Moonshots for Holi

For two nights before holi we were away from any city. Holi is always on the first full moon day after the spring solstice, so, being away from cities, we had very clear views of the moon at any time between sunset and sunrise. I took a few photos of the last days of its waxing phase. Later when I looked at them, I remembered that I’d heard about how much more is known about the moon today than when I was in school. But I hadn’t ever found out what. So I looked. Apart from a Wikipedia article, there aren’t any books or popsci articles, but there’s a lot of scientific literature. Most of it was beyond me, but I did find a few that referred me to more and more recent papers until I landed on one that gave a nice and brief account of the current state of our knowledge.

Two days before full moon

Why don’t people photograph the moon more often? It is the only other planet whose landscape we can see with the naked eye. Most good zoom lenses allow us to take good photos of sunrise over lunar mountains, and the changing soil across its landscape. I find it fascinating to live on the only double planet in our solar system, constantly gazing up at a companion whose diameter is a bit more than a fourth of the Earth. There’s a mystery about it. Since the Earth’s diameter is (more accurately) three and two thirds as large as the moon’s, its volume should be about fifty times larger. If the mass of a planet is in proportion to its volume, then why does every source say that the earth’s mass is 85 times that of the moon’s? Does this mean that the moon is not made of the same material as the earth?

The day before full moon

The moon rocks that the Luna and Apollo missions brought back fifty years ago showed us that lunar minerals are very similar to that of the earth. But that’s just a comparison of the crust. Almost 15 percent of the earth’s volume is in its iron core. The moon’s core is much smaller, perhaps less than a percent of its volume. This clue, along with detailed chemical analysis of moon rocks, and the ability to simulate numerically many alternative hypotheses about the early solar system, have led to tremendous advance in the understanding of the origin of our double planet. This dates the assembly of the earth-moon system at four and a half billion years, a scant 50 to 60 million years after the explosion of a nearby supernova compressed a cloud of gas and dust into the star we call the sun. When you look back this far, the story of the earth is the story of the sun and the moon.

The day before full moon

The part of the story that is no longer in dispute is that two planets, the proto-Earth, a little smaller than today’s Earth, and the other, now named Theia, about the size of Mars, had a glancing collision at a relative speed of more than twice the speed of sound in rock. The collision threw off some debris. But the larger planet swallowed much of the mass of the smaller, especially most of the core, and became the earth, leaving a little iron, and a lot of rock, to become the moon. A large fraction of the energy of the collision went into melting rock, leaving too little energy for the two planets to escape each others’ gravity. As a result they became a double planet perpetually circling their common center. The explanation bears up against the test of detailed simulations.

The day after full moon

Controversy has not yet completely settled on the immediately preceding history of our planetary system. Did this era contain a few dozen planetary “oligarchs” which had swept up all the material of the nebula from which the sun condensed? Numerical simulations show that multiple collisions between them could create a system where four or five rocky planets circle the sun inward of Jupiter, but none of them look very much like our solar system. This scenario also involves different mechanisms for the formation of the outer giant planets and the rocky inner planets. Nowadays the preferred scenario is that the solar system condensed into pebble-sized rocks which formed both the nuclei of the outer planets and five inner proto-planets, and only one major collision happened later to form our double planet. But this keeps open the question of why there was a collision. Perhaps the Mars Sample Return mission will tilt the balance of opinion in this remaining controversy. Perhaps we will find a simpler explanation of this older epoch in the assembly of the planets.

The one true new year!

Niece Mbili sent The Clan a New Year’s greeting card which shows two aliens puzzled about why humans celebrated yet another turn of their planet around the sun. That’s exactly what a year is: one complete orbit around the sun. The year begins each time you reach a fixed point on the orbit. Which point? Aye, there’s the rub. All calendars in use are too ancient to have made an informed choice.

But not the one true calendar (“One of the two true calendars”, Simplicio interjects). Since the orbit of the earth is an ellipse, and not a circle, there are two points on the orbit which are special: the point at which it is closest to the sun (perihelion), and the one at which it is furthest away (aphelion). The earth comes closest to the sun some time today: January 4. That’s pretty close to what you may have been celebrating, so remember to make that little correction next time (“Easily solved,” Sagredo chides Simplicio). And this naturally gives us a second holiday: mid year on July 4, when the sun is furthest from us.

