Advanced science, Astrophysics, Environmental, Technical

How global warming is impacting on Earth’s spin

Anthropogenic greenhouse gas emissions might be affecting more than just the climate. For the first time, scientists at NASA presented evidence that the orientation of the Earth’s spin axis is changing because of global warming.

global_warming_1[1]The Earth spins from west to east about an axis once every 24 hours, creating the continuous cycle of day and night. The north-south spin axis runs through the North and South Poles and is tilted by 23.5 degrees from the vertical. The axial tilt causes almost all the seasonal changes.

But the tilt is far from constant. It varies between 21.6 and 24.5 degrees in a 41,000-year cycle. This variation together with small fluctuations in the Sun and Moon’s gravitational pull, oblate shape and elliptical orbit of the Earth, irregular surface, non-uniform distribution of mass and movement of the tectonic plates cause the spin axis, and hence the Poles, to wobble either east or west along its general direction of drift.

Until 2005, Earth’s spin axis has been drifting steadily in the southwest direction around ten centimetres each year towards the Hudson Bay in Canada. However, in 2005, the axis took an abrupt turn and started to drift east towards England at an annual rate of about 17 centimetres, according to data obtained by NASA’s Gravity Recovery and Climate Experiment satellites. It is still heading east.

After analysing the satellite data, scientists at NASA’s Jet Propulsion Laboratory in California attribute the sudden change in direction of the axis mainly to melting of Greenland’s ice sheets due to global warming. The reason: Melting of ice sheets and the resulting rise of the sea level are changing the distribution of mass on Earth, thereby causing the drift of the spin to change direction and become more oblique. The axis is particularly sensitive to changes in mass distribution occurring north and south of 45 degrees latitude. This phenomenon is similar to the shift in the axis of rotation of a spinning toy if we put more mass on one side of the top or the other.

Since 2002, ice sheets of Greenland have been melting at an annual rate of roughly 270 million tonnes. Additionally, some climate models indicate that a two-to-three degrees Celsius rise in temperature would result in a complete melting of Greenland’s ice sheets. If that happens, it could release the equivalent of as much as 1,400 billion tonnes of carbon dioxide, enhancing global warming even further. It would also raise the sea level by about 7.5 meters. By then, the wobbling of the Poles would also be completely out of whack.

The ice in the Arctic Ocean has also decreased dramatically since the 1960s. For every tonne of carbon dioxide released into the atmosphere, about three square meters of Arctic’s ice were lost in the last 50 years. This reflects a disquieting long-term trend of around ten percent loss of ice per decade. Furthermore, Antarctica is losing more ice than is being replaced by snowfall. The influx of water from the melting of ice of the Arctic Ocean and Antarctica together with the melting of glaciers and the subsequent redistribution of water across the Earth is also causing our planet to pitch over.

What does this mean for us? Although something as small as we humans shook up something as massive as the Earth, it won’t turn upside down as long as the Moon, which acts as a stabiliser of the Earth’s spinning motion, stays in the sky as our nearest neighbour. However, if the shift of the spin axis maintains its present rate and direction, then by the end of this century, the axis would shift by nearly 14 meters. Such a large shift will have devastating consequences for climate change and our planet.

The orientation of the Earth’s spin axis determines the seasonal distribution of radiation at higher latitudes. If the axial tilt is smaller, the Sun does not travel as far north in the sky during summer, producing cooler summers. A larger tilt, as could be in the future, would mean summer days that would be much hotter than the present summer days. In addition, it would impact the accuracy of GPS and other satellite-dependent devices.

Since global warming is causing the Earth’s mass to be redistributed towards the Poles, it would cause the planet to spin faster, just as an ice skater spins faster when she pulls her arms towards her body. Consequently, the length of a day would become shorter.

Our biological clock that regulates sleeping, walking, eating, and other cyclic activities is based on a 24-hour day. Faced with a shorter day, these circadian rhythms would be hopelessly out of sync with the natural world. Moreover, a rapidly spinning Earth will be unstable to the extent that the Poles would wobble faster. This would create enormous stress on the Earth’s geology leading to large-scale natural disasters that will most likely be disastrous for life on Earth.

We may not witness the effects of a rapidly spinning Earth by the end of this century or the next. Nevertheless, the effects will be perceivable a few centuries from now if the global temperature keeps on rising and the ice sheets keep on melting in tandem.

