Comets, asteroids, … and writers

 kw: book reviews, nonfiction, memoirs, astronomy, comets, asteroids, astronomers, poetry

My introduction to the Internet was when my company made it available to our desktop computers in June, 1994. Just a month later I was able to see the wonderful telescopic pictures of Jupiter, bruised and battered by Comet Shoemaker-Levy. At night, I would get out my 3-inch diameter telescope and look at Jupiter. I could just see the black spots of the impacts at 120x, which is about the limit with such a small telescope. The planet appeared about the size of a pea.

In preparation for an online lecture by David H. Levy, co-discoverer of the comet, a friend in a local astronomy club gave me a copy of Levy's recent book Star Gazers: Finding Joy in the Night Sky. It is a lovely little book; I finished reading it in two days. I could have finished even faster, but Dr. Levy's writing rewards close reading.

I find that he has discovered or co-discovered 23 comets and hundreds of asteroids. Once in a while a comet gets bright enough for any of us to see, and then star parties like this one multiply (Image generated by GPT-Image 2.5 via Leonardo AI).

In this memoir he also reports witnessing about 200 eclipses, mostly lunar eclipses, but including at least ten solar eclipses. In Chapter 4 he includes the discovery photos of Comet Shoemaker-Levy. Most comets are discovered photographically, by taking a photo of a likely spot (generally along the ecliptic, the Sun's apparent path in the sky), and then another one of the same spot an hour or two later. Looking at the images as a stereo pair, you can see something that moved as an object that seems to hover above the apparent plane of view. This also works for finding an asteroid, which appears as a "hovering" star, while a comet image is more like a smudge or tiny cloud. Right up until today, human binocular vision is superior to any technological imaging method. It is why asteroid hunting with wide-frame cameras is being carried out by citizen science to verify tentative machine identifications.

The book is composed of small essays, just one or two or three pages each, that the author has published elsewhere, with added introductions to most chapters. They are arranged by topic, not chronologically. The book ends with an ode to his late wife Wendee.

I wish to comment on writing itself. Dr. Levy writes lyrically without any loss to scientific merit. He calls himself an amateur astronomer, as do the references to him I have found. He is perhaps the poster child for amateur science, understanding that "amateur" derives from a Latin word for "lover". He has his own observatory with a few telescopes in it, named Jarnac Observatory. Many of his discoveries were made there, but numerous others were made in the company of friends, including Gene and Carolyn Shoemaker, co-discoverers with him of the "hammer that hit Jupiter." 

His doctoral dissertation dwelt on references to astronomy and astronomical objects in the writings of Shakespeare, and he has written of other literary lights who loved astronomy. He tells of reciting or reading poetry at most meetings of astronomical societies he attends. Many great scientists have also been lovers of the arts, from Leonardo DaVinci, of course, to Albert Einstein, who played violin to relax, and a great many others. Having an artistic mind seems to lend itself to having a scientific outlook.

For this reason I prefer STEAM to STEM: Science, Tech, Engineering, Arts, and Math. They all wrap up together and buttress one another in a wonderful synergy.

I intend to track down other books he has published, and I look forward in just a couple more days to attending his online lecture.

The first Mars generation

 kw: book reviews, nonfiction, science, astronomy, astronomers, biographies, mars, social phenomena

In 1877, Mars and Earth had a "great opposition". The two planets were close together, just about 56 million km (35 million miles). The orbit of Mars is somewhat elliptical, so at "less favorable" oppositions, dates when Mars is directly outward from the Sun and high in our night sky at midnight, the distance can be as great as 102 million km (63 million miles). Astronomer Giovanni Schiaparelli took advantage of the great opposition to observe Mars nightly, for weeks. In addition to blotches and pale areas, he saw a few seemingly linear features, which he called canali, the Italian word meaning "channels".

The word canali does not refer to artificial waterways; other meanings are "troughs" and "gullies". Unfortunately for the next generation or two of the American and European public, when Schiaparelli's  work was translated into English, the translator chose to use the word "canals".

About seventeen years later, Percival Lowell, nearing the age of forty, having observed Mars in telescopes located in Boston and elsewhere, built his observatory near Flagstaff, on "Mars Hill". With the 24-inch diameter telescope he installed there, he watched Mars obsessively during every period of opposition. The drier, steadier air in Flagstaff enabled him to see the planet more clearly. Over time, he discerned numerous linear features, writing of them as "canals". He inferred that they were produced by intelligent Martians.

Lowell's articles, books, lectures, drawings and later photographs of Mars stirred a kind of Mars Mania for a generation, as described by David Baron in The Martians: The True Story of an Alien Craze that Captured Turn-of-the-Century America.

Percival Lowell was rich, driven, obsessive, and probably bipolar. He had earlier had a varied career, including being a kind of envoy for Korea and Japan. Once the observatory was completed, and he had released his book Mars, the planet and his theories about the Martians and their engineering abilities dominated his life and enthralled the public.

His public lectures and writings kept Mars Mania going for the rest of his life, in spite of opposition from roughly half of the scientific establishment. One particularly telling blow came from an experiment conducted by Walter Maunder, which became known as the "Small Boy Theory". Maunder began with maps of Mars produced by Schiaparelli and Lowell. He removed all the canals and replaced them by scattered dots or bits of riverine shapes. For each of several tests, such a doctored map was hung high on the wall at one end of a large classroom, and schoolboys were seated throughout the room. They were asked to copy the map as well as they could, without moving from their seats. Those closest to the front made the best facsimiles, of course. The farther back a boy sat, the more likely he was to add straight lines where dots and fragments seemed to run together in his vision.

Lowell never wavered from his view of a canal-riddled Mars. This image from page 62 shows one of his maps showing the "canals" and "oases" (dots) he drew. Just below it is an image I captured from Google Mars, taking in the approximately same view of the planet. The straight edges of some dark areas are artifacts of different camera views stitched together.

The scattered dots in the lower image are craters. I remember in 1965 when the Mariner 4 spacecraft sent us images of Mars that resembled a moonscape: loads of craters, and no canals. This was just a century after the Flagstaff Observatory was established.

Have you looked at clouds to see "cloud animals" and other fantasies? Various amorphous shapes can look like faces. There is a blotch in the abstract pattern in my shower that looks a little like a panther's head, only when I have my glasses off. This is called pareidolia. A roughly lined-up string of spots can look like a straight line when seen from a certain distance.

But what further affected Lowell as he aged was a bad case of confirmation bias. It's something we are all prone to: when we like an idea, we remember facts that support our view and discount those that don't.

At one point, Lowell spent some time looking at Venus. He produced the map in the upper part of this pair (from page 76). He was told that the "map" seemed to just reflect the blood vessels in his retina; he apparently agreed, and retracted the map. 

I've viewed Venus a number of times with various size telescopes. To a normal human eye, it is featureless, a blank white disk. However, if Lowell had lived a century later, and had a cataract operation, he might have seen features on the surface that are visible in ultraviolet light, particularly if he used a dark blue filter such as Cobalt glass. The lower image simulates such a view; I just "blued up" an ultraviolet photo of Venus. The natural lenses in our eyes are yellow, to filter out deep blue and UV light, which are hard to focus and tend to blur the vision. Cataract operation patients can see more UV than the rest of us.

Well, that would only be true before 1980. Since then, the plastic lenses that are inserted to replace the natural lens also filter out UV light. Oh, well, my hopes of getting my cataracts out and gaining UV vision are dashed!

Percival Lowell married at age 53. Eight years later, somewhat a fallen hero but still well remembered by the public that had been enthralled by his lectures, he passed away at age 61. When Clyde Tombaugh discovered Pluto in 1930 Lowell was still sufficiently famous that the planet was given the symbol ♇ using Lowell's initials.

