brief:
'Q phenomenon occurring just before and after the summer solstice,
in which the sun sets in alignment with the streets that run east to
west on Manhattan's street grid; this year's first opportunity for
seeing Manhattanhenge's glory came Tuesday night.'
This a bit TOO brief! It makes no mention of the Stonehenge effect
of the flanking towers! This definition could apply for any linear
sightline into the sunset.
It also is awfully fuzzy about the date of the event in 'this
year'. I'm guessing, since the word entered the OED in 2013, taht it
refers to May 28, which is a Tuesday in 2013. This is the start of the
season, which runs thru May 31.
Let's see how Manhattanhenge is treated next year on the OED
website or in a paper edition of the book.
Manhattanhenge was a joyful highlight of the 8th conference
'Inspiration of astronomical phenomena' on 2013 July 7-12 at the
American Museum of Natural History. Altho the weather was hazy and
humid, the delegates enjoyed satisfying views on July 11 by standing
in 79th Street near the Museum. The street by prior arrangement was
closed from road traffic for safety sake.
Each season the hayden Planetarium offers a public show, as was
done during the conference, to explain Manhattanhenge and prepare for
clearsky viewing of it from a nearby street corner.
Other towns with an interesting sunset, or sunrise, alignment try
to embed 'henge' in a name related to the town, like 'Chicagohenge'.
None so far has the distinctive ring of Manhattanhenge and none has
the Stonehenge effect any way close to that on Manhattan.
Public spectavle
--------------
Yhe Stonehenge sunset was initially a private show within the
City's astronomy world. The was no pyblic announcement for it, except
as passers-by saw astronomers examining the setting Sun and asked
what's going on. I myself recall the many occasions in the 1980s and 1990s when I
had local astronomers stop at my housesitting crib on the Upper East
SIde. It had a terrace with a west view along a street over the trees
of Central Park. The effect in this situation was muted because there
was no palisade of tall towers along that particular street.
As word of the Stonehenge sunset spread, thru dialog with the
Museum and NYSkies, ever more people watched it. From small gaggles of
curious folk until 2005 the event blossomed into a massive public
outpouring of celestial awareness.
With perhaps a hundred good accessible locations for viewing,
there was no need to congregate in one special location. Dozens to
hundreds assemble at each viewing site.
According as the interest and enthusiasm in each district, a
certain street may be closed from traffic to let people stand safely
on its centerline. This is arranged thru civic associations or the
Community Board. They have the political liaison to get such favors
done for at least one of the several sunsets in each season.
Without a street closing, there are instances of people filling a
street, as if for a rally or demonstration, and clogging traffic from
it. I do not encourage such behavior for safety and legal reasons!
So far there seems to be no organized public parties, like for the
Venus transit or an eclipse, to watch the Stonehenge sunset. The shows
at Hayden Planetarium seem to be the only ones. I suppose there are
socials for friends and family at apartments with sightline over
ground obstructions.
By 2010 the Stonehenge sunset, rapidly shifting name to
manhattanhenge, was a fully-enrolled feature of civic life in New
York. Among the myriads of spectators are tourists. They learned of
Mangarrangenge in the planning of their visit to the City. It is one
more show to see that's so much part of the city as the theater,
museums, neighborhoods, sports, monuments.
Practicalities
------------
Ideally, you would stand in the middle of a street, like 42nd
Street, and wait for the Sun to sink to the horizon. If you try,
you'll be rudely shoved off by vehicular and pedestrian traffic. You
can make do by standing on the sidewalk at curbside and looking down
the street. In this case, you'll see the Sun set on your same side of
the street rather than dead centered on it.
Or you can let the Sun set a bit off center, but brought back to
center by your vantage point at curbside.
Pick a street with no obstructions. 27th Street is blocked by
Fashion Institute and 64th Street is blocked by Lincoln Center. If
you are on the Upper East Side, you better get to the west side to
avoid the trees of Central Park. Check out an addiurnate street map
of Manhattan.
Standing on Broadway to get on the central spine, gives a good
sightline along the street. On your peuliar block, the summit may be a
a hundred or so meters to either side of Braodway.