Another magic of this new year is that it occurs at the same instant around the globe: whether you are in Mumbai or Mombasa, in Madrid or Manitoba or Manila, in Melbourne or Motsomi or atop Monte Darwin. When the earth comes closest to the sun has nothing to do with where on earth you are. So I’m planning a wild New Year’s party at just after noon today. You can check the local time of your party in this calculator, but it will be at the same instant as mine.

Now you might ask whether there is a special meridian on earth, one where the party happens at midnight every year. Very strangely, the answer is no. The length of the day and the length of the year have (almost) nothing to do with each other. As you know, a day is the time that the earth takes to spin around itself once, the year the time to spin around the sun. The word “almost” is important: the year being an exact multiple of the day is forbidden by an interesting piece of physics: resonance. The story seems to be that when two times (such as the day and year, or the month and year) become multiples of each other, the orbits become unstable. So in a solar system which has lasted for billions of such orbits, you’ll never find these “resonances”. It’s an amazing piece of physics, discovered only about seventy years ago (at the height of the cold war) by the Russian physicist Andrey Kolmogorov.

All that for the time of the new year. Now the counting of the year zero. Since the definition of the new year’s celebration depends on the shape of the earth’s orbit, one has to have a special place in the calendar for the date of the discovery of this shape. Johannes Kepler published this discovery 403 years ago. So that’s why the new year, 403 Modern Era, starts today.

A very happy new year to you.

Unfortunately, the universe is also a little more complicated than the pretty picture which gives us calendars. Einstein would have us know that this is all approximate, and that when you try to pin down the time of the new year’s party to an accuracy of a few parts per hundred thousand, the whole idea of a new year, indeed of a cyclic calendar, becomes meaningless. Lucky for us that our senses do not have that accuracy, and we can live generations with the lie called a year.

The delicious in 402

Two more days to go till the end of year 402 ME. Enough time for me to stop making these count-my-blessings sort of end-of-the-year lists. I’ll postpone that, since the earth still has to travel more than 4 million Kilometers (4 Gigameters!) before it reaches that point in its orbit when it is closest to the sun. That’s when it’ll be time to break out the long-preserved cashew feni, chilling now for days at 20 Celsius below freezing, and have a shot to celebrate the new year. In the mean time, I can savour the aroma of winter’s fruits.

When you look at a simple bowl of oranges or apples you realize what a riot of colours you have in front of you. The apples range from a green streaked with red to a black. It’s not just the diversity of colours from one to the other, but also the riot of colours in each: the streaking that tells of the diffusion of the plant hormone ethylene from the branch into the fruit, the consequent activation of genes which produce pectinases, amylases, and hydrolases, and their action in breaking down the long-chained carbohydrates of the fruit into simple sugars. The thicker skin of an orange cannot completely hide this diffusion either. If you look closely, there are differences in the orange hue across each fruit.

I tried out a recipe which I hadn’t used before. I quartered the apples, put them face down on a buttered baking dish, sprinkled them with nutmeg and garam masala, and baked them for 40 minutes in an oven which had been brought to 150 Celcius. Then I transferred them to a bowl, dusted them liberally with powdered sugar and poured some Mahabaleshwar strawberry wine over them. Let them stand for a couple of hours. When you take them on a plate, pour cream over it. It is a high calorie dessert, just what you need to balance out those long walks you take on our spinning ball as you wait for it to travel a few Gigameters more.

Conjunction

We woke with the alarm. The Family had already woken to the sound of trilling water, but it was only when birdcalls twittered over it that the alarm broke into my sleep. We’d missed the conjunction of Moon and Far for several Diwalis. They’ve been coming at odd times. Just before dawn is not the most convenient, but at least it was not the middle of the day, nor was Diwali on a completely overcast monsoon month.

We came out of the house, cups of warm tea in our hands. We had made the viewing into a vacation, flying off to the middle of India where there is a chill in the dawn air at this time. It is only when Far and Moon are so close together that you realize that they are slightly different colours. I still call the bluer one Far, but The Family grew up calling it Less, which is more in these days. We stood close together as she asked “Do you remember the reason why they are always in the same phase at conjunction?” I didn’t, but it was a standard puzzle picture in school. I decided I would look it up later in the day. The calendar computations for Diwali are complex, but I remember thinking in my school days that this bit of astrological mathematics was fairly straightforward.