I have just skimmed over Lowell's life. I sympathize with his "neurasthenia", which was probably depression in the "low" phase of bipolar syndrome. I've been there. David Baron did an amazing amount of research to put this book together. The apparatus—source notes, bibliography, list of illustrations, and index—take up a quarter of the volume, almost 80 pages. Many other people who surrounded Lowell and the Mars phenomenon, including Nikola Tesla, Sir Arthur Conan Doyle, and Camille Flammarion, play their parts in this narrative. The fabric of these lives is a fascinating tapestry of the American and European societies of the thirty years surrounding the year 1900, when so much happened.

Why did I title this piece "The first Mars generation?" A new Mars generation has arisen, enthralled by the vision of Elon Musk, who wants to establish a colony on Mars with a million inhabitants. He hopes the first humans to reach mars will do so in the early or mid 2030's. Maybe it will work...

Strong support for blue sky research

 kw: book reviews, nonfiction, science, astronomy, serendipity

To abbreviate a saying usually attributed to Isaac Asimov: Science begins with the phrase, "Hmm, that's funny!" 

I once worked as a machinist at Cal Tech, often in the big room where the mirror for the Palomar Telescope was formed and polished decades earlier. Later half the room was taken over to build an early synchrotron (atom smasher), which had been disassembled but big concrete rings remained. Also, a cabinet in a corner of the room was filled with manuscripts of experiments that had been performed using the synchrotron, often attached to copies of PhD dissertations, which indicated the student had been awarded the degree. We were assembling an innovative radio telescope in the room, and its reflective surface was being machined semi-automatically. I had to be present to monitor and adjust the machinery, listening for anomalies in the process. During chunks of semi-free time I read here and there in the manuscripts. I found that many of the students using the synchrotron had eventually proved their original idea to be incorrect, but had discovered something else along the way, so they got their Doctorate anyway. Scientific serendipity at work!

Scientific serendipity is the theme of Accidental Astronomy: How Random Discoveries Shape the Science of Space by Chris Lintott. I would broaden the scope of the title, because much science is built on "random" discoveries, things found while looking for something else. Recent case: A medicine for treating Type II Diabetes, semaglutide, marketed as Ozempic® and Wegovy®, was found to promote weight loss, which is now the biggest market for it. Weight loss is making billions for the drug companies.

In nine chapters Professor Lintott leads us through the history of several important discoveries. One amazing example is the Hubble Deep Field. Several astronomers took a big risk and managed to convince the folks in charge of the Hubble Space Telescope to have it point towards a spot in space near the Big Dipper, where nothing could be seen on earlier photographs of the sky. For four days!

This is part of the result; it is about a quarter of the whole image, which included an area of sky about 0.6% the area of the Moon. Thus this image is about 0.15% of the Moon's apparent area.

This is at 1/3 the scale of the original image, so each pixel here is the average of 9 original pixels. I darkened the background to get rid of very low-level jitter. Just left of center, the bright white item with spikes is a star. Near top center is a dimmer, more yellowish star. Both stars are too dim to be seen by most telescopes. Besides these two stars, everything else in this image bigger than a single pixel is a galaxy. Hundreds are shown here, and nearly 2,000 galaxies have been enumerated in the entire full-scale image. Each galaxy contains billions to hundreds of billions of stars.

This Deep Field image triggered deeper and deeper-field images, because the longer a telescope records the light from an area, the more stuff is seen. More recent work with the James Webb Space Telescope (hereafter JWST), including infrared deep fields, shows that we can record information for at least a few trillion galaxies in the visible universe. The tiniest (apparently tiniest!), and thus farthest, galaxies shown may be at a distance of 12-13 billion light-years, showing us what things were like when the Universe was one or two billion years old.

For "older" light than that, we must rely on microwaves. The continuing expansion of the cosmos means that older light has been red-shifted, and at 12.5 or 13 billion years back, any "light" that could be visible here and now has been red-shifted to far infrared or even to microwaves. We have pigeon droppings and the unstoppable determination of two scientists to thank for first recording those microwaves, depicted here over the whole sky:

The features of this image are the highly amplified variations in a generally uniform radiation field, over the whole sky, that is characteristic of a blackbody with a temperature of 2.73K, or -270.42°C or 454.8°F. This corresponds to a peak microwave frequency of about 160 GHz, a wavelength of about 1.9 mm. This can be compared to the microwaves in your microwave oven, with a frequency of 2.45 GHz and wavelength of 120 mm.

In 1964 Arno Penzias and Robert Wilson weren't looking for anything astronomical. They were trying to reduce the noise in a large antenna being used to bounce signals off the Echo satellite. At one point, they evicted a nesting family of pigeons and cleaned out the droppings. That did reduce the noise, but some remained. The "stray" signal was eventually found to be coming from literally every direction at the same frequency range and intensity. That meant it was not on Earth, and probably outside the Solar System, or even the Milky Way galaxy. It is actually "light" (originally X-rays and gamma rays) that was emitted when the age of the universe was about 360,000 years, red-shifted to microwave radio frequencies.

The features of the image above represent variations of only 0.01% of the total intensity. They were measured by spacecraft, because there are too many noisy microwave emitters on Earth.

I love astronomy, and I could go on and on, but I'll leave it to you to read the book. We haven't found solid evidence of aliens, visiting or elsewhere, but that would be the biggest discovery of all. And I suspect further serendipity will lead to it.

Stepstones to infinity

 kw: book reviews, nonfiction, science, astronomy, space science, popular treatments

My favorite astrophysicist, Neil deGrasse Tyson, published a new book last year in collaboration with Lindsey Nyx Walker, in the Startalk series: To Infinity and Beyond: A Journey of Cosmic Discovery. With apologies to Buzz Lightyear, the title makes it clear this is no scientific treatise.

As one might expect, the book is fun to read, pitched at just the right level for a popular audience, and copiously illustrated. Rather than chapters, the book has four sections, with a subtitle every couple of pages. The sections are titled "Leaving Earth", "Touring the Sun's Backyard", "Into Outer Space", and "To Infinity and Beyond". Broadly speaking, the sections are like layers of an onion, starting at the center.

The second section, on the planets and their satellites and asteroids and other denizens of the solar system, is the longest, as befits the greater knowledge we have "in the Sun's back yard", where at least we have sent instruments to pass by or even orbit the planets and selected objects. The book went to press before the capsule of material returned from Asteroid Bennu was opened, so that's not mentioned. What is mentioned is the quest to colonize Mars, which cannot realistically be done without terraforming it. Engineering solutions, including carpet bombing the polar ice caps with nuclear weapons, have been proposed. Dr. Tyson has this to say:

"In any case, if humanity ever develops enough geoengineering know-how to terraform Mars as our escape plan after we trash Earth, then we should certainly be able to use that intelligence to make Earth livable again and save ourselves from requiring a planet B in the first place." (p. 135)

To which I add a strong, "Amen!"

The fourth section, after treating what we know of the distant cosmos in a general way, gets a bit philosophical. The authors have this to say about "beyond", that is, about the many-worlds interpretation of quantum uncertainty: "The many-worlds solution may not be simple, but it is the simplest explanation for the oddities at quantum scales." I must contend with that:

Consider sunlight shining through an ordinary window. When the light encounters the glass, ~4% is reflected from the outer surface and ~96% passes into the glass. Then about another 4% is reflected from the second surface and the rest, ~92%, continues onward. Interestingly, the light that reflected back into the glass pane is partly reflected and then most passes through. Some smaller and smaller fraction of the original light bounces back and forth inside the glass pane. Glass is not 100% transparent, to soon whatever has not escaped is absorbed. Considering only visible light, sunlight has an intensity of around 500 watts per square meter, or 0.05 watt (50 mw) per square centimeter. Skipping the math, the number of photons of visible light that encounter the glass each second is about 1.4x10¹⁷, or 140 quadrillion (140 million billion). Each photon "decides" whether to reflect or pass through, twice because the glass has two surfaces. According to the many-worlds interpretation, 280 quadrillion entire universes are created every second, because of sunlight shining through one square centimeter of glass. I have a picture window in my family room that has an area of two square meters. On a sunny morning, every second, about 5.6x10²¹ universes spring into existence, along what dimensions we have know way to discern. Five and a half sextillion. Every second.