Elevation helps. Viewing from a terrace or roof fronting an east
west street throws you far off the line but gets you above trees and
traffic obstructions. The ideal case would be a skywalk spanning an
east-west street with a clear prospect of the City. One popular site
is the Tudoe City overpass on 42nd St.
The stayed-cable bridge on 63rd Street, joining two parts of
Rockefeller University, would be a possible viewing site. So would
the skywalk within Hunter College. You must have prior admittance to
these facilities..
Wide or narrow street?
--------------------
The Manhattan streets potentially suitable for viewing
Manhattanhenge are from 14th Street to about 120th Street. At fist
this seems like a choice of some 100 sightlines. Closer examination of
the cityscape soon demonstrates that many streets are not suitable for
Manhattanhenge. Among the reasons are
* too short a line of sight, only a couple hundred meters
* lack of towers lining the street for no true Manhattanhenge
* interception by obscuring superblicks and parks
* adverse slope of terrain along street
It may at first seem that viewing along a narrow, one-way, street
is better because the towers are closer together and more tightly
frame the setting Sun. It turns out that the sightline in many narrow
streets are blocked by streets, scaffolds, trucks, construction
machinery, barriers, double-parked cars. The obstruction for a given
street can change on short notice, like a truck that stands for
unloading right within the sunset period.
A wide, two-way, street tends to be less prone to capricious
blocking of the view. Most obstructions that ruin the view on a narrow
street are for he wide streets off-centered in the curb lanes. The
center lanes are usually clear.
Over the years there settled out a prime set of wide streets for
the Manhattanhenge. They are 14th St, 23rd St, 34th St, 42nd St, 57th
St, 72nd St, 79th St. The last are the segments on n the west side of
Central park. All these streets are endure dense traffic as a major
hazard against standing in the middle of the roadway.
All of these streets are at or near busy transit stations with
dense train flow in the hours bracketing sunset.
Weather
-----
The two windows for viewing the Stonehenge effect are in the New
York summer hot & humid season. You could be waiting for the sunset
under oppressively uncomfortable conditions. In such combination of
temperature and humidity, the body can not transpire properly, leading
to sweatiness, drowsiness, internal loss of water.
Wear light loose clothes, have a bottle of fresh water. Walk and
climb stairs slowly, don't run or jog. If feasible, view at a site
with nearby shade like trees or walls. Bring a folding stool or chair
to rest on. A battery -- or solar! -- powered fan can be very
refreshing.
One horrible threat against comfortable Stonehenge viewing is the
late afternoon thunderstorm. In New York commonly on the summer days a
tumultuous storm erupts in the mid to late afternoon, throwing many
centimeters of rain with blinding lightning and crashing thunder.
You will, if at all possible stay out of such a storm. Most likely
it'll occur while you are indoors at work or school, or when you can
retreat into a store or eatery.
The typical storm lasts only a half hour, but hour-long deluges
are annoyingly frequent. On the whole, regardless of the start and
duration, the storm abates before sunset. In fact, the sky usually
clears up rather nicely for the Stonehenge effect.
However, you could then be soaked thru and thru, taken on a nasty
disheveled feeling. The ground and street furniture, parapets may
still be wet. Grassy sites may still be soft and squishy under the
foot. In the event of the afternoon thunderstorm, arm yourself with
newspaper to lay on wet furniture, be willing to take splashes and
drips. Protect your photo gear from water by keeping it in a carry bag
or under your shirt/jacket between shots.
Rainbows?
-------
While the Sun is setting in the northwest along a Manhattan street,
the antisolar point is rising in the southeast along that same street.
If there was a rain before ou arrive at your viewing site, there is
the chance to spot a rainbow.
On the whole, storms sweep over the City from west to east, When
the sky is clearing in the west for the sunset, rain could still be
falling in the opposite direction. This makes a wall of raindrops
catching the rays of the setting Sun to generate rainbows.
There's plenty of slack time before the actual sunset to turn
around and look down the street, away from the Sun, and look for a
rainbow. The shadow of your head is the center of the rainbow.
