Year 402, modern era

The eerily empty Park Street in Kolkata heralded the imminent end of the year 401 of the modern era. Usually this street is crowded with party goers in the evenings of the ten days between Newtonmas and Perihelion day. Not this year. We ducked into an old favourite of a coffee shop, nearly a hundred years old now, but still filled with young people. This year the wait for a table was only two minutes, not two hours. The Family’s face was glowing, she’d heard a lot about the street at this time of the year, and she was happy to be there.

The long nights of this season seem to be made for fairy lights, and in this pandemic year people have put a little extra into them. We decided to come home for the new year. The new year? There are so many different calendars in India, that the arbitrariness of choosing a date to begin a year is obvious. Is there really a special date to celebrate as we roll along around our star? It turns out that there are two such dates: one when we are closest to the sun (perihelion), and another when we are furthest (aphelion). If we want to choose something close to the new year in the common calendar, then Perihelion day, January 4, today, it must be. A different new year’s day deserves a different era to go with it. In the 16th century of the common era, Nicolaus Copernicus first realized that the earth goes around the sun. And then, in the early years of the next century, Johannes Kepler realized that the path of the earth was not a circle, but an ellipse. It is because of the ellipticity that there are special points in the orbit, a perihelion and an aphelion. So this discovery should mark the beginning of the modern era of a rational calendar.

Welcome to the year 402 of the modern era. The last of Kepler’s laws was published that many years ago. The start of the fifth century was traumatic for many, filled with losses. I seem to have spent mine in the safety of my kitchen, judging from my favourite photos of the year. But this is a new year, with new hopes of accommodating this virus without harm to ourselves through a vaccine. This is a year to celebrate careful study of the world around us, and to act on this understanding for the preservation of our place in the world around us. So a happy new year, 402 ME. ☀

Happy Newtonmas

I would like to wish you a very happy Newtonmas today. As everyone knows, Isaac Newton was born prematurely on this day in the village of Woolsthorpe in England, a few months after his father’s death. His mother abandoned him in his infancy when she married again. His birth, 378 years ago, coincided with the year of the death of Galileo Galilei. There were heavenly portents of course, the solstice and perihelion bracketed the day of his birth.

I have celebrated the three days of the advent of Newtonmas by writing three posts, one about the great conjunction, one on the irregularities in the motion of the earth, and one about the surprising chaos in the Solar system. Today there is no esoteric knowledge to be shared, just a wish for happiness and a quiet time.

Tides and glad tidings

At first it seemed to be a piece of weirdo news on TV “Super-highways in space discovered. The way to the planets is now open”. I checked the NASA website, and it showed an older piece of news, but it had context. I had to hunt little to find the paywalled article (Todorovich, Wu, Rosengren) in a prestigious scientific journal. It was new, but it was in the same context as the older press release from NASA. Indeed there are fast lanes in the solar system. “Gravity assist” can help you speed a spacecraft with little fuel. This was known in the 1970s, when the world’s first interstellar probes were launched. How is all this new? Is it a discovery?

After 1687 CE, Newton’s ideas on gravity were available to the world through successive editions of his book, Philosophiae Naturalis Principia Mathematica. To many it seemed that the universe had suddenly been understood. Poets wrote heroic verses: Nature and nature’s laws lay hid in night; God said “Let Newton be” and all was light. That was Alexander Pope writing Newton’s epitaph. Almost two hundred years later, Wordsworth in his posthumously published poem “The Prelude” wrote about Newton: The marble index of a mind for ever Voyaging through strange seas of Thought, alone. But other thoughtful people were not so (what is the word?) sanguine. Tides could be understood, but the details were devilish. More observations revealed strange anomalies in the motions of the known planets, and eventually led to the discovery of new planets, even to a new theory of gravity: Einstein’s (but that is a different story, and as Aragorn says at the black gate of Mordor, “Today is another day.”)

The paintaking computation of tides eventually told us that within this wonderful theory of Newton lurk dangerous waters. Tides require computations of the three way dance of the earth, the moon, and the sun. And these turned out to be rather difficult. About the time that Einstein was thinking about gravity, Henri Poincare was thinking about this three body problem, and discovered something as astounding. He found that within the seemingly determined motions of the planets lurk dangerous instabilities, some of which eventually became known as chaos. The three body problem, and its modern descendants, such as the study of the stability of the solar system, gave rise to the headlines that I saw. This is the discovery that there are unstable orbits which can throw small bodies (think spacecrafts and asteroids) into rapid transits across the solar system, and even eject them with high velocity into interstellar space. Some of this was known for about 50 years, but this is a systematic study, and a great addition to our knowledge. Maybe one day, if we can set up a space shipyard, travel across the outer solar system can be a matter of decades rather than centuries.

Goedel Escher Bach and beyond, a nice post on typography by Pooja Saxena

But after this long detour through history and the solar system, let me get back to my original question. What is discovery? If someone gives me the rules of the world, do I know the world? The answer is clear to anyone who has struggled to learn chess. It need not be less clear when it comes to science. Newton and Einstein discovered some of the rules of gravity, but much of the game remains to be played. Is the confusion due to the fact that in science you first need to discover the rules, and then discover what it means to play them? Perhaps we should have two different words for these two uses of the word discovery.