Folks, that's just silly. Whatever photons and other quanta are, they are doing something we fundamentally don't understand, and interpretations such as many-worlds reveal how immensely far we are from achieving such understanding.

We are like the pilgrim in this famous engraving from an 1888 book by Flammarion, trying to see beyond our own horizon. Our imagination falls short. Newton imagined himself as a beach comber being fascinated by this shell or that pretty pebble, being ignorant of the expanse of the ocean that tossed them up.

All that aside, and aside from a few errata I'll get into shortly, the book is as entertaining as it is comprehensive. I strongly recommend it.

---------------------------

I have to bring out a few matters where the authors, or a copy editor, ought to have known better:

1. On p. 22, about warming by infrared light, "…once they absorb the various wavelengths of radiation, molecules on Earth's surface are transformed into infrared and are reemitted by the ground." This is a rather dramatic blunder. The molecules are not transformed into infrared! The relevant phrase should read, "…molecules on Earth's surface emit infrared radiation." All the wavelengths of sunlight that reach the ground warm its substance, and it then emits some of this energy as infrared.
2. On p. 119, about the slowing of Earth's rotation, mostly by its interaction with the Moon, it is stated, "After two centuries, days are four milliseconds faster." In this context, the word "faster" is misused. The days are "four milliseconds longer." Gah!
3. On p. 131, "Today, Mars is a frigid tundra." The word "tundra" implies a cold landscape with cold-resistant plant cover. There are no plants on Mars. I don't know what word to use, but the word "tundra" is wrong.
4. On p. 206, on relationships between the intrinsic brightness of stars and their apparent brightness because of their varying distances, "Sirius, the brightest star in our night sky, is smaller than Earth and 8.6 light-years away,…" Siriusly?!?!? As it happens, Sirius is 1.7 times the size of the Sun. Its companion, the white dwarf designated Sirius B, which is much too faint to see without a large telescope, is indeed smaller than Earth.
5. Finally, look carefully at this illustration of a prism producing a spectrum:

This is found on p. 212, where spectroscopy is being discussed. The illustration is from Getty Images. The way the beam of light bends upward as it enters the prism implies that the prism has a refractive index less than 1, which is impossible. Such a material would require the light to go "faster than light" within it.

Compare with this illustration:

This is from Britannica online. It is more correct, showing the light entering being refracted toward the perpendicular to the glass surface as it passes into the prism, and then refracted away from the perpendicular of the second glass surface as it exits. P.S. I was a spectroscopist for a few years…

This illustration isn't totally accurate, however. The best spectroscopic glass disperses the spectrum by a little less than one degree. The spectrum at the right is being dispersed about 15°. However, this bit of scientific license is needed to make the principle more clear.

I put the query "prism spectrum" into a Google Images search. I found that a great many repositories of stock photos have it wrong; only about one-third have it right! Don't Getty and all the others have anyone with scientific understanding on their staffs?

Exoplanets survey

 kw: book reviews, nonfiction, astronomy, astrophysics, exoplanets, surveys

Imagine what planetary astronomy would be like if there were frequently two or even three planets visible in the sky that appeared similar in size to the Moon as seen from Earth. And I do mean "frequently." The planet currently known as Trappist-1e, the fourth planet around the small star Trappist-1, has a six-day year. From a dark-sky location, on the side away from its sun, the next planet outward (-1f) would reach superior conjunction about every dozen days, having a visible size of 34 arc-minutes; we see the Moon as about 33 arc-minutes across. The apparent size of -1g, another step outward, ranges up to 19.5 arc-minutes, nearly 2/3 of a "moon unit". From locations near the terminator (the star-rise or star-set line), the next planet inward, -1d, approaches 32 arc-minutes at inferior conjunction, as a crescent, just as Venus at its brightest is seen as a crescent because it is nearly between the Sun and the Earth. Even when the other six planets are at opposition (on the other side of the star), they always appear larger than any of the planets in our solar system ever do: even Venus at near-conjunction is too small to show a visible disk, except to a few folks with test pilot vision. All the Trappist-1 planets are always seen as disks.

From planet -1e, however (and any of the others, from -1b through -1h) there probably is no star-rise or star-set. So far as we can tell, they are all in tidal lock with Trappist-1, the way the Moon is with the Earth. It is also unlikely that three big neighboring planets can be seen in the sky at the same time because the orbital periods are all in resonance, which keeps them from lining up in the sky simultaneously.

If you were on the brighter side of the planet, the star would appear much larger than the Sun, about seven times its size. But its surface brightness is lower, by far, than the Sun's. It would still be risky to look right at it. Imagine looking at a ball of near-molten tungsten at a temperature of about 2,560K (~2,290°C or ~4,150°F), just slightly cooler than the filament in an incandescent light bulb. Although astronomers call this star a "red dwarf", one of the reddest known, visibly it appears orange-white. It would be dazzling, even though our Sun is 1,800 times as bright.

All of these facts are consequences of the small size of the Trappist-1 stellar system. The outermost known planet, Trappist-1h, revolves at a distance of only 8.8 million km from the star (from Earth to the Sun is 149 million km). The star's faintness, however, means that the habitable zone is between 3 million and 5 million km. Both Trappist-1d and -1e are within this zone, and maybe -1f and -1g, while -1h is "out in the cold" and always frozen (like Mars) and -1b is rather like Mercury and subject to searing heat (from 125°C to 230°C, or 255°F to 505°F).

All of this has been learned from viewing the Trappist-1 stellar system using several telescopes (at least 3 of them in space) and spectroscopes. The procedures and the kinds of data needed to discover and characterize exoplanets are described in a very understandable way by Joshua Winn in The Little Book of Exoplanets. Considering that there are more than 5,500 known exoplanets presently known, Dr. Winn makes a good point that we need to set aside the term "exoplanet" and just call them "planets." Our stellar system, which includes eight planets, is just one of more than 4,100. More planets, and more systems having two or more confirmed planets, are being discovered daily.

All of the earliest discoveries were made using the Doppler method, which measures how much the star is moved back-and-forth by a planet. Naturally, the easiest sort of planet to discover, by nearly any means, is one that is large (that is, massive) and close to its star. Big Doppler shifts are easier to discern, and shorter orbits take less time to confirm (days or months rather than years or decades). For one method, though, direct observation using a coronagraph, big planets that are far from the star are easiest to see. Finding smaller, less massive planets, in years-to-decades-long orbits is between difficult and (so far) impossible. None of our current methods could reliably discover Mercury, Venus, Earth, or Mars, and also Uranus and Neptune. Saturn and Jupiter are on the "possible edge". So it is no surprise that systems similar to our own have not yet been observed. Proclamations that our system represents something very rare are premature. We don't yet have a way to know!

The most prolific method so far is the transit method. When the system is lined up just right, one or more of its planets will periodically cross in front of the star, which dims its light a tiny bit. This illustration compares observations of a transiting planet made from Earth's surface with observations made using the Kepler Space Telescope. The atmosphere, even using adaptive optics, is a big handicap to precise observation.

During the useful lifetime of the Kepler telescope I used Zooniverse to make some of the measurements in a Citizen Science project called Planet Hunters. I don't think I made any new discoveries, but I think my work helped others confirm at least a few of them; the stats show that I made 6,866 classifications. Most of them were "no planet".

This image, Plate 16 in the book, shows the Starshade concept: A space telescope will have a co-orbiting daisy-shaped shade that blocks the light of one particular star with sufficient efficiency that direct observations of planets near the star can be made. The shape of the bladed disk is optimized to "spread around" diffraction effects so that a star's light can be reduced by a factor of several million or even a billion, while the nearby space, within a fraction of an arc-second, is unimpaired.

Such a system could see Earth, probably Venus, and maybe Mercury. "Co-orbiting" in this case means the telescope and the shade are about 30,000 km apart in a very high orbit! They would need to be supplied with large amounts of fuel to allow for frequent re-positioning and re-aiming. Perhaps by the time these are commissioned, paid for, built and orbited, we'll finally have a successor to the Space Shuttle that can reach high orbits so they can be refueled. Running out of fuel is the bugaboo of space observatories.

