Masquerade of the Spheres - FEATURE ARTICLE
←
→
Page content transcription
If your browser does not render page correctly, please read the page content below
FEATURE ARTICLE
Masquerade of
the Spheres
Aditi Ghose
E
CLIPSES are treasure troves of scientific explorations.
They have almost always led to new insights into the
physics, chemistry, biology and mathematics of the
world around us. But how do meticulous calculations work
so that scientists and their equipment wind up in the right
place at the right time? What happens if they don't? Predicting
whether our place will experience this year’s last solar eclipse
in December is akin to a challenge – and like all challenges,
the rewards of getting it right are huge too!
Advice to an Umbraphile
"Before you die, you owe it to yourself to experience a total
solar eclipse."
That was an advice from an astronomer to David Baron,
a science writer and much later, self-confessed eclipse
evangelist. Baron was skeptical of such a profound and
intimate counsel. Eclipses have advanced our knowledge of
the sciences in more ways than one. Because a total solar
eclipse, like the one next due in India on 20 March 2034, is
the only time a masked Sun allows us a glimpse into its outer
atmosphere.
Moon's shadow seen falling on Cyprus and coastal
Eclipse experiments have included, but never been Turkey, as seen on 29 March 2006, 230 miles above
limited to tests of general relativity, studies in coronal physics the planet from the International Space Station.
and chemistry, investigations of solar prominences, diameter (NASA)
26 | Science Reporter | July 2021
lity Entail?
What does Tota ing, 2017)
rn er, A Par tia l Eclipse is Interest
(Edwin L. Tu
es an annular
r between A’B’ se
se . Wi th the mo on at M1, an observe se is se en (J. B. Zirker, Total
lip lip
the Mo on ’s sh ad ow during solar ec es a tot al ec lip se ; at C, a partial ec
Geometry of r between AB se
on at M2, an observe n, 1980).
eclipse. With the mo Eclipses of the Su
y experience.
se is a multi-sensor
y, a total solar eclip
Far from seein g a hole in the sk a temperature of
Su n du ring totality is at
visible arou nd th e e seen with white
ro na ̶ th e halo of the gas ce . It gl ow s with a light unlik es our
• The so lar co an the solar su rfa to the eye, it mak
w m illi on de gr ees, far hotter th e. Ap pe ar in g sli ght bluish white
a fe rent hu
a completely diffe
sunlight and has an d va gu ely unreal. e
everyday objects
look we ird e black circle insid
ac k of th e M oo n's night side (th at m os ph eric
ght sky, the bl tificial lighting an
d clear
an the normal ni ack. Little or no ar
• Much blacker th of ou nd ly da rk bl
light) is a pr
the halo of white e fullest.
s he lp to appreciate it to th t the horizon.
condition
d a 36 0° tw ilig ht 'frame' all abou
sty winds an
mpanied by a gu l come out.
• The eclipse is acco to re tu rn while nocturna
y-timers prep ar e
s behave weird, da
• Animals and bird es.
20° in a few minut
s dr op su dd en ly ̶ around 10 to play. If observed
• Temperatu re
d 'Sh ad ow Bands' come into ross
ey's Bead s' an en to race past ac
al ef fe ct s lik e 'D iamond Ring', 'Bail in , th e M oo n's shadow can be se
• Optic high terra
ne location like a d of a jet plane.
from an opportu pe r ho ur ̶ close to the spee
1,000 m ile s even a drug-
the lower valley at m e so rt of ot he r-worldly CGI and
l it to being in so
perienced paralle real.
People who've ex d in this case is, totally
d ha llu cin at ion that feels, an
induce
ian
on the southwest Ind
scene at Bekal Fort, 1872).
Artist’s sketch of the ate d Lo nd on Ne ws
er 1871 (The Illustr
coast, on 12 Decemb pre pa ring a bonfire to en
courage
we re se en relief of
Local inhabitants Mu ch to the
g Su n to be come bright again. t of
the da rke nin for the Advanc en em
British Association
observers from the ec ific ally to ob se rve the
ce , ga the red on the watch tower sp sq ua dro n
Scien s put out by a
g the eclipse, it wa
Sun’s corona durin tal ec lips e, partial failure: Sc
ientific
de n, To
of police (Barbara Ry nn ed , 20 17 ).
ays go as pla
expeditions don’t alw
July 2021 | Science Reporter | 27
measurements, search for interplanetary dust, study of gravity
waves in the Earth's atmosphere, effects on aerosols in the
earth's atmosphere, measurement of water-quality in seas and
experiments on the biological effects of animals and humans
(J.B. Zirker, Total Eclipses of the Sun, 1980).