Because of a rainbow's large diameter, about 23 degrees, you
should ideally be at a site with an open view to the east and
southeast. With a street hemmed in by towers, you may see only the
upper segment of the bow centered over the street.
Nothing is promised, even if there was a rain that by sunset is
retreating into the east. The rain may have ended, moved out of
alignment with the Sun, or shrunk too small to make rainbows.
You could get a double or multiple bow! The extra ones are outside
of, and concentric with, the main bow.
Photographing a rainbow is a bit tricky. Metering off of the sky
itself can produce an overexposed picture. The rainbow is diluted with
weak color. Meter off of the foreground scenery, lock the setting, and
shoot with it at the bows.
Selenehelion
----------
A particularly rare treat during the Stonehenge sunset is seeing
the rising full Moon. This happens only a few times in a lifespan,
The instance on 2014 July 11 was, as far as inquiries could determine,
the first occasion that was purposely announced in advance. It was an
extra treat for the NYSkies Seminar on that night. Astronomers took a
break from the Seminar to watch the two orbs face off along 14th
Street! The scene to the east was spectacular with the towers on both
sides of 14th Street lighted by the Sun and the big round Moon cradled
by them!
This 2014 Moon-Sun alignment was not known to the public, even tho
hundreds of city folk -- and tourists! -- were on 14th Street outside
the NYSkies meeting hall to watch the Stonehenge sunset. We
astronomers had to yell to make the people look east, away from the
Sun, to see the Moon.
There is a spectacle called 'selenehelion' (seh-leh-neh=HRH-lee-
yonn) when an eclipsed Moon rises at sunset or sets at sunrise. At
such times the Moon is almost exactly full, being covered by the
Earth's umbra.I checked for a possible future lunar eclipse occurring
during a Stonehenge sunset. Thru the entire 21st century there are
none. All lunar eclipses visible from New York fall away from
Manhattanhengee, so there is no chance to witness a traditional
selenehelion at Manhattanhenge.
Selenehela at lunar eclipses are rare without Manhattanhenge. We
were treated to lunar eclipses rising at sunset in 1975 and setting at
sunrise in 1963 and 2014. These are examples and there could be a
couple more since the mid 20th century.
full Moon rising
--------------
A milder definition is that any full Moon & Sun line-up, not only
during a lunar eclipse, is a selenehelion. A question arises in that
the Moon still has to be 'full'. She looks awfully round up to a
couple days around the geometric full Moon point. I here offer that
the Moon rising at sunset must be within twelve hours of geometric
full phase. Else she is too far from being full, even if to the eye
she looks full.
In order to see the Moon at sunset she must be a little before
full phase, being east of the full Moon point and just above the
horizon as the Sun is setting.
It's unreasonable to insist that the Moon actually rise, breaking
thru the east horizon, exactly as the Sun sinks under the west
horizon. I allow that the Moon may rise up to 10 degree altitude at
sunset. This means the geometric full Moon occurs later in the night.
The lead time lets Manhattanhenge watchers to inspect the Moon once in
a while as they follow the Sun to his setting.
To better ensure that the Moon lines up with the street as she
rises, the Moon must be close to the ecliptic with only a small
latitude from it. For a large latitude, up to 5-18-/2e degrees from
the ecliptic, the Moon stands too far right or left of the street and
may be blocked from view.
Having a full Moon close to the ecliptic is the condition for a
lunar eclipse,.I looked thru all of the 21st century and found no
lunar eclipse during Manhattanhenge!
In the end it is possible to have a selenehelion with the Moon too
far from the ecliptic to actually see in the line of the street. She's
hidden behind the towers on the left or right side. If she is on the
left, diurnal rotation brings her into view along the street. This may
be many minutes after sunset, perhaps after the Manhattangenge
observers dispersed. A Moon too far on the right is not at all seen.
Rotation keeps her behind the right-side towers.
I examined Stonehange sunsets from 1995 thru 2049 for Sun-Moon
line-ups. 1995 is about the earliest clear memory of astronomers
purposefully observing the event, altho I personally recall occasions
in the 1980s at a rooftop terrace overlooking Central park. The view
was muted because the district where this site was located had no real
tall towers along the street.