This is more than just curiosity. Every space observatory since Hubble has had as part of its ambit, "Help find habitable planets and planets with life, even intelligent, communicating life". Whether or not Earth is utterly unique in the Galaxy (if not the whole universe) is the biggest question science can address. (My note: It's curious that the budget of NASA is in the range of 1/200th of the Federal budget. The yearly spend of SpaceX and all the other private rocket companies that have sprung up in the past decade or so totals between 1/10 and 1/5 of NASA's budget. To get a "supershuttle" into operation and to genuinely support "big space astronomy", these numbers have to increase by a factor of ten or more.)

I am quite enamored of exoplanetary science. This "little book" is packed with great info and stories about its current condition.

Becoming a star, two ways

 kw: book reviews, nonfiction, astronomy, astrophysics, memoirs

Sarafina had a tough row to hoe, and has done better than even she expected. If she hasn't already (by this date in July 2023) received her PhD, I expect she soon will, to become Dr. Sarafina El-Badry Nance. In her memoir, Starstruck: A Memoir of Astrophysics and Finding Light in the Dark, she presents herself to us as one seeking to know the universe as a way to know herself. The memoir is a catharsis for her.

Each chapter begins with a nugget of astronomical or astrophysical understanding, which then leads to events in her life, some of them happy, many of them painful, even agonizing. She is studious, so her response to her parents' unhappy marriage was to work herself practically to death. She survived a year or so with a very abusive boyfriend, blaming herself for his failures, which all too many abused women do. Her father had cancer treatment (it seems he has so far survived, although it was advanced), which led to genetic testing for him, which led to genetic testing for her: she found she was at great risk of breast cancer, and no matter what she did with her breasts, she would have to monitor several potential risks frequently. She chose total removal and reconstruction (something I recall that the actress Angelina Jolie also chose…and so did a friend of ours for similar reasons, but after already having one lumpectomy). Amidst all that, she was, by the end of the book, close to completing her doctorate in Astrophysics.

She had happy moments and happy periods. Her father encouraged her love of astronomy, and encouraged her to ignore naysayers (She reports on several. Be careful what you say to children; you can destroy them needlessly). She fondly recalls sitting outside with him just to watch the sky. She had women friends, and a supportive therapist or two, at key moments in her life. She prevailed.

She studies supernovae (AKA supernovas). Her big discovery so far relates to determining that large amounts of hydrogen remain in many supernovae, between a few percent and 30% of the stars' masses. She doesn't mention whether these are Type 2 or Type 1a, which I wish she had mentioned (Type 1a supernovae provide the key bit of data underlying the hypothesis of Dark Energy. According to that, about 75% of the mass/energy of the entire universe is bound up in Dark Energy, if it exists. I happen to think this proportion, if it is not zero, is greatly exaggerated.).

As a rising star in the astrophysics community, she also became a star in the community of cancer survivors. She researched her genetic condition and her options relentlessly, and reported her Odyssey on social media. Pushing aside a few trolls, she had enormous positive feedback from women who appreciated her work and the knowledge she was able to confer to them.

This book is most touching, incredibly illuminating (in sundry ways), and a painful joy to read.

The view from everywhere!

 kw: book reviews, nonfiction, astronomy

At its closest approach to Earth, Venus is about 38 million km away. Just before this or just after this (a few weeks), the planet is a bright crescent in the morning or evening sky, and its apparent diameter is just over one minute of arc (1/60th of a degree). Someone with keen eyesight would be able to tell it isn't an unresolved dot, and could see that it looks elongated. That's the closest we can come on Earth to seeing any body in the Solar System besides the Sun or the Moon as anything more than a tiny dot.

If any of the seven known planets of the Trappist-1 system is habitable, the sky would be quite a bit more interesting as the short year (19 days or less) transpired. Some of what we might see is described in the sixth chapter of Under Alien Skies: A Sightseer's Guide to the Universe by Philip Plait, PhD, an astronomer who lives in Colorado. Rather than repeat what he wrote, I analyzed the system a bit to provide this summary:

• The 7 planets are designated by letters from b to h.
• Their sizes are similar, ranging from 0.775 the size of Earth (h) to 1.13 (g).
• Planet d is the most likely to have liquid water on the surface, though it is thought to have little atmosphere, comparable to that on Mars.
• The star is about 12% the size of the Sun, and is a "cool" red dwarf, with a temperature of 2,550K (~2,275°C or ~4,065°F).
• The planets orbit between 1.73 million km and 9.26 million km from the star.
• By contrast, Mercury's orbit ranges from 47 million km to 70 million km from the Sun.

We see both the Sun and the Moon as having a size of 32 arcmin or arc minutes (0.53°) on the sky. Nearly every one of the seven planets in the Trappist system can be seen from any of the others as a disk, any time they are in the sky:

• From planet b, the nearest to the star, planet h, the farthest, appears as large as 4.5 arcmin at closest approach, a tiny but clear disk.
• When planet g is nearly opposite planet h, from g the other appears as small as 2 arcmin, barely discernable as "not a star". All other cases, the sizes appear larger, even quite large.
• From planet d, planet c appears as large as 50 arcmin, or 1.55 times the size of the Moon as seen from Earth.
• From planet d, planet e appears as large as 39 arcmin, or 1.2 times the size of the Moon as seen from Earth.

How does the star look? Its visible brightness is one hundred-thousandth that of the Sun, while it is 45 times closer to planet d, compared to Earth and the Sun. This works out to a visible brightness of 2%, compared to the Sun. This dim light is spread out over a disk more than five times the apparent size of the Sun. Also:

• From planet b, the star's apparent size is just over ten times that of the Sun to us.
• From planet h, the apparent size is about twice that of the Sun.

Finally, what is the color of the sky? As mentioned, so far, planet d is thought to have very little atmosphere (perhaps like Mars), and planets b and c probably have none (like Mercury); the other four planets may have atmospheres, but we don't know. Such a sky would likely be black, or nearly so. The top row of this diagram shows how the Trappist-1 star would appear, firstly from off-planet, and then under a sky as dense as Earth's atmosphere.

Trappist-1 is one of the reddest of red dwarf stars. It is slightly "cooler" than the filament of an incandescent bulb, so it appears orange from space. Under a clear noontime sky with no dust in the air, it would be just a little more reddish because of blue light scattered away to illuminate the sky. The physics of light scattering mean that the sky still would have a slightly blue color. However, if there were even a little dust in the air, the sky would be pinkish, or perhaps salmon-colored as the sky of Mars is due to fine dust that never settles, even in its thin atmosphere.

The other stars I compiled here show the star color from space, its reddened color seen through an atmosphere (this is why the Sun is called a "yellow-white star"; from Earth it seems so), and the color of a clear sky. The relative brightness of sky and star are certain to be quite different from what this diagram shows, depending on the density of the atmosphere. From atop a high mountain on Earth, the sky is much bluer than it could ever be when seen from sea level.

A few words about the four stars other than Trappist-1 and the Sun:

• Proxima Centauri is a red dwarf, known to have at least two planets. It is a little hotter than Trappist-1 and is the closest star to the Sun. Its visible brightness is quite a bit brighter than Trappist-1, but still a tiny fraction of the Sun's brightness. The noontime color temperature is a little more orange than its space appearance, though against a bluish sky it appears closer to bright yellow.
• Sirius is about twice the size of the Sun and is several thousand degrees hotter. A planet would have to be five times as far from it as Earth is from the Sun, to avoid all its water being boiled away.
• Rigel is one of the "knees" of the constellation Orion. It is a blue supergiant about twice as hot as the sun, and so bright that a planet would need to be about 350 times as far away as Earth is from the Sun, to be habitable. But this star won't last long. It will burn out or go supernova in a few million years.
• There are very few of the super-hot "O" type stars. One of four that is naked-eye visible from Earth is Alnitak, the leftmost star in Orion's belt. Such a star doesn't last long. They burn bright and exhaust their fuel quickly. Most of their "light" is ultraviolet and soft X-rays.

