FEATURE ARTICLE Masquerade of the Spheres Aditi Ghose

CLIPSES are treasure troves of scientific explorations. They have almost always led to new insights into the Ephysics, 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 ’s last solar 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 ." 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. 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 allows us a glimpse into its outer atmosphere. '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)

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What does Totality Entail? (Edwin L. Turner, A Partial Eclipse is Interesting, 2017)

A’B’ sees an annular M1, an observer between C, a partial eclipse is seen (J.B. Zirker, Total Geometry of the Moon’s shadow during solar eclipse.AB sees With a the total moon eclipse; at at M , an observer between eclipse. With the moon at 2 Eclipses of the Sun, 1980).

Far from seeing a hole in the sky, a total solar eclipse is a multi-sensory experience.

• The solar corona ̶ the halo of the gas visible around the Sun during totality is at a temperature of a few million degrees, far hotter than the solar surface. It glows with a light unlike seen with white sunlight and has a completely different hue. Appearing slight bluish white to the eye, it makes our everyday objects look weird and vaguely unreal.

• Much blacker than the normal night sky, the black of the Moon's night side (the black circle inside the halo of white light) is a profoundly dark black. Little or no artificial lighting and clear atmospheric conditions help to appreciate it to the fullest.

• The eclipse is accompanied by a gusty winds and a 360° twilight 'frame' all about the horizon.

• Animals and birds behave weird, day-timers prepare to return while nocturnal come out.

• Temperatures drop suddenly ̶ around 10 to 20° in a few minutes.

• Optical effects like 'Diamond Ring', 'Bailey's Beads' and 'Shadow Bands' come into play. If observed from an opportune location like a high terrain, the Moon's shadow can be seen to race past across the lower valley at 1,000 miles per hour ̶ close to the speed of a jet plane.

People who've experienced parallel it to being in some sort of other-worldly CGI and even a drug- induced hallucination that feels, and in this case is, totally real.

1872). Artist’s sketch of the scene at BekalThe Illustrated Fort, on the London southwest News Indian coast, on 12 December 1871 ( Local inhabitants were seen preparing a bonfire to encourage the darkening Sun to become bright again. Much to the relief of observers from the British Association for the Advancement of Science, gathered on the watch tower specifically to observe the Sun’s corona during the eclipse, it was put out by a squadron Total eclipse, partial failure: Scientific of police (Barbara Ryden, . expeditions don’t always go as planned, 2017)

July 2021 | Science Reporter | 27 measurements, search for interplanetary dust, study of gravity waves in the '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 . 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 . 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 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 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 | 29 Numbering the Saros (Fred Espenak, Eclipses and the Saros) ‘Odd’ Saros numbered eclipses, occurring near the Moon’s ascending node, shift progressively southward with each successive Solar eclipse. In contrast, ‘ numbered eclipses occur near the Moon’s descending node and shift progressively northward with respect to the Earth’s centre. even’ Saros Dutch astronomer G. van den Bergh, in his ‘ (and Lunar) Eclipses Periodicity and Variation of Solar numbering system used’ (Tjeenk for the Willink, Saros Haarlem,series. He Netherlands, began by placing 1955) all introduced 8,000 solar the eclipses in von Oppolzer’s matrix. Each Saros series was‘Canon arranged der Finsternisse in a separate column with the eclipses in ’ (1887) in a large 2-dimensional chronological order. The Saros series columns were then staggered so that the interval between any two eclipses in adjacent columns was 10571.95 days (= 29 years -20 days). That was the eclipse cycle . The resultant Saros-Inex Panorama was helpful on organising eclipses. For example, one-step down in the panorama is a change of one Saros period (6585.32 days) later, while one step to the right is a change of one Inex period (10571.95 days) later. The rows and columns were consequently numbered with the Saros and Inex numbers. Saros numbering sequences are independent of when the series begin or end. Instead they follow the order in which the series peaks ̶ that’s when the umbral shadow axis passes closest to the centre of the Earth.

Saros-Inex Panorama

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 (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 [email protected]

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