In the table, column S indicates the event occurred on a
selenehelion. The column LCER indicates that the Moon was left,
center, right in the line of the street when she is still less than 10
degree altitude at sunset. The last column gives the number of hours
that sunset occurred before geometric full Moon.
--------------------------------------
RISING MOON DURING MANHATTANHENGE
--------------------------------------
date | S | LCR | remarks
------------+----+----+--------
1995 Jul 11 | S | R | 11h before full Moon
1996 May 31 | - | R | 20h before full Moon
1998 Jul 9 | S | C | 8h AFTER full Moon
1999 May 29 | S | C | 6h before full Moon
2006 Jul 9 | - | R | 51h before full Moon
2006 Jul 11 | S | --- | 3h bef full Moon, not up yet
2007 May 30 | - | R | 25h before full Moon
2014 Jul 11 | S | C | 11h beoref full Moon
2015 May 31 | - | C | 40h before full Moon
2017 Jul 9 | S | --- | 4h before full Moon, not up yet
2025 Jul 9 | - | R | 20h before full Moon
2025 Jul 10 | S | --- | 4h before full Moon, not up yet
2026 May 30 | S | R | 8h before full Moon
2033 Jul 11 | S | C | 9h before full Moon
2037 May 29 | S | --- | 4h before full Moon, not up yet
2044 Jul 9 | S | --- | 6h before full Moon, not up yet
2045 May 29 | - | R | 14h before full Moon
-------------------------
The event of 2014 July 11 is the first ever specificly anticipated
by astronomers. They made it a feature of the NYSkies Astronomy
Seminar meeting on the same night. All the previous ones seem to have
been missed or observed privately by individual astronomers.
I put in one exception. The Manhattanhenge of 2015 May 31 has the
Moon at nearly 14 degree altitude. Full Moon occurs on June 2nd. This
is the very next passable instance, after the 2014 July 11th event.
Astronomers were so fired up about seeing the Sun and Moon together
that they clamored for the next occasion. Altho the 2015 May 31
Stonehenge sunset is not a true selenehelion, the Moon does line up
along the street. All the others in the table are within the 10-degree
altitude limit.
There are several misses when the Moon-Sun alignment is close but
not on the street centerline. These occur a day before or after the
Stonehenge sunset windows. The view can still be pleasing but the Sun
is aa bit off-centered on the street.
Rule-of-19
--------
The Moon with Manhattanhenge illustrates the the 'rule-of-19'.
This cycle of Moon, Sun, stars is a derivative of the classical Saros
cycle for eclipses and is a lot easier to work with. If a given aspect
of Sun, Moon, stars occurs on a given date, that aspect closely
repeats on the same date 19 years apart. Like for the Saros, the rue-
of-19 cycle eventually loosens up and the alignments no longer taKE
place. That series of instances is finished.
The table above is rearranged to show the spacing of rising Moon
at a Stonehenge sunset.
--------------------------------------
RULE-OF-19 MANHATTANHENGE-MOONRISE
----------------------------------
1995 Jul 11, 2014 Jul 11, 2 033 Jul 11
1996 May 31 , 2015 May 31, 2034 May 31
1999 May 29, [2018 May 29], 2037 May 29
2006 Jul 9, 2025 Jul 9, 2044 Jul 9
2007 May 30, 22026 May 30, 2045 May 29
--------------------------
Yhe sequence 1999-2018-2037 is interrupted. The Moon in 2018 is
too high in altitude to be 'rising' at sunset. On the next day the
30th, she is under the horizon at sunset and comes up too late to
associate with the sunset.
There are other interruptions, usually a miss of Manhattanhenge by
a day. The Rule-of-19 has these glitches because we added arbitrary
terrestrial conditions for Manhattanhenge. The rule operates on only
celestial factors.
Viewing the Sun
-------------
While it is not healthy to stare at the Sun without protection, it
is safe to take quick glances at the setting Sun of summer. The air is
almost guaranteed to be shmutzed over, making the Sun a red ball of
tempered brilliance. You can safely photograph this Sun without fear
of burning out the shutter. Just don't look steadily into the Sun or
gaze at it for long moments.