OK, that's a bunch of info about planets around other stars. Dr. Plait tells us what it's like to view the sky and space from the Moon, Mars, an asteroid, a comet, a moon of Saturn, and near the Pluto/Charon system. Then he takes us to the Trappist-1 system, and on to a planet orbiting two stars, into a globular cluster (imagine a sky with 100 times as many stars), and near enough to a nebula and a black hole or two to see their fireworks (but from a safe distance!).

I was particularly taken by the description of approaching Saturn. Passing the rings (which would take days at the "sane" speeds of "only" a few miles per second), seeing things like their "spokes" and "propellers", the moonlets and gaps…what a travelogue!

The author writes of the way the absence, or near-absence, of an atmosphere can trick the eye because there is no haziness to distant objects. Distances on the Moon or Mars or an airless asteroid would be very hard to judge. We learn how the different levels of gravity might feel on a different planet or satellite or asteroid…and how landing "on" an asteroid might just take you right inside it (oops!). He writes with compelling grace and subtle humor. I loved the book.

Planets outnumber stars

 kw: book reviews, nonfiction, astronomy, astrometry, exoplanets

We have so far detected about 5,000 exoplanets (planets of other stars). Since the first confirmed detection in January 1992, astronomers have developed five methods to detect exoplanets, over most of the range of plausible sizes, and quite a range of orbital periods. That's enough to learn a few things.

In Worlds Without End: Exoplanets, Habitability, and the Future of Humanity, author Chris Impey describes the most common type of planet: Diameter larger than Earth but smaller then Neptune, in an orbit on the warm side of the habitability zone, or inside of it. These are called "super-Earths" and "mini-Neptunes", with the dividing line about twice the diameter of Earth. Neptune weighs just over 17 times as much as Earth, so variations in density increase the range of masses from about 17:1 to perhaps 25:1 (or 20:0.8).

The technology of exoplanet discovery makes up the first of four sections of the book. The other three sections consider habitability, how we might search for life on exoplanets, and the possibilities for us or our machines to visit them.

I hadn't known that there are five ways to detect an exoplanet. In particular, I didn't know that astrometry can be used for that. Astrometry means "star measurement", and in this application, it refers to precise measurements of a star's location or position. While quite a number of exoplanets have been detected by the doppler shift in stellar spectra, using telescopes on Earth's surface, the use of a star's position is many times more delicate, and can only be done from telescopes in space. A bit of figuration will illustrate the difference.

Considering the mass of Earth as a basis, and calling it 1, the mass of Jupiter is 317.8 and that of the Sun is 332,946. The Sun's diameter is 1,392,000 km, the average distance of Earth from the Sun is 149.6 million km, and the average distance between Jupiter and the Sun is 778.3 million km. The orbital velocity of Earth is 29.78 km/sec = 107,200 km/hr and that of Jupiter is 13.1 km/sec = 47,160 km/hr.

The doppler shift caused by the Sun's reaction to the planetary motions is calculated by mass and distance ratios. Thus, for Jupiter, the mass ratio is 317.8/332,946 = 0.000 954 5; so the Sun's velocity is that times 13.1 km/sec = 0.0125 km/sec = 12.5 m/s. It takes a very precise spectroscope to measure the doppler shift caused by this motion, but it has now been done many times. 

The closer Jupiter is to the Sun, the faster it goes, and therefore the faster the Sun goes. Let's put Jupiter in Earth's orbit and check the consequences: 0.000 954 5 x 29.78 = 0.0284 or 28.4 m/s. This is more than twice the earlier figure. This is much easier to detect, and explains why the first exoplanets to be detected were "hot Jupiters" that orbited very close to their host stars. Also, doppler shift is the same from any distance, as long as you can gather enough light to get a good and precise spectrum.

Now we consider hyper-precision astrometry. The diffraction limit of the Hubble Space Telescope in visible wavelengths is around 0.02 milli-arc-seconds (5.5 billionths of a degree). It would be the same for any space telescope of equal size. However, even though star images are enlarged by diffraction to that degree, the position of a star can be measured with greater precision than this. One must magnify star images to cover many pixels of the detector, and the centroid of the star image can be calculated with great precision, in the range of millionths of an arc second (trillionths of a degree). The longer the exposure (the more photons captured), the more precisely this can be done, as the statistics of the "shot noise" of photon detection reduce the errors that would cause.

Specialized orbiting telescopes are being planned that can do this for a number of stars in a field of view. The positions of many stars would be measured again and again over long periods, looking for tiny shifts. How tiny?

For Jupiter again, when the planet moves from one side of its orbit to the other, it moves 1.56 billion km. The Sun moves 1.56 billion × 317.8 / 332,946 = 1.49 million km, or 1.07 times the Sun's diameter! However, this motion requires six years...starting at the right place.

How far away can we detect the shift? One millionth of an arc second has a tangent of 0.000 000 0159; dividing this into 1.49 million km yields 93.6 trillion km. That's almost ten light years (9.9). To reach a reasonable number of stars with this technique requires astrometric measurements with a relative precision from star to star of a ten millionth of an arc second, or smaller if possible. This takes big telescopes and long exposure times. But it has been done!

OK, that's a long discussion of two methods: Doppler Shift (the first method to work) and High Precision Astrometry (the most recent). To round out the methods, the third is the most prolific to date: the Transit method, which measures the little dip in brightness that occurs when a planet passes in front of a star. The fourth is Microlensing, for which stars are watched for brightening that occurs during the period (measured in days) that one passes in front of another and its gravity magnifies the star behind; a small extra glimmer signals that the star in front has a planet. The fifth is Direct Imaging, which works best for large planets farther from their host stars. Each method has a useful range of planetary size and orbital distance, which means we are getting a more and more complete overview of what is out there.

I will give rather short shrift to the latter three sections of the book. They are very interesting, but secondary to my interest in the subject. Only a small percentage of exoplanets so far detected are at a suitable distance from their host stars to have a chance of having liquid water at or near the surface. Thus, the discussion of habitability and life are more speculative. The author does bring up an interesting subject: Could the Earth be detected by any of these methods, from suitably placed stars in "nearby" space, the nearest few hundred light years? Very possibly!

The statistics of what we now know indicate something even more interesting: Nearly every star seems to have at least one planet, and wherever the viewpoint and associated method(s) are favorable we find a few planets, usually 3, 4 or 5. Precision timing of Transits is beginning to reap a harvest of added planets in many of the systems initially found using that method, for example. That means that there are more planets than stars, overall.

Furthermore, the Solar System has, so far discovered, 200 moons, most of them around Jupiter and Saturn. BUT! Although the surface temperature of satellites that distant from the Sun is far too cold to allow liquid water, the interiors of several larger satellites could hold a large liquid ocean, which could then host life. It may be that the greatest number of objects in the Universe that host living beings (microbes, at least) will prove to be satellites of large planets!

That in itself made the book worth reading.

Cool stuff about the Universe

 kw: book reviews, nonfiction, astronomy, universe, humor, essays

Can you see the difference between the two lower rows of light-colored ovals? We'll mention the dark blue ones in a moment. The three ovals in the bottom row are "white", meaning they have the color value #FFFFFF or (255,255,255). According to Dr. Jan Scudder, author of The Milky Way Smells of Rum and Raspberries … and Other Amazing Cosmic Facts, that very pale yellow, which she calls "light beige", is the average color of the Universe. The color value is #FFF8E7 or (255,248,231). I used PowerPoint to produce the ovals and to set them on backgrounds of white, black, and sky blue. 