The shift in the Earth’s spin axis due to climate change highlights how real and profoundly large impact humans are having on the planet. The dire consequences of the shift in the axial tilt towards a larger obliquity, as noted above, is not a wake-up call, but an alarm bell. There is still time for our leaders to listen to the scientists and formulate a long-term approach to tackle the problem of climate change instead of a short-term Band-Aid approach, as outlined in the 2015 Paris Agreement, which will see us through only to the end of this century. Therefore, our foremost goal before the death knell should be to reverse global warming, or at the least, to stop further warming instead of limiting it to 1.5-degree in the next 75 years or so.

The author, Quamrul Haider, is a Professor of Physics at Fordham University, New York.


Advanced science, Astrophysics, Bangladesh, Economic, International, Technical

Orbit of Bangabandhu-1 and other satellites

May 12, 2018 is a red-letter day in the history of Bangladesh. On this day, “Bangladesh started a glorious chapter in the history with the launching of Bangabandhu-1 satellite,” President Abdul Hamid said in a message to the nation. Indeed, Bangabandhu-1 added a new milestone to the path of continued advancement of the country. Proudly displaying the flag of Bangladesh on its solar panels, the satellite is orbiting the Earth in a geostationary orbit located at 119.1 degrees east longitude.

The physics of a satellite’s orbit is remarkable. For our current knowledge of orbital motion, we owe tons of gratitude to Johannes Kepler who, in the early 17th century, relentlessly pursued the planetary orbits by putting the Sun at the centre of ‘his’ Universe. In this pursuit, he gave us three laws of planetary motion that endure to this day. Of particular interest to the motion of satellites is his third law, which states that the square of a planet’s orbital period (in years) is equal to the cube of the planet’s average distance (in astronomical unit) from the Sun. One astronomical unit is the average distance of Earth from the Sun, which is approximately 150 million km.

By working with his laws of motion and the universal law of gravitation, Isaac Newton found that Kepler’s third law is a special case of a more general law. He showed that in addition to the cube of the average distance of a planet from the Sun, square of the orbital period is also inversely proportional to the mass of the Sun. Moreover, according to Newton, the orbital speed of a small object orbiting a much more massive object depends only on its orbital radius, not on its mass. Accordingly, if satellites are closer to Earth, the pull of gravity gets stronger, and they move more quickly in their orbit.
The speed, however, depends on the mass of the massive object. That is why an astronaut does not need a tether to stay close to the International Space Station during a space walk. Even though the space station is much bigger than the astronaut, both are much smaller than Earth and thus stay together because they have the same orbital speed.

Satellites can be placed in different kinds of orbit – geosynchronous, geostationary, Sun-synchronous, semi-synchronous, orbit at Lagrange points.When a satellite is placed in a ‘sweet spot’ where, irrespective of its inclination, it orbits the Earth in the same amount of time the Earth rotates with respect to the stars, which is 23 hours 56 minutes and 4 seconds, it would appear stationary over a single longitude in the sky as seen from the Earth. This kind of orbit, where communication satellites are placed, is called geosynchronous orbit.

A special case of geosynchronous orbit is the geostationary orbit, which has a circular, geosynchronous orbit directly above the Earth’s equator. Besides communications, both orbits are also extremely useful for monitoring the weather because satellites in these orbits provide a constant view of the same surface. Using the rotational time and known mass of the Earth, we find that the orbital radius of a geostationary orbit is about 42,220 km from the centre of the Earth, which is about 35,850 km above the Earth’s surface.

Just as geosynchronous satellites have a sweet spot, satellites in a near polar orbit have a sweet spot too. If the orbits of these satellites are tilted by about eight degrees from the pole, a perturbing force produced by Earth’s oblateness would cause the orbit to precess 360 degrees during the course of the year. Satellites in such an orbit, known as Sun-synchronous or Helio-synchronous orbit, would pass over any given point on the Earth’s surface at the same local time each day. Additionally, they would be constantly illuminated by the Sun, which would allow their solar panels to work round the clock. Orbiting at an altitude between 700 and 800 km with an orbital period of roughly 100 minutes, satellites in a Sun-synchronous orbit are used for reconnaissance, mapping the Earth’s surface and as weather satellites, especially for measuring the concentration of ozone in the stratosphere and monitoring atmospheric temperature.