There will be time

“What a lovely moon,” The Family said as I took the featured photo of clouds at sunset. Often we do not agree about the proper scale of things. I was looking at ephemeral sunlight on passing clouds, things which would fade in two minutes. She was looking at things which change slowly, and would take two weeks to come to fruition. I scanned the sky. Moon? I looked at her, followed the direction of her gaze, and asked “What? Where?” “Right there, where I’m pointing.” I looked along her arm and shook my head “No.” She took my head in her hands, turned it, port to starboard, then a little adjustment horizon to zenith. “There. You see it now?” “Mmm. Oh yes. Nice.”

I fixed that bearing in my mind and zoomed a little to see that wonderful sliver of the new moon. Such a constant in our lives: the periodic unchanging appearance of the new moon. But actually, the earth, the moon, and the sun dance a slow dance, mediated by tides and gravity. If we had enough time, say about 50 billion years, the earth and moon would be tidally locked: the day would be about 1130 hours long, and the moon would stand still above a single place on earth. Unfortunately this will never happen, because in a mere 5 billion years the sun will eat the earth. Tidal friction is that small! The length of the day has increased by about 1/4 of a minute in the last 100,000 years. That is the time from which we have the oldest human architectural remains.

I zoomed a little more. The constancy of astronomy has been the way wandering armies and ships have told direction and time from as long as our records tell us. When you continue the imaginary line between the poles of the earth, it points towards Polaris, the pole star, today. But this direction moves in a little circle every 26000 years or so. As a result, the direction towards the rising sun on the day of the equinox changes with the same period. The Babylonians had found that this direction points towards the constellation of Aries. By the late years of republican Rome, the direction had moved to the constellation of Pisces. This was a shock to the Romans, and gave an impetus to the spread of the imported Indo-Persian religious cult of Mithra (मित्र, Mitra, the Vedic god of sunrise). All the trappings of conspiracy theories of today (secrets which can be discovered merely by looking, cabals and secret handshakes, governments keen to hide facts) come from that history, a sign of the trauma caused by the knowledge that the skies are changing. This fact is forgotten again and again. Shakespeare had Julius Caesar declare “I am as constant as the Northern Star.” Ironical, since this particular lack of constancy was creating an immense ferment in his armies. Even otherwise, this is an anachronism, since there was no pole star in Caesar’s day. By Shakespeare’s time, when the earth’s axis had moved to Polaris, the equinox had moved further towards Aquarius, and the pole towards Polaris. Not so constant, after all, and much faster than tidal locking. Two million times faster!

Time for you and time for me,

And time yet for a hundred indecisions,

And for a hundred visions and revisions,

Before the taking of a toast and tea.

The Love Song of J. Alfred Prufrock, by T. S. Eliot

I put the dust cap back on my camera and we resumed walking. The deeply peaceful surroundings, and the view of the Panchgani plateau on one side, can make your mind wander. But my time was here and now, and The Family said we should walk back to the hotel before dark, “Time for tea,” she said. Our meals are as constant as the moon and the tides; we seem to change daily, but we are more constant than the Northern Star, in our own ephemeral way.

Winter solstice 2020: the great conjunction

Every twenty years or so, we can see Jupiter and Saturn come very close in the sky. This is called the great conjunction. I’d been looking at the two planets in the sky since the last full moon, watching them draw closer and closer. Today they looked like a single bright star to my naked eye. I could separate them by using my camera to zoom in. That’s the featured photo, displayed one pixel for every two on my sensor. The disks of the planets are clearly visible. The brighter planet, Jupiter, shows as a disc. The fainter planet, Saturn, looks slightly elongated; that is the best I can do about capturing the rings of Saturn with this camera. I may have done better if I’d bothered to set up a mount, or gone down to the lawn where the common sense of distancing was forgotten in the excitement of viewing the planets through a good telescope.

Why is one planet more dim? Because Jupiter is both larger and closer to us, it seems to be brighter. The different colours have an interesting explanation. Both are gas giants, with atmospheres of Hydrogen and Helium. But the colours come from the small amounts of other gases they have. Jupiter’s atomosphere has a little water and ammonia, and it is the latter which gives the yellow tinge. Saturn’s has in addition phosphene and hydrocarbons, which give it a much redder colour.

A great conjunction happens roughly every twenty years (the fact that it happened on the night of the solstice was a lovely extra), but it is not always visible at night. In the previous millennium it would have been clearly visible only thrice: in 1226 CE, during the lifetime of Genghiz Khan, then again in 1563, in the early days of the Mughal emperor Akbar in north India, and the last days of the Vijayanagar kingdom in the south. The last time it was visible was in 1623 CE, in the reign of the Mughal emperor Jahangir in India. It will be visible next in 2080 CE. Everyone alive today is lucky to have lived through such a rarely visible event, but today’s generation of young adults and children are specially lucky; most of them will see this spectacle twice in their lifetimes.

A partial eclipse

Once again I’d not paid attention to the news that I would be in the path of a partial solar eclipse. When this happened to me in December I realized two things: first, that without filters photos of the sun are no good, and second, that you can’t use your phone for the landscape because it is too smart to be fooled by bad light. So this time, I set my camera on manual, fixed the aperture and exposure (1/60 of a second and f6.3, if you want to know), so that as the moon passed over the sun, I would be able to record how the landscape darkened.

The eclipse was partial over Mumbai,with a maximum of about 60%. It started at 10:09 AM and was supposed to end at 1:27 PM. As you can see from the time lapse animation above, it got pretty dark at its maximum. Unfortunately, clouds obscured the sun before the eclipse ended, so I just got the first half of the eclipse.