This is found in the second chapter of the book, in which color values are discussed briefly, but one fact is reversed: A footnote on page 9 states that #000000 is white and #FFFFFF is black, but the reverse is true. Zero means "no illumination" and FF (or 255) means "full illumination". Otherwise, the usage of color values is correct, as I verified with the top set of ovals, #0D0ACB (13,10,203), called "a particularly pleasing deep blue"; the little bit of red and green slightly desaturate the dark blue so it doesn't overwhelm the eyes. The pure blue color of computer screens is a bit harsh all by itself:

In this image, the oval on the left has color value #0000C8 (0,0,200) and the one on the right is "full-on blue": $0000FF (0,0,255). Some people's eyes are more sensitive to the slight difference between the leftmost oval and the one in the center. By the way, values prefixed with the hash are hexadecimal, or base 16, in which the letters A through F represent quantities from 10 through 15.

The book consists of 34 essays, enlightening, humorous essays. The fifth chapter, from which the book's title is taken, is "The galactic center tastes of raspberries and smells of rum". The "dense" gas clouds near the center of the milky way are still hard vacuum compared to the air we breather, but are 3,000 times as dense as most interstellar gas. That makes these gas clouds capable of blocking much of the damaging UV that breaks apart most molecules, so that deep within them (they are hundreds to thousands of light years across) molecules such as ethyl formate survive. Ethyl formate is an ester that is found in abundance in raspberries. Also found is another ethyl compound, ethyl alcohol (ethanol), the "kick" in rum, vodka and whiskey. The author also points out that, if we were to somehow gather a few cubic parsecs of this gas and concentrate it by a factor of ten billion billion (ten quintillion), it would be a rather toxic brew. It may have hints of raspberry rum, but would also contain cyanide compounds and formaldehyde, for example. So it would really be more like the smell (don't taste!) of a preserved corpse of someone who died of cyanide-spiked rum, with an odd raspberry note.

I was interested in the chapter titled, "There's a pitch-black exoplanet". A distant planet designated WASP-12b is as dark as fresh asphalt; it reflects only 6% of the light that hits it. The dark patches on the Moon reflect about 7%, so you can look in the sky at a full moon to get the idea. By the way, the lighter parts of the moon are more like fresh, dry dirt, and reflect perhaps 15%, making the overall "brightness" of the moon about 12%. If the moon were papered over so it reflected 90% or more, it would be six or seven times as bright as it is. I wish Dr. Scudder had mentioned this. I take issue with a statement in that same chapter: "You'll never get a reflection off a star". In a close double, a pair of co-orbiting stars that are perhaps as close to one another as Mercury is to the Sun (36 million miles, or 58 million km), one of the stars is frequently much brighter than the other, and the dimmer star does indeed reflect a little of the brighter star's light. This has been observed spectroscopically. It stands to reason that some of the dimmer star's light will also reflect off its partner, but this would be extremely hard to detect.

There's an interesting timeline in "Jupiter's magnetic field will short-circuit your spacecraft, but Venus will just melt it." According to this Wikipedia article, Earth's magnetic field ranges from 0.25 to 0.65 gauss (refrigerator magnets have around 50 gauss at their surfaces). The larger unit, the tesla, is 10,000 gauss. The high-dollar superconducting magnet in an MRI machine has a strength of 3 to 10 tesla. That can pull the wristwatch off your wrist (or right through it!), which is why you daren't wear any metal into the MRI room. Electronic conductors moved through a magnetic field produce an electric field; that's how generators work. Move a typical laptop or smart phone around in space near Jupiter, and it will generate thousands to millions of volts, throwing sparks all about. Venus is less spectacular, but just as deadly to almost anything not make of tungsten. Its surface temperature is 450°C (~840°F), and the atmospheric pressure is 100 times that of Earth. In the timeline, starting with Venera 4 in 1967 and ending with Vega 2 in 1985, every spacecraft that landed or attempted to land on Venus had the same experience: crushed and then melted, after times ranging from 20 to 127 minutes. That's 13 spacecraft (all sent by Russia) that gathered a total of somewhat over 880 minutes (14.7 hours) of experience of Venusian weather. It's been a while since anyone tried to send something to the surface of Venus, but the Russians intend to try again in 2029. They hope for a "lifetime" of 3 hours on the surface. Perhaps special electronics made of diamond instead of silicon can be developed. And don't leave any air pockets inside your craft so it doesn't get crushed.

Another quibble, sorry to say: In the chapter "An Exoplanet we thought was made of diamond might be lava instead", the planet 55 Cancri e (the letter "e" indicates 5th body in the system, or 4th body that isn't a star) is "twice as physically large as the Earth, and eight times more massive, which tells us it's substantially more dense…" As stated, this is nonsense. 2×2×2 = 8, so the sentence would only make sense if the last phrase were "exactly as dense". However, here we find that the diameter isn't twice that of Earth, but 1.88, and this number cubed is 6.64; we also find that the mass is indeed 7.99 that of Earth, so now, we're in business. 7.99/6.64 = 1.2. The same article states the density of 55 Cancri e as 6.66. The average density of Earth is 5.51. Now the numbers work together properly. This error shows the danger in over-simplifying science when writing for the public. The early thought that this planet might be made of diamond was based on an erroneous measurement of the diameter. Diamond has a density of 3.5, or less when it is impure. And diamond doesn't compress well, so even under great pressure inside the planet, it's not going to rise to 6. Iron-rich silicate magma/lava also has a density near 3.5, but is much more compressible.

In spite of occasional minor blunders the book is delightful. I like the author's writing style.

Asteroids, the reality

 kw: book reviews, nonfiction, science, astronomy, asteroids

Chances are, the word "asteroids" conjures up an image a lot like this for most people. We hear about the millions of rocks of all sizes roaming the spaces between the planets, especially between Mars and Jupiter. We think of that space as crowded with space debris.

The reality is somewhat different. Before getting into that, however, I want to recommend a book about the asteroids, about how we came to know about them and what they are like. Asteroids, by astronomer Clifford J. Cunningham, doesn't pretend to be a comprehensive survey. Rather, the author has two aims: to survey the history of our knowledge, and theories, of asteroids and "small bodies" in general; and to show how they are classified.

The telescope was invented in the early 1600's, just over 400 years ago. Galileo made it famous by seeing craters on the moon and discovering satellites around Jupiter. Although several asteroids are bright enough to be seen using small telescopes, even binoculars, you need to know where to look. Two centuries were required to gather sufficient knowledge of the skies, until the first "new planet" was seen January 1, 1801.

It took a number of years for astronomers to determine that this new planet, Ceres, was 1/11 the diameter of the Moon, and even longer to discern its mass to be 1/800 that of the Moon. By then a number of small, "new planets" had been found. Over the decades, the number grew to hundreds, then thousands, and the current number of asteroids whose orbits have been worked out is more than a million.

Astronomers also discovered that these little bodies weren't evenly spread out in the "asteroid belt", the realm between the orbits of Mars and Jupiter where more than 90% of them are. There were some gaps, which are caused by gravitational "pumping" by Jupiter either adding or removing orbital energy so that those special orbits stay clear. There are also certain "families" of asteroids, most famously a small number of Trojan asteroids that are in the L4 and L5 orbital points ahead of and behind Jupiter about 60° in (and near) its orbit. More recently, a small number of asteroids have been found to precede or follow Earth, Mars, Saturn and Uranus, so the designation "Trojan asteroid" has been expanded to include them all.

Other orbital subtypes are focused on the ones that could threaten Earth. Four classes of Near-Earth Asteroid (NEA) are defined by orbital parameters. The ones of most concern are those that pass through Earth's orbit ("through" meaning anywhere within a few thousand km of the exact orbit). It's just a matter of timing before one of them winds up on a collision course. So far, though, none are known with certainty. But we only know about half of the NEAs that are there, which are big enough (more than 140m, or 460 ft), to devastate an area 100 km across or more.

Even though there are tens of thousands of NEA's, we are saved by the bigness of space. At present, I see a notice at least every month in online news about some asteroid "as big as the Empire State Building" or "school bus sized" that is going to pass "near" the Earth. It always turns out that the "near miss" will be a million miles or so. This is not to discount that some big, possibly devastating asteroids are out there, and we may not know about them yet. But the last asteroid hit to cause a "nuclear winter" happened 65 million years ago. Our portion of "asteroid space" has a low population. (At this point, I'll stray from what's in the book.)