Many Global Positioning System (GPS) satellites are in another sweet spot known as semi-synchronous orbit. While geosynchronous orbit matches Earth’s rotational period, satellites in semi-synchronous orbit, at an altitude of approximately 20,000 kilometres, are in a 12-hour near-circular orbit. With a smaller orbital radius, a satellite would have a larger coverage of ground area on the Earth’s surface.

Other orbital sweet spots are five points located on the Earth’s orbital plane. The combined gravitational force of the Earth and the Sun acting on a satellite placed at these points, known as Lagrange points, would ensure that its orbital period is equal to that of Earth’s. Hence, the satellite will maintain its position relative to the Earth and the Sun.
The two nearest Lagrange points, one between the Earth and the Sun and the other in the opposite direction of the Sun, each 1.5 million km away from the Earth, are home to many space-based observatories. Some of them are the Solar and Heliospheric Observatory designed to study the internal structure of the Sun, the Deep Space Climate Observatory producing accurate forecasts and providing warning by monitoring dangerous space-weather conditions, and the Wilkinson Microwave Anisotropy Probe measuring the cosmic background radiation left over from the Big Bang.
The writer is a Professor of Physics at Fordham University, New York.

Advanced science, Astrophysics, Cultural, Environmental, Life as it is, Religious, Technical

Ranking of Human Civilisation

Despite what the great ‘Divine Books’ such as Torah, Bible, Quran, Bhagavat Gita and so on and so forth say about the existence of life on earth, scientifically life on earth originated from single cells which then mutated to form multi-cellular organisms. The evolution of primates (comprising apes, chimpanzees, gorillas and eventually humans) can be traced back to over 65 million years. Primates are one of the oldest of all placental mammal groups, which withstood the vagaries of life.

There is now a consensus of opinions among the evolutionary scientists that evolution of Hominidae (apes) took place around 28 million years ago and then subsequently subfamilies – homininae (humans, chimpanzees, bonobos, gorillas), homo genus (humans, Neanderthals, homo erectus), homo sapiens (intelligent humans) and finally anatomical modern humans took place about 8 million years, 2.5 million years, 0.5 million years and 200,000 years ago respectively. This chronological development of evolutionary chain is what is accepted now as incontrovertible scientific fact.

The anatomically modern human beings who first appeared in South West Africa – near the coastal borders of Namibia and Angola – were intelligent animals with highly developed brains, and this intelligence led them to become savage animals in the rough and tough world to survive. Around 50,000 years ago, they started migrating to other continents (as permafrost offered them land migration routes) and colonised other areas. When they came across Neanderthals (a subspecies of homo genus) in Europe and other hominins in Asia, they were systematically eliminated. Neanderthals completely disappeared around 30,000 years ago. The victorious modern human beings were, nonetheless, hunter gathers competing for food with four legged animals like wolfs, hyenas, dogs etc. That was the time when one can call human civilisation at level 0.

Since that time, human brain rather than brawn evolved drastically, which is directly attributable to evolutionary mechanism. Although evolutionary process was in action for millions of years, it took a step change. Humans as a distinct species (two legged animals) coalesced together and started to fight jointly against other species. They developed cooperation, communication, collectivism etc, all of which gave them superior strength which no other animal species could muster. Human civilisation was gradually progressing, but still it was stuck at the primitive level 0.

A step change in civilisation came about at around 10,000 years ago, when ice in the Ice Age started to recede after hundreds of thousands of years of permafrost. As ice melted, soil started to surface and vegetation, plants, grasses etc appeared. The human beings with their ingenuity started to farm land, domesticated animals such as cows, horses, dogs etc., produced agricultural products, formed communities and tribes. The hunter gathers were no longer solely reliant on animals for food, they developed diversified food products and eating habits. Whereas previously they used animals for food, now they started to produce food with their own hands. The energy they expended per capita could be estimated as around quarter of a horse power (~200W). This development can be designated as level 1 of type 1 civilisation.

From that time on, human civilisation started to progress at accelerated pace. Humans started to appreciate, admire and even worship the powers of nature; wondered about the might of the sun, rain, storm, fire, earth and so forth and created in their minds and thought processes various deities, gods etc, who were perceived to be more powerful than mere mortal human beings. These fictitious constructs gradually got embedded in the minds as irrevocable entities and these formed the seed corns of numinous undertakings, which flourished eventually as religions.