Physicist Baron knew any given place on Earth
experiences a total solar eclipse once in 400 years. This
totality is visible on a narrow path, merely 100 miles wide.
Then again, if the Moon is further away, a solar eclipse, like
that in December 2067, will feature a very small umbra and
only for 8 seconds of totality (Caleb Scharf, Eclipse: It’s all
about the Umbra, 2017).
But the moon definitely casts this shadow on some region
of Earth every six months. So, to improve his odds of heeding
the astronomer's counsel, Baron decided to travel to a place
due to experience the next total eclipse — the Caribbean in
1998. What he experienced there changed his life forever. "...
pictures just don't do it justice. It's not a ring or halo around Prime Minister Narendra Modi watching Kozhikode's live feed
the sun; it's finely textured like it's made out of strands of of the 26 December 2019 annular solar eclipse.
silk." Of course, he was only talking about the solar corona
there ̶ the muse of scientists and artists alike. But Baron It was noticed that after roughly half a year, the Moon had
claims that it was this moment that transformed him into a an opportunity to cross the Earth-Sun plane within the fabled
life-long Umbraphile ̶ the eclipse chaser. So what does it take 17° alignment. This second eclipse season could be expected
to predict these awe-inspiring eclipses accurately, and how at about 173.3 days after the first. It did not exactly amount
deep does it hurt to mess up? to half a year as the location of lunar crossing nodes shifts
19° in longitude per year. This led to around 11% successive
Getting the Date & Venue Right solar eclipses occurring roughly a synodic month apart, 23%
There have been 11,898 solar eclipses in the past 5 millennia occurring 5 synodic months apart and the remaining 66%
(Caleb A. Scharf, 11,898 Solar Eclipses in 5,000 Years) being 6 synodic months apart. But the celestial masquerade
and even before the mastery of orbital natures and three- was only just beginning.
dimensional state of our Universe, we have been doing a pretty
good job at pinpointing them ̶ almost. The mechanics are The Symphony of Saros
subtle. The Moon crosses the Earth-Sun plane, at the 'node' On a longer timescale, the 'Saros Cycle' comes into play
twice in each lunar orbit ̶ because the lunar orbit is inclined (Fred Espenak, Eclipses and the Saros). Derived from the
by 5.1° to the Earth's orbit around the Sun. With the classic Babylonian term 'sar', an interval of 3600 years, the Saros
New Moon orientation of the Sun and Earth encompassing cycle as an eclipse period is much shorter. Chaldeans
the Moon, there will be a visible solar eclipse, partial or observed that just like the harmonies wafting across a good
total, within around 17° (actually 15.4° to 18.6° owing to masquerade, lunar eclipses, much alike solar eclipses, seemed
the elliptical orbits of the Earth and Moon) on the sky of this to repeat themselves periodically.
crossing. The Sun takes 34.5 days to appear to cross this 17° The beat frequency of this Saros Cycle recurs periodically
radius eclipse zone. The Moon's 'synodic period' of 29.53 over 6585.3 days (18 years, 11 days and 8 hours). The
days with respect to this alignment, slightly longer than its harmonies owe their periodicity to the fact that the Moon's
actual orbital period of 27.3 days, allows at most 2 solar orbital periods share a natural harmony. The Synodic Month
eclipses during this 'season'. The challenge is then to figure (average period of the Moon's orbit with respect to the line
out the next ones. joining Sun and Earth) of 29.53 days is quite similar to the
Geometry of the solar and lunar
apparent disks near a node in
the lunar orbit. If the moon in its
eastward motion overtakes the
Sun at S (the eclipse limit), it
eclipses only the tangent point. If
the moon overtakes the Sun closer
to the node (for instance, at S1), a
total annular eclipse can occur.