What if Earth sat right between Mars and Jupiter? Then we'd have between 10x and 100x the chance of getting a significant collision in our lifetimes. But that chance is still low. We know that because many spacecraft have been sent to Jupiter and beyond, right through "the Belt", without mishap. Let's see why. This table lists the approximate (more approximate with smaller size) number of asteroids in the main belt, from 100m (0.1 km) and larger:

The 100m sized ones are big enough to cause plenty of trouble if they hit Earth. But what about a spacecraft, such as Voyager or New Horizons? Even a centimeter-sized pellet that hits a craft going 20 km/s can destroy it. Spacecraft can be shielded from smaller bits, so we need to know how many tiny bits of millimeter size there are. It isn't easy to extend this table to smaller sizes, because there are a few theories about the size distribution. Many publications posit a "scale free" distribution, which I think is extreme, but we'll use that for one sideboard of our estimates. The Theory of Breakage by Andrey Komolgorov predicts a lognormal distribution, which some think is too conservative, because the tail of small objects dies away so much faster. I happen to favor that hypothesis; I'll use it fo rthe other sideboard. Here is a table of the sideboards:

Diam.  Scale free N   Lognormal N
100m     25 million    25 million
 10m      4 billion     1 billion
  1m    300 billion    35 billion
100mm    22 trillion  1.1 trillion
10mm  1.7 quadrillion  33 trillion
 1mm  125 quadrillion  1 quadrillion

The volume of the main belt is about 4 billion billion cubic miles, or 10 billion billion cubic km. If the lognormal hypothesis is correct, there are a quadrillion (million billion) sand grain size bits in that volume, each has 10,000 cubic km to itself. That puts it about 25 km from its nearest neighbors, on average. On the other hand, the scale free hypothesis has 125 grains in that same 10,000 cubic km, and the average spacing is "only" 5 km. 

However, we want to sail through this mess, hoping to hit nothing. The appropriate analysis is to figure the collision cross-section, as though everything along the path were pasted to a surface the craft must pass through. This is like wrapping a big, big ribbon 40 million miles wide between Mars and Jupiter, and sticking all those sand grains to it, pulling or pushing them along radii from the Sun. This ribbon has a total area of about 80 quadrillion square miles, or 200 quadrillion square km.

This puts each sand grain "in possession" of either 200 km² or 1.6 km². Now the spacing, for the lognormal case, is 16 km, and for the scale free case it is 0.7 km.

Whichever way one analyzes the distribution, there is either a "pretty good" spacing between possible collisions, or a huge space. In any case, plenty of fragile spacecraft have passed through the main belt without incident. That crowded picture above is just not the way things are. From any particular asteroid, you can't see any others without a good telescope.

A word about "kinds" of asteroids. Most asteroids are dark colored, and some are extremely black. Some are comparatively bright, but even the metallic ones have a dusty surface, so the albedo (reflectivity) of a few asteroids may be 0.25 (25%), but most are in the 0.1 to 0.05 range, with some as dark as 0.02. That makes them hard to see, and it is harder yet to find out how big they are. Is a new body, just spotted, dark and large, or bright and smaller? Gathering observations over several days and then several weeks, we can figure out how far away they are. Size and albedo are harder.

One tool to help determine this is the reflection spectrum. The darkest asteroids are akin to the darkest meteorites (because the latter originate as the former), the carbonaceous chondrites. They not only reflect less light than other types, the distribution in the spectrum is different; they are called "red" (really a blackish brown). The brightest are metallic, with their own spectral distribution; and in between are the stony asteroids, with spectral features all their own. Although the book discusses these types and several subtypes, much is still being learned. Spacecraft that have visited asteroids, and the one or two that have brought back samples, are increasing our knowledge of them.

Finally, there is no "lost" or "exploded" planet that once resided in an orbit where the main belt is now. The pre-planetary bits didn't get organized into a planet, and Jupiter is probably mostly to blame. The empty gaps testify to Jupiter's power to eject objects from certain areas. Over time, it must have ejected a lot; the total mass of all the asteroids is thought to be less than 1/250th that of our Moon.

As we learn more about them, perhaps we'll learn enough to be able to detect and deflect any NEA that is found on a collision course with Earth. Perhaps.

I greatly enjoy books like Asteroids. I didn't know what to expect, and I learned a few things about the different kinds and different "places" of asteroids. 

The billion-decade pie recipe

 kw: book reviews, nonfiction, geology, cosmology, astronomy, nucleosynthesis, cooking

This chart was mentioned in How to Make an Apple Pie From Scratch: In Search of the Recipe for Our Universe, From the Origins of Atoms to the Big Bang, by Harry Cliff. The book's title, indeed its raison d'être, is a humorous aside by Carl Sagan on an episode of Cosmos: "If you wish to make an apple pie from scratch, you must first invent the universe."

Harry Cliff is a particle physicist and researcher on the Large Hadron Collider, specifically the experiment/detector called LHCb. The "b" means "beauty", for the Beauty Quark, which most physicists now call the Bottom Quark (the "t" and "b" quarks were initially called "truth" and "beauty"). The short answer to "What is 'scratch'?" would be, "Something smaller than a quark." Quarks are what we call the (possibly) indivisible bits that make up protons and neutrons, which with electrons, form atoms.

I think of the book as a microscope that uses higher and higher powers to probe the makeup of the universe. Dr. Cliff actually began his investigation by obtaining an apple pie and pyrolizing a few grams. That gave him a rough estimate of the phases present, gas/vapor, liquid, and solid. The final product of pyrolysis is charcoal, although he found later that he didn't cook it hot enough; his charcoal still had some volatile stuff in it. It matters little: the end product was mainly carbon, the "gateway element" to producing the entire suite of elements from hydrogen and helium. The chart above shows the various "ovens" in which the elements were made.

Much of the book is history, the history of the discovery of the chemical elements during the Enlightenment, then the discovery of subatomic particles a bit more than a century ago. Although I've read the stories again and again (because writers seem compelled to cover it all every time), I find it enjoyable to rehearse the way alchemy became chemistry, and experiments with "cathode rays" and pitchblende came together to discover that atoms (from "a-tomos", "un-cuttable") are actually cuttable, and the "easy" sub-parts are further cuttable.

The book skips over the range of magnification available to a light microscope. There is nothing about the plant cells in the apples, or the microstructure of a perfectly baked crust. We go from some burnt pie right to atoms, which can only be distinguished when the magnification exceeds 10,000,000X, the magnification of this STM image. The best electron microscopes are hard pressed to deliver magnifications greater than 1,000,000X. Thus STM, or Scanning Tunneling Microscopy, has to be used. The white spheres here are atoms of lead, on a silicon surface.

The reason for this omission is soon apparent. The author's quarry is smaller compared to an atom of lead than that atom is to a sports arena.

An ordinary light microscope "maxes out" when viewing items smaller than half a micrometer (or micron, or µ). An E. coli bacterium is about 2µx6µ. The photons of green light, with a wavelength of 0.55µ, have an energy of 2.25 eV. One eV, or one electron volt, is the energy of an electron that has "fallen" across the gap between an anode and a cathode when the voltage is 1V. Photon energies in the range 1.75 eV to 3.1 eV are used by the retinas of our eyes to detect "light". Things smaller than about 0.5µ, or 500 nm (nanometers), can only be studied using "light" of a shorter wavelength. And here is the important principle: shorter wavelength means higher energy per photon (or other particle).

Why is it hard to "see" an atom? It is because they are so much smaller than the wavelength of visible light. The lead atoms in the image above are about 0.35 nm across. That's 0.00035µ. The silicon atoms in the surface below them are much smaller, with an interatomic spacing of 0.078nm. An electron microscope with beam voltage of a million volts uses electrons with energy of 1 MeV (million eV), and a wavelength of 0.0012 nm. However, such an electron beam simply blows off most of the electrons from the atoms you want to look at, while a more "modest" beam of about 16,000 volts, and a useful magnification of a million, can produce images without causing total disruption. The STM technique sidesteps this by using atomic forces to get higher-resolution information, with a limit in the range of 10 to 20 million X magnification.