About 5,000 years ago, Abraham in the land of Canaan (in the Middle East) merged all these disparate and conflicting gods and divine constructs into a single entity and created a unitary God. That was the beginning of monotheism which culminated into three major Abrahamic religions – Judaism, Christianity and Islam. The unitary God was proclaimed to be all powerful, all knowledgeable, all pervasive, eternal creator of everything. Over the centuries, these three versions of the unitary God fought for supremacy and allegiance of human beings.

Whether the advent of religions, either monotheistic or polytheistic, is a progress in human civilisation or a sheer retrogressive step is open to question. This religious mindset, relegating human beings to moronic state totally reliant on the whims of abstract all-powerful non-existent God is delusional, to say the least. This transfer of human accountability to this God is so tempting and enduring that religions have taken over the thread of civilisation in a way that no other philosophical undertaking could possibly do. For centuries since Abrahamic time, through Jesus Christ and Mohammad, literature, art, culture, architecture, philosophy etc were dominated by religious ideas. Numerous sculptors, painters, poets, authors and so forth all eulogised the existence and powers of God.

Around 300 years ago, another civilizational step took place with the coming of industrial revolution. Steam engines started to drive machines and locomotives. No longer humans were dependent on their bare hands or on animals. Cars, trucks, trains etc were driven by steam engines or internal combustion engines. Electricity was produced by steam engines (turbo-generators) due to the motion of electromagnets. Industries of various sorts started to develop, human population increased, towns, cities started to develop. Population grew not only due to the availability of food but also due to the advancement of biological/medical sciences taming all diseases in general and diseases like cholera, TB etc, in particular, causing epidemic among population. Progress in science and technology steamed ahead and civilisation went up few notches.

Another enormous step change came during the past few decades. This time it was not the physical expansion of wealth generation and prosperity, but the increase in information technology. No longer humans were dependent on mode of communication by notes on papers, letters, telegrams or even fixed line telephony, but on electronic communication, where electrons danced through cables, fibre-optics etc. People now communicate live in various continents, send photos, documents etc instantaneously. A man in the UK can talk simultaneously to people in Japan, Australia, America and Argentina all at the same time. People can move from one place to another at enormous speeds.

Satellites in the sky can detect an object anywhere on the ground as small as few meters. Satellite navigation is a common mode of identifying location, particularly for transport vehicles, replacing age-old traditional maps. Letters, parcels etc can be delivered by drones, flying in air and descending at the back of gardens within a matter of hours. Although drone technology is available now, but it could not be put in practice until some safety provisions and regulatory requirements are enforced. This advanced state of civilisation can be placed as level 7.

There are yet many more technological advancements to be had in this world and we can gradually move towards civilisation levels 8, 9 and 10. At that stage, human beings would be looking beyond our planet into the outer skies.

Now the readers must be admired at this stage who had come this far without knowing what this ranking of civilisation is and what are these levels? Back in 1964, a Russian astrophysicist by the name Nikolai Kardashev was probing the outer skies – planets, stars, galaxies etc – for signs of civilisation. But then he was confronted with the very fundamental question of ‘what is civilisation’? Is civilisation just an abstract concept which cannot be quantified and ranked, only felt and sensed? If that is the case, are we not constrained in categorising a civilisation as to its level of achievement?

Kardashev realised that different professions would tend to define civilisations differently – an artist might define a civilisation by the creative flavour of paintings by its inhabitants; a poet might define it by the quality of poems, culture and the society; a philosopher might try on the basis of abstract theological ideas, its society, government and so on. A physicist might like to quantify on the basis energy it needs. And that is how the scientific ranking of the civilisation is portrayed here.

According to Kardashev if the civilisation of a planet or heavenly body is solely dependent on the energy or power it receives from its primary source – Sun in the case of Earth – then that civilisation is Type I. He then quantified that a ball point figure of 1017 watts as the limiting power for Type I civilisation. A Type II civilisation is one which harnesses stellar energies – energies beyond the constraints of the planet itself. A Type III civilisation is galactic, harnessing energies in the outer skies coming from millions and billions of stars and galaxies.