28 | Science Reporter | July 2021
Anomalistic Month (time the Moon takes to go between its cycle. For solar eclipses, this entails the westward shift of
closest approach to Earth on its slightly elliptical orbit) of each successive eclipse path by 120°. The Saros series returns
27.55 days and the Draconian Month (time between passages to the same geographic region every 3 saroses (54 years and
through the same orbital node) of 27.21 days. One Saros, as a 34 days).
result, is equal to 223 Synodic months. So are 239 Anomalistic No Saros series lasts indefinitely. With the Moon's
Months and 242 Draconian Months (to within a few hours). node shifting eastward by ~5° with each cycle, the typical
223 Synodic Months (New Moon to New Moon) Saros series for a solar eclipse begins when the new Moon
= 223 x 29.530589 days = 6585 days 07 hours 43 occurs ~18° east of a node. Suppose the first eclipse occurs
minutes at the Moon's descending node, the Moon's umbral shadow
239 Anomalistic Months (Perigee to Perigee) will pass ~3500 km below the Earth, with a partial eclipse
= 239 x 27.554550 days = 6585 days 12 hours 54 visible from the south polar region. On the following return,
minutes the umbra passes ~300km closer to the Earth, with a partial
eclipse of a slightly larger magnitude.
242 Draconian Months (Node to Node)
About 200 years and 10-11 Saros cycles later, the first
= 242 x 27.212221 days = 6585 days 08 hours 35
central eclipse occurs near the South Pole on Earth. Over the
minutes
next 950 years, a central eclipse occurs every 18.031 years
By another masterstroke, these 6585.3 days of the Saros (=Saros) but displaced northward by an average of ~300km.
Cycle also approximately equal 19 revolutions of the Sun in Midway through this period, eclipses of longer duration
its apparent path around the sky with respect to a node (J.B. occur near the equator, while the last central eclipse of the
Zirker, Total Eclipses of the Sun, 1980). This implies that series occurs near the North Pole. With successively smaller
eclipses (both solar and lunar) separated by 18 years, 11 days magnitudes, the next approximately 10 eclipses are partial.
and 8 hours, share similar geometries. After a dozen or more centuries, the Saros series ends
Occurring at the same node, with the Moon at nearly the at the pole opposite to where it began. With two to five solar
same distance from the Earth and also at the same time of eclipses every year, there are 40 different Saros cycles in
the year — these eclipses cast similar shadows too. But just progress at any one time. Thanks to the ellipticity of orbits of
because the Saros period is not equal to a whole number of Earth and Moon, the exact duration and number of eclipses
days, these shadows are cast on different parts of the Earth in a complete Saros series are never constant. A single series,
each time. The extra 1/3 day displacement causes the Earth comprising 69 to 87 eclipses, of which about 40 to 60 are
to have rotated an additional ~8 hours or ~120° with each central (total, hybrid or annular) may last anywhere between
Eclipses from Saros 136 — 1937 through 2081 (Courtesy of Michael Zeiler), currently producing the longest total solar
eclipses of the 20th and 21st centuries. Producing 71 eclipses over 1262 years, the westward ~120° shift of each eclipse
path is a consequence of the extra 8 hours in the length of the Saros period. The northward shift is due to the progressive
motion of the Moon with respect to its descending node at each eclipse.
July 2021 | Science Reporter | 29Numbering th
(Fred Espenak e Saros
, Eclipses and th
‘Odd’ Saros nu e Saros)
mbered eclipse
progressively so s, occurring ne
uthward with ea ar the Moon’s
numbered eclip ch successive So ascending node
ses occur near lar eclipse. In co , shift
northward with the Moon’s desc ntrast, ‘even’ Sa
respect to the ending node an ros
Dutch astronom Earth’s centre. d shift progress
er G. van den iv ely
(and Lunar) Ec Bergh, in his ‘P
lipses’ (Tjeenk eriodicity and
numbering syst Willink, Haarle Variation of So
em used for th m, Netherland lar
eclipses in von e Saros series. s, 1955) introduc
Oppolzer’s ‘Can H e began by pl ed th e
matrix. Each Sa on der Finstern acing all 8,000
ros series was isse’ (1887) in a solar
chronological arranged in a large 2-dimen
order. The Saro separate colum sional
interval betwee s series colum n with the eclip
n any two eclip ns were then stag se s in
-20 days). That ses in adjacent gered so that
was the eclipse co lumns was 1057 the
helpful on orga cycle Inex. The 1.95 days (= 29
nising eclipses. re sultant Saros-In ye ars
For example, on ex Panorama w
e-step down in as
(6585.32 days) la th e pa no ra m
ter, while one st a is a change
days) later. The ep to the right of one Saros pe
rows and colum is a change of on riod
Inex numbers. ns were conseq e Inex period (10
Saros numberin ue ntly numbered 57 1.95
begin or end. In g sequences ar with the Saros
stead they follo e independent of an d
the umbral shad w the order in when the serie
ow axis passes w hi ch the series pe s
closest to the ce aks ̶ that’s w
ntre of the Eart hen
h.