If the Sun is at all uncomfortably brilliant, don't try to
overcome the natural impulse to turn away. Monitor the Stonehenge
effect by your shadow in the street or reflection in a clear window.
Traffic hazard
------------
Viewing the Stonehenge sunset from the ground can be dangerous!
Standing in the centerline of a street puts you in the line of
traffic, with potential abrupt termination of life. I'm almost sure
one or two east-west streets have a safety median, but I'm not sure
which., nor if they offer the required sightline to the west.
For the quick and nimble viewer, there is a trick, but you REALLY
MUST stay alert. Watch the traffic flow for a few cycles of traffic
light changes. Between the flow in one direction and that in the
other, there may be a sensible delay, when there is for the instant no
traffic in the street. Once you get the timing just right, you can
walk across the street in this dead instant, look at the sunset, then
continue to the opposite curb.
The window of opportunity is brief, only mere seconds. You may
have to keep trying on following cycles of the traffic lights to get
in a good view. SInce it takes the Sun a couple minutes to touch,
cross, and sink at the horizon, you can get in several attempts.
To take pictures of the sunset, prepare the camera while on the
sidewalk,aim it at the Sun, then hold the camera parallel to itself
while walking across the street. Snap the shutter, and move off to the
opposite side. This takes a bit of practice!
These cautions are tough enough to mind for a typical summer
sunset with a subdued Sun. On the occasional clear dry summer day the
Sun can be blinding. It will then take substantial discipline to keep
the Sun from distracting you from the traffic.
You may have to, after dilligent effort, be content with an offset
view, where you stay on the sidewalk and watch the Sun set into that
same sidewalk.
Other towns
---------
The Stonehenge effect can be experienced in other towns with a
long straight road aiming within the Sun's amplitude. The road should
be at least one kilometer long westward from your vantage point and
have a clear horizon beyond. A little relief is a plus so you can
stand on an elevated part of it.
The azimuth of the street is obtained from county or town street
maps or land surveys of property along the street. Calculate the
amplitude of the Sun by
cos(azimuth) = sin(23.5deg) * cos(latitude)
= (0.3987) * cos(latitude)
The answer will be the azimuth from north round to east, or the
azimuth of the summer solstice SUNRISE. This comes from the behavior
of inverse trig functions and quadrant quandary.
Forget all the crazy rules for finding the correct quadrant for
the sunset point. Use the symmetry of the sky. That is, count off the
azimuth round to WEST, backwards from 360 degrees. Then reflect this
to the left (south) side of west to get the azimuth of the winter
solstice sunset. Your street better aim between these two azimuths.
If your road passes the above test, you next find the declination
of the Sun such that he does set along the road. Rotate the above
equation
sin(declination) = cos(azimuth of road) / cos(latitude)
From a solar ephemeris or astronomy calculation program, find the
dates when the Sun has this declination. These are the two dates the
Sun sets along your road. You should double check all this number work
with a computer planetarium program. It's up to you to include a
nominal atmospheric refraction or not, according as the program allows
you to switch this feature on or off.
The dates may have no relation to the equinoxes or solstices, but
could be close to some local celebration, like a county fair or
founder's day. You can include a viewing of the special sunset as part
of that celebration.
Rectified street grid
-------------------
A very common street pattern aligns with the cardinal compass
points. Streets run due north-south and due east-west. Sunset along
the east-west streets occurs at the two equinoxes. The Sun culminates
at true local noon along the north-south streets.
There is a bonus for such a favorable street pattern. The clock
hour of the Sun's meridian crossing, when he is shining exactly along
the north-south street, may be far off from 12:00. I leave out the
silly shift of the clock for daylight savings time.
There are two main reasons for this deviation from clock noon.
First is the equation of time, combining the variable speed of the
Sun
in the ecliptic and the inclination of the ecliptic from the equator.
These conspire to put the Sun alternatively a little ahead or behind
his position based on a steady motion. It's the latter that governs
the setting of clocks, due to the mechanical simplicity of uniform
movement of the hands around the clock face.