The human civilisation has not even reached the zenith of Type I civilisation. With all the advanced technologies, we may be hovering around level 6 or 7 and so we have three more levels to go before we could be harnessing around 1017 watts to reach the end of Type I civilisation. It might take a century or two before we reach that stage.

Two more articles will be presented here dealing with Type II and Type III civilisations. So, watch out readers for stellar and galactic civilisations!


A. Rahman is an author and a columnist.

Advanced science, Astrophysics, International, Technical

Stephen Hawking: The supernova of cosmology

In 1974, by predicting the apparently paradoxical concept of radiation emanating from black holes, Hawking reminded us that mass and energy are two sides of the same coin.


We humans are a recent phenomenon in the Universe that is very old, mostly imperceptible and beyond our comprehension. Had it not been for great scientists like Isaac Newton, Albert Einstein, Edwin Hubble, Karl Schwarzschild, Subrahmanyan Chandrasekhar, Stephen Hawking and many more who unlocked the enduring mysteries of the boundless Universe, it would have been a struggle for lesser mortals like us getting our bearings straightened about our place in the cosmos. Their ground-breaking work, forever, changed our view of the “heavens.”

Postulated in 1687, Newton’s law of gravity was a beautiful synthesis between terrestrial and celestial phenomenon, reaching across the vast expanse of the Universe. It allows us to study the waltzing motion of the planets, moons, stars and other objects in the sky with clockwork precision.

Einstein’s special relativity, published in 1905, tells us that time is not only elastic, it is also the fourth component of the spacetime fabric of the Universe. Ten years later, his general relativity redefined gravity as matter’s response to the curving of spacetime caused by surrounding massive objects.

In 1916, Schwarzschild found that the solution of Einstein’s general relativity equations characterized something that confounds common sense ‒ an unfathomable hole drilled in the superstructure of the Universe. Today, we call this voracious gravitational sinkhole a black hole, a single point of zero volume and infinite density.

Much to Einstein’s consternation, in 1929, Hubble discovered that the Universe is expanding in size. His “constant” enabled us to estimate the age of the Universe. In 1930, Chandrasekhar’s calculations indicated that when a massive star runs out of fuel, it would blow itself apart in a spectacular but violent explosion and then collapse into a black hole.

Black holes were discovered in 1971, when astronomers detected a hint of radio wave emissions coming from an object in the constellation Cygnus. The emissions were later interpreted as the fingerprint of the black hole Cygnus X-1. Since then, numerous black holes, including supermassive ones, have been detected in our own Galaxy ‒ The Milky Way, and elsewhere in the Universe. According to NASA, supermassive black holes are growing faster than the rate at which stars are being formed in their galaxies.

Cloaked behind the event horizon, which is not a physical barrier but just an information barrier, it must seem that there is no way of getting mass from the black hole back out into outer space. No way, that is, not until the British physicist Stephen Hawking, arguably one of the greatest minds in scientific history, joined the Big League of Cosmology in the mid-twentieth century. With his seminal contributions to the fields of astrophysics, general relativity, quantum gravity and black holes, he raised the field of cosmology from a niche topic to a well-developed subject in the forefront of science.

In 1974, by predicting the apparently paradoxical concept of radiation emanating from black holes, Hawking reminded us that mass and energy are two sides of the same coin. He was able to show that a black hole, like any other body whose temperature is not absolute zero, emits energy in the form of radiation, energy now known as Hawking Radiation.

The continual emission of radiation causes the black hole to shrink in mass. In other words, black holes “evaporate,” although the time it takes for a solar-mass black hole to evaporate completely is immensely long ‒ vastly larger than the age of the Universe, which is 13.7 billion years. The implications are nonetheless important ‒ even black holes evolve and die.

One of the Gordian knots of cosmology is the missing mass of the Universe. There is irrefutable evidence that visible matter accounts for only four percent of the Universe’s mass. The remaining 96 percent is invisible of which 73 percent is attributed to a pervasive “dark energy,” believed to be manifestation of an extremely powerful repulsive force that is causing the expansion of the Universe to accelerate. The additional 23 percent is thought to be dark matter whose origin obviously is the many black holes spread throughout the cosmos. However, their total mass does not add up to account for all the dark matter.