Saros-Inex Panoram
a
1,226 to 1,550 years. Last 26 December 2019 annular eclipse,
visible from southern India was the 46th of 71 eclipses of Saros
cycle 132. The 21 June 2020 annular eclipse, visible from
northern India was part of Saros cycle 137.
Solar Eclipses of Saros 137
Eclipse Type Number Percent
All Eclipses 70 100.0%
Partial 15 21.4%
Annular 36 51.4%
Total 10 14.3%
Hybrid 9 12.9%
36th series member of the 70 eclipse Saros Cycle 137, causing the
21 June 2020 annular eclipse visible in India. The series started
30 | Science Reporter | July 2021 with a partial solar eclipse on 25 May 1389 and shall end with one
on 28 June 2633, more than a millennium later.Williams' illustration in his report of the eclipse. 'Baily's Beads' are visible in Fig. VII
on the upper right. (Memoirs of the American Academy of Arts and Sciences)
Lingering in the Shadows Today we can churn out the numbers by the dozen
"The longitude of our place of observation agrees very well due to the computational prowess of our digital world. But
with what we had supposed in our calculations. But the humans across millennia, have depended on their meticulous
latitude is near half a degree less than what the maps of that observations and accurate bookkeeping alone in an attempt
country had led us to expect." to predict the recurrence of eclipses. Yet even with the most
precise calculations and best-in-its-class experimental gear,
This was Harvard College's professor of mathematics and eclipse expeditions have always been a game of chance. And
natural philosophy, Samuel Williams' report to the American chance, as they say, favours the prepared mind.
Academy of Arts and Sciences. He had dodged all obstacles. It took one such eclipse to prove Einstein's theory of
With the Revolutionary War in full force, Williams had relativity right, when Arthur Eddington viewed light from
gained a pass into the hostile territory of Maine, to the island the Hyades star cluster going "askew" under the enormous
of Isleboro, three miles offshore from the mainland on 27 gravitational influence of the Sun, three years after Einstein’s
October 1780, was equipped to study the Sun's corona and prediction was published (Rebecca Boyle, America in the
had been blessed with a cloudless sky ̶ only to realise that Shadows, 2017).
he wasn't in the path of totality of the solar eclipse as he had Back in Maine, Samuel Williams had barely missed
calculated. On the way back he reasoned — half a degree of totality that day. But he never stopped observing or recording.
longitude corresponds to 30 nautical miles. They were merely The narrow sliver of partly eclipsed Sun he observed through
bad maps that led William too far south, causing him to miss his smoke-blackened glass that day appeared "broken or
his once-in-a-lifetime opportunity that day (Barbara Ryden, separated into drops". He had just seen and recorded the Baily's
Total eclipse, partial failure: Scientific expeditions don't Beads ̶ sunlight streaming through valleys and depressions
always go as planned, 2017). along the Moon's visible edge. Of course, he would never
So, what's the key to nailing the celestial masquerade get credit for their discovery and it would take astronomer
of our spheres? Is it the Saros Cycle? The 'Inex' ̶ period Francis Baily another 56 years to observe, describe and have
of 358 synodic months (a little under 29 years)? After all, the beads named after him. But Williams’ recordings, in spite
assuming a solar eclipse is visible in the southern hemisphere, of his inaccurate maps and crude devices, are an ode to all
exactly one Inex later there will be one visible in the northern eclipse hunters down the ages ̶ amidst a load of uncertainties,
hemisphere. There are others ̶ the Tritos (11 years 1 month), they inspire us to take a shot.
the Metonic Cycle (19 years), the Exeligmos (triple Saros).
Of course, they never exist in isolation. Some periods are
combinations of Saros and Inex periods spanning a couple
of thousand years that allow for prediction of the geographic Ms Aditi Ghose is an Education Officer at the Birla Industrial &
Technological Museum, under the National Council of Science
latitude and longitude of the central path of the eclipse shadow Museums, an autonomous organisation for science popularisation
— the Accuratissima and Heliotrope respectively. Do they of the Government of India. She is passionate about communicating
help? science in all its forms and can be reached at aditincsm@gmail.com
July 2021 | Science Reporter | 31You can also read