Two days from now, on the day of Diwali, both moons would show their dark face to us. I would wake up again in the early morning tomorrow to see Moon begin to occlude the thin visible sliver of Friend. So lucky that Diwali comes in a cool season this year. Lamps and firecrackers are impossible in monsoon, and uncomfortable in summer. This is a good year for Diwali and the viewing of the conjunction.

Sunrise

At the beginning of Navaratri I watched the moon rise in the east through a thin haze of clouds. The atmosphere affects our view of the sky quite a bit. On the moon, the line of sunrise had just crossed the shores of the Sea of Crisis (Mare Crisium). The same sun that rises over the moon also rises on earth.

The next morning in Bera I watched the sun rise. The sky turned from black to red. And then, as the horizon fell away below the sun, the air turned blue and bright. On the airless moon will you only see the bright yellow sun pop over the horizon in an airless black sky? Interestingly, the sun creates its own drama as it rises over the moon. The solar wind kicks up dust in a narrow 150 km band around the terminator. Diffraction of sunlight through the dust will produce spectacular, albeit dimmer, colours. I can’t wait to see the first photos of the colours of sunrise from the moon.

An equinoctal moon

Luna glided overhead as we looked for nightjars. It was easier to spot the triad of lunar seas, serenity, tranquility, fertility, than a savanna nightjar in flight. Certainly photographing them at night with my equipment was out of the question, even with the moon waxing to nearly three quarters. I turned my camera up to the moon.

Top to bottom: Seas of Serenity, Tranquility, and Fertility (detail)

The lunar seas of showers and of clouds had become visible a couple of days ago. These fancifully named seas are actually basalt shields, the frozen remnants of lava flows which were caused by an extensive bombardment by meteors around four billion years ago. The earth was also shaped by this shower, and very few fragments of continental crusts are older. Life began on earth soon after that. On the moon the lava seas in these enormous craters had solidified more than three billion years ago. By that time photosynthesis had begun on earth. Our atmosphere was changing even as the splotchy appearance of the moon took shape. The new photosynthetic life made the earth unlivable for most anaerobic bacteria and caused the first age of extinction.

Plato crater at lunar dawn, just north of the Sea of Showers (detail)

Near the northern end of the terminator, my camera could pick out the far edge of Plato crater catching the morning sunlight. This crater is as old as the sea of showers (Mare Imbrium) just south of it. If you were to stand inside that crater then and looked up at the cliffs on the far edge, what a sight the morning sunlight must be! At the southern end of the terminator you can see a jumble of craters. Just inside it, at roughly mid-morning, is the bright young Tycho crater, only a 108 million years old. The dinosaurs may have seen it forming. In a few days, the whole of the visible half of the moon would have day. That lunar day is what we call a harvest moon. It was still more than a week away.

In the next two days we were to cross the Tropic of Cancer several times, as we scouted for more of the winter’s birds passing through the Rann of Kutch. It was a funny astronomical coincidence. The Tropic of Cancer marks the furthest point north where the sun can be at the zenith. And we were near that at the time the sun was crossing the equator! As I took photos of the signboard someone remarked that it had seen better days. True enough. So had the moon, by my reckoning.

Devasthal

As we drove through Dhanachauli, we realized that we were extremely close to the Devasthal observatory, and decided to take a detour. This observatory, on top of a 2450 m tall peak, houses the largest telescope in India at this time. Visitors have to take an appointment from the Aryabhatta Institute in Naini Tal, a process I’d completely forgotten about. But scientists are usually an accommodating lot, happy to take you by the hand and walk you through the mysteries of the universe. A scientist whom I knew was willing to talk to the local administrator. The administrator was willing to let us in, but apologized that because we had not booked an appointment, there would be no one available to explain to us the working of the telescopes.

We could park at the gate, and walk up to the telescope, and we were not, under any circumstances, to take off our masks. We deposited our ID cards with the security at the gate, and before walking in, I took the photo that you see above. The place houses a 4 m diameter liquid mirror telescope. A container of mercury is spun at a constant speed, so that its reflective surface becomes a paraboloid. The liquid mirror was under construction, and the 3.6 m telescope was under maintenance. This would have been a wonderful opportunity to see these marvelous pieces of technology. If only I’d thought of making an appointment! Still, it was a nice walk through the campus, photographing beetles and laughing thrushes, far above the smoke in the valleys below.

The winter had been very dry, but even so, the observatory in Han Le in Ladakh (altitude 4500 m) would have had better viewing conditions. I would love to visit it once they start building the thirty meter telescope up there.

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.