To address this issue, in 1971, Hawking advanced the idea that in the intergalactic space, there may be “mini” black holes with very small masses ‒ much smaller than the mass of the Earth ‒ yet numerous enough to account for most of the unaccounted dark matter. He hypothesized that they may have been formed during the first instants of chaos following the Big Bang when matter existed in a hot, soupy plasma. Since mini black holes have not been detected so far, Hawking lamented: “This is a pity, because if they had, I would have got a Nobel Prize.”

During the 1980s, Hawking devoted much of his time contributing to the theory of cosmic inflation ‒ the expansion of the Universe at an exponential pace before settling down to expand at a slower pace. In particular, he demonstrated how minuscule variations in the distribution of matter during this period of expansion, known as the Planck era, helped shape the spread of galaxies in the Universe.

As noted above, the core remnant of a high-mass star would eventually collapse all the way to a point ‒ a so-called singularity. Having said that, singularities are places where laws of physics break down. Consequently, some very strange things may occur near them. As suggested by Hawking, these strange things could be, for instance, gateway to other universes, or time travel, but none has been proved, and certainly none has been observed. These suggestions cause serious problems for many of our cherished laws of physics, including causality ‒ the idea that cause should precede the effect, which runs into immediate problem if time travel is possible ‒ and energy conservation, which is violated if matter can hop from one universe to another through a black hole.

While scientists know Hawking for his work on cosmology, millions of others know him because of his book “A Brief History of Time.” His lucid explanation of the mechanism leading to the creation of the Universe, our place in it, how we got there, where did space and time come from, and where we might be going made the notoriously difficult subject of cosmology more understandable to the layperson.
In a follow-up book titled “The Grand Design,” Hawking outlines his consuming quest for the long-dreamed-of “Theory of Everything,” the quantum theory of gravity. Such a theory would unify the two pillars of twentieth century physics, general relativity and quantum theory.

Known as the M-Theory (M stands for Mother-of-All), it would enable us to understand all phenomena in space-time, especially the first split second of cosmic creation, when everything was unimaginably small and densely packed.

Hawking was about as pure an atheist as one can be. He dismissed the existence of an omnipotent by noting that “regularities in the motion of astronomical bodies such as the sun, the moon, and the planets suggested that they were governed by fixed laws rather than being subjected to the arbitrary whims of gods and demons.” Nevertheless, in December 2016, he had a surprising but cordial encounter with Pope Francis at a convention on Big Bang in Rome.

Besides being a genius, Hawking’s celebrity status derives from his spunk in the face of physical adversity. Born on 8 January 1942 in Oxford, England, Hawking was diagnosed with a debilitating, incurable neuromuscular disorder, commonly known as motor neurone disease (MND), when he was just 21 years old. Although doctors predicted that he has only two more years to live, he lived another 55 years and died on 14 March, 2018. There are some interesting anecdotal coincidences. Hawking was born on the 300th anniversary of Galileo’s death and died on the 139th anniversary of Einstein’s birth. Following his cremation, his ashes will be interred on 15th June 2018 in Westminster Abbey’s nave, next to the grave of Isaac Newton and close to Charles Darwin.

Instead of ruing about his mortality, Hawking considered his illness as a blessing, allowing him, in his own words, “to focus more resolutely on what he could do with his life.” Indeed, with a crumpled, voiceless body ensconced in a wheelchair, he soared and established an exalted scientific reputation as the most recognizable scientist of the modern era. The name of this supernova of cosmology will be engraved in the sands of time as long as humanity lives.

The writer, Quamrul Haider, is a Professor of Physics at Fordham University, New York


Astrophysics, International, Technical

Chandrasekhar and Eddington


Around 1020 BC, a shepherd boy named David took on the mighty Goliath and felled him with just a pebble and a sling on a battlefield in ancient Palestine. Since then, the names of David and Goliath signify battles between underdogs and giants. Now fast forward to early 20th century. The David of the scientific world is an Indian child prodigy named Subrahmanyan Chandrasekhar, an outstanding astrophysicist and a towering figure of 20th century science, who published his first scientific paper in the Proceedings of the Royal Society of London when he was just 19 years old.

Born in Lahore on October 19, 1910, Chandrasekhar studied physics at the Presidency College in Madras (now Chennai). He obtained his BSc degree in 1930, the year his paternal uncle CV Raman became the first Indian to win the Nobel Prize in Physics. Due to his stellar academic achievements, Chandrasekhar was awarded a scholarship to pursue doctoral studies at Trinity College in Cambridge, UK. Accordingly, he set sail for London in July 1930. He earned the doctorate degree in 1933.