The other is the offset of your town from the central meridian of
your timezone. With the gerrymandered frontiers of timezones, the Sun
may be so far off as 3/4 hour from clock noon! This is specially true
if you are west of the central meridian because over the decades there
is a slow creep westward of the zone boundaries. This effectively
builds into 'standard' time a defacto allyear daylight savings time.
Sunrises
------
All of the considerations for the sunset apply to the sunrise. The
dates of the sunrise along your road are found in exactly the same
manner. The reason sunrises are not so well observed is that they
occur in the hour when you're still asleep or fixing up for a day of
work or chores. However, by knowing that on that certain day the Sun
rises in the line of a certain road, you may shuffle your daily
routine to go and watch that sunrise.
The Islamic Center
----------------
Spinoffs of New York's Stonehenge effect are at least two major
collateral features of astronomy interest. These may be experienced
without regard to date, so please include them in your next visit to
the City. They are the Islamic Center and the McGraw-Hill Gnomon.
In Islam, the congregation in prayer faces toward Mecca. Ideally,
the prayer house, the mosque, also faces Mecca, but in New York most
mosques are built into existing buildings with no such perfect facing.
In all mosques, old and new, there is placed on the wall a marker so
the people inside can correctly face Mecca.
The largest mosque outside the Islamic belt was built on Manhattan
in the late 1980s. It's the Islamic Center on 96th Street and 3rd
Avenue, taking half of the block. Being a new facility, it faces Mecca
so that it is all twisted relative to the street grid.
What is the direction toward Mecca?
Early Islamic astronomers wrestled with this problem and
developed some good geography and navigation. The direction to Mecca
is the 'qibla' and is the fundamental point of reference in the
surrounds of the Moslem in prayer. The term is used in English for a
person who is disoriented, like in an unfamiliar shopping mall. He
lost his qibla! In modern navigation, the qibla is the azimuth of the
great circle joining the praying person to Mecca. It is now a trivial
exercise in spherical geometry to calculate this azimuth; for New
York it is 59.5 degrees.
The Islamic Center, therefore, sits turned by 30 degrees against
3rd Avenue or 60 degrees against 96th Street, making it look, well,
twisted out of line. It is correct for its purpose based on astronomy.
The McGraw-Hill gnomon
--------------------
At 48th Street on 6th Avenue stands the headquarters tower for
McGraw-Hill publishers. In its sunken plaza stands a stainless steel
triangle on a tall stalk. It at first looks like some funky artpiece,
like so many others along this reach of 6th Avenue. For sure its
twisted on the street grid.
This structure is in fact a real noon marker or gnomon. When the
Sun is culminating on the meridian, the shadow of this gnomon
collapses into a straight line. Moreover, the sides of the triangle
are inclined to aim at the Sun at the summer solstice (south upright
side), the two equinoxes (upper longest side), and the winter solstice
(lower side on the stalk). Alas, a tower in 6th Avenue at 47th Street
blocks the very noon Sun at the winter solstice. You'll see him about
ten minutes later when he moves out from behind this building.
Why is this thing here at all?
In the 1960s McGraw-Hill figured to build in its tower the
largest fanciest planetarium on Earth, being that it then owned the
Spitz planetarium company. The plaza would be the grand entry to this
monster facility and had already been built to have three astronomy
exhibits.
The gnomon is one. The second is the stone maps on the floor
showing the continent drift over the eons. This is now intact but
ignored by McGraw-Hill. The last was a model of the solar system, now
a jazz cafe. The diameter of the circular plot, once having a stone
parapet, represented the Sun's diameter. Mounted on short standoffs on
the parapet were polished steel globes proportioned to the planet
sizes. Their placement on the parapet was angularly proportional to
their linear distance from the Sun. I leave out the tedious
explanation but that's how they were placed.
In a short time, like a few months, the globes succumbed to
liberations and eventually were removed by McGraw-Hill. Then McGraw-
Hill sold off the Spitz company and gave up on the planetarium
project. The vast belly of the tower was remade into the New York
Experience multimedia tourist show. It ran for some fifteen years
before closing for being outmoded and outdated. Today the space is
occupied by community rooms, a theater, and various stores.