During the long voyage to London, 19-year-old Chandrasekhar had enough time to pore over a problem that had bothered him for a long time – what happens to stars in the terminal stage of their life. On board the ship, he completed the calculations showing that the fate of a star depends on a critical mass, which is 1.4 times the solar mass.

Now known as the ‘Chandrasekhar Limit’, it is the limiting mass of white dwarfs – the end-stage of Earth-sized stars, but about 200,000 times as dense. If a star’s mass falls below the limit, it would end up in the stellar graveyard as a white dwarf. Otherwise, it would blow itself apart in a spectacular but violent supernova explosion and then collapse into a smaller – about 20 km in diameter – remnant called a neutron star, or possibly into a single massive point with no dimensions and infinite density. Indeed, this was the first prediction of what we now call a black hole – an entity from which nothing can escape, not even light.

Unfortunately, Chandrasekhar’s view was obstinately opposed by Arthur Eddington, the Goliath of astrophysics of the era, who knew about the possibility of black holes but refused to believe they could exist. And, thus, began the fight between David and Goliath of the scientific world. Eddington found Chandrasekhar’s conclusion about the fate of the stars unacceptable and launched an attack on his work, both publicly and privately.

On January 11, 1935, after Chandrasekhar presented the results of his research at a meeting of the Royal Astronomical Society in London, Eddington ridiculed the Chandrasekhar Limit as a “reductio ad absurdum”, meaning a logically absurd conclusion. He steadfastly refused to consider the idea that stars might collapse to nothing. He trashed Chandrasekhar’s theory as mere mathematical gimmick with no basis in reality.

Eddington’s arrogance and criticism devastated Chandrasekhar. He was shocked that instead of giving him credit for solving a challenging problem, Eddington was bent on destroying his work. But Chandrasekhar held his ground. In his fight to counter Eddington, he was assured by Niels Bohr, the 1922 Physics Nobel Laureate, that Eddington was patently wrong and should be ignored.

Nevertheless, the 1935 incident led Chandrasekhar to believe that an influential figure like Eddington could derail his career if he stays in Europe. He, therefore, moved to Chicago in 1937, where the University of Chicago provided him with an intellectual home – first at the Yerkes Observatory in Wisconsin and then at the physics department in the city campus, where he stayed until his death on August 21, 1995.

Two years after he moved to Chicago, Chandrasekhar and Eddington had their final squaring off in Paris. Undeterred in his conviction that there must be a law of nature “to prevent a star from behaving in this absurd way,” Eddington claimed that there was no experimental test that could lend support to Chandrasekhar’s theory. Nonetheless, he apologised to Chandrasekhar for questioning his calculation. “I am sorry if I hurt you,” Eddington said. When Chandrasekhar asked Eddington whether he had changed his mind, he retorted, “No.” Chandrasekhar then replied, “What are you sorry about then?” and walked away.

Although late in life Chandrasekhar and Eddington exchanged some cordial letters, they never discussed the issues concerning the fate of the stars. He eventually made peace with Eddington, who promoted his election to the Royal Society in 1944. Eddington died on November 22, 1944.

The eulogy Chandrasekhar gave for Eddington at the University of Chicago says it all about his graciousness and magnanimity. “I believe that anyone who has known Eddington will agree that he was a man of the highest integrity and character. I do not believe for example, that he ever thought harshly of anyone,” he said.

Thirty-one years after the infamous encounter with Eddington, physicists finally acknowledged the relevance and importance of the Chandrasekhar Limit. Moreover, in 1971, the first black hole was discovered. And as a tribute to Chandrasekhar’s contribution to astrophysics, NASA named one of its space-based observatories after him – the Chandra X-ray Observatory, specially designed to detect stars spiralling into black holes. Since its launch on July 23, 1999, this flagship observatory of NASA has not only discovered numerous black holes, quasars and supernovas, but also allowed us to look at a side of the cosmos that is invisible to the human eye.

Chandrasekhar’s ultimate vindication was the Nobel Prize in Physics awarded to him in 1983 for his ground-breaking work on the structure and evolution of stars. In 1984, he received the Royal Society’s highest award, the Copley Medal.

The writer, Quamrul Haider, is a Professor of Physics at Fordham University, New York.