When the biggest constituents of atoms were discovered, electrons, protons, and neutrons, they were soon found to be a whole lot smaller than the atoms. One analogy states that an atom of hydrogen magnified to the size of a stadium (a magnification of two trillion) would be "seen" to be an electron cloud with a speck at its center the size of a small pea, perhaps 6mm diameter: the proton.

How do you "see" a proton? Since it is about 50,000 times smaller than the atom, you would need 50,000 times the energy. At a minimum, 16,000 eV x 50,000 or 800,000,000 eV, just under a billion eV (GeV). Now, let's think a minute. A million-volt power supply needs a lot of insulation. In radio, the rule of thumb is that in dry air a spark will jump about a centimeter per 10,000V. So a million-volt potential can jump at least a meter. I remember seeing a picture of an early million-volt electron microscope. It was eight feet high. What do you do with a billion volts? Such a voltage can jump a few miles. Indeed, lightning has voltages in the billion-to-ten-billion-volt range.

Here it gets fun. Particle accelerators finesse the situation by using magnets and rhythmic pulses to take a bunch (that's the scientific term) of electrons or other charged particles from an "easy" energy of 10,000 eV to higher and higher energies. It's sort of like swatting a tetherball again and again to make it go around faster and faster, except these "tetherballs" are soon going 99% of the speed of light, or more.

When I worked at Cal Tech (as a machinist), I worked part of the time in a room with a dismantled synchrotron about 30 feet in diameter. Energetic electrons or protons lose energy when you turn them to go around in a circle, so the more energy you want, the bigger the circle has to be. The LHC, where Dr. Cliff works, is about 8.5 miles in diameter. It produces beams of protons with energies that exceed 10 trillion eV. It also runs them in both directions, and steers them into head-on collisions, so you get enormous penetration. All that to "see" the insides of particles a few thousand times smaller than protons, which is what it took to prove the existence of the Higgs Boson (but not see into its insides…if it has any).

Chapters and chapters earlier, the author discussed where the atoms came from. The chart that begins this article shows where. Things we can eat, and we ourselves, are primarily CHON, that is, Carbon, Hydrogen, Oxygen, and Nitrogen. Hydrogen makes up 75% of the weight of the matter in the universe. Or, at least, of the matter that is either visible or potentially visible because it can respond to electromagnetic energy ("light"). We need to ignore dark matter and dark energy here, because we still have no idea how to interact with them. Most carbon and nitrogen are made in "dwarf" stars, main sequence stars smaller than 1.25 times the mass of the Sun. The jury is still out on whether the white dwarf stars that result from the demise of a main sequence dwarf star have to be blasted apart to release carbon and nitrogen, or if the red giant phase releases enough to amount for what we see in the sky. Most oxygen, at least most of it that gets into the interstellar medium, is forged during supernova explosions. So at an atomic level, that's where the basic ingredients of the apple pie arise.

The reason for using big atom smashers like LHC to dig into the protons for their smaller bits (quarks and gluons, mainly), and into the quantum fields that modulate (or create) their properties such as mass, is that we aren't really back to "scratch" yet. By the end of the book, if we have understood it all (I am not quite there yet), we have the beginnings of matter traced back to the end of the first one-trillionth of a second after the Big Bang. 

Does that sound pretty good? Not to a cosmologist! The Big Bang is thought to have begun with everything we might call space and time located within a radius of about the Planck Length, which is about 1.6x10^-35 meters. The initial "Bang" got rolling in Planck Time, or about 5.4x10^-44 seconds. Let's just call it 10^-45 sec., and compare it to a trillionth, or 10^-12 sec. There are about 10³³ Planck Times in a trillionth of a second; a little matter of a billion trillion trillion of them. A lot happened that we will be hard pressed to probe. The author describes the ultimate particle accelerator, wrapped around the center of the galaxy (where it has a chance of being gravitationally stable), with a diameter of several thousand light years. The biggest we have a chance of building might wrap the Earth at the equator. The particle bunches would circle the planet seven times per second, so we have long enough lives to do experiments with it, with energies as high as perhaps 50,000 TeV. That's still a long way from the Planck Energy, but it might be close enough to be "interesting".

Future beings with very long lifetimes—because each experiment takes a million years or more—might probe the Planck Length using the Galactic Collider. But beyond a certain level of energy, the only output of the experiment will be tiny black holes. According to Hawking's principle, such a black hole would soon explode into a shower of energetic particles, but they would carry no information about what was going on inside, so the fancy machine would simply be a huge fireworks generator.

The book ends with a description for beginning from scratch, to the point where matter exists, including a middling size planet with apple trees and wheat fields and such. Then it ends with a pretty good recipe for making an apple pie. There ain't a quark anywhere that can explain the great taste of fresh apple pie.

The Man Who Shaved the Universe

 kw: book reviews, nonfiction, science, astronomy, philosophy of science

I was a developer of scientific software for forty years. One bit of my "Coder's Credo" is, "A complex system that works began as a simple system that works." In practical terms, this meant that I had to first "get the science working", which was usually simple, at least conceptually. The complications that had to be added all derived from the user interface (making the software usable for humans) and the data interface (coupling it to the database or knowledge base). I built my career on a minimalist approach: Add new stuff only when there is a clear advantage.

Millennia ago, the Universe seemed simple compared to the Earth. In the night sky, stars were thought of as distant lamps stuck to a "firmament". The Sun, Moon, and five rather bright "wanderers" (in Greek, πλανόδιοι, which became "planets") were a complication that most folks ignored. But certain curious ones began to theorize; they wanted to figure out how the sky worked.

Fast-forward to a mere 21-22 centuries ago. The prevailing theory of the sky, at least in Europe and north Africa, was a nest of concentric, "crystalline" spheres. The outer sphere held the "fixed stars", and the seven wanderers were each ensconced in its own sphere. Over time, observations of the motions of these "planets" showed something odd: they didn't all march across the face of the "fixed stars" at a steady rate, and some looped back on themselves. Also, the Moon's apparent size changed a little. By about 150 AD, a system of epicycles attached to the spheres had been developed to better model the movements of the planets, including the Moon and Sun.

This illustration from an Arabic document of the 1300's shows the epicycles needed to model the motion of Mercury, shown at four times during a particular year. This image is from Alamy (a commercial site), where its epigraph says,

"Ibn al-Shatir's model for the appearances of Mercury, showing the multiplication of epicycles using the Tusi couple, thus eliminating the Ptolemaic eccentrics and equant."

This shows that Arabian astronomers went beyond Ptolemy. At its height in the first half millennium of the Christian era, about 80 epicycles were needed for a "good" model, and the notion of "crystalline" spheres was politely ignored. Here, I count six epicycles needed to produce motions for Mercury that matched astronomical observations.

We all know that Copernicus tried to simplify the Solar system by recognizing the Sun as its center. However, he also needed epicycles to model planetary motions accurately, because he thought all orbits were perfect circles centered on the Sun…or, at least, the rotational center of a cluster of circular epicycles followed a circle about the Sun.

Leaving behind circles in favor of ellipses, Kepler, using Tycho Brahe's data for positions, produced a greatly simplified model of the Solar system, such as that seen here (this one leaves out Saturn, at twice the distance as Jupiter).

This particular image also shows the orbits of several major asteroids and three comets. Comet Halley's ellipse extends to 35 AU, seven times as far as Jupiter. The orbit that just brushes past Jupiter belongs to Comet Kopff, one we never hear of because it is visible only with a telescope at least 4" in diameter.

The older tradition of natural philosophers, exemplified by Ptolemy, resulted in models of natural phenomena with steadily increasing complexity. Something happened about the time that Ibn al-Shatir began writing his astronomical manuals, that began to turn the study of nature from natural philosophy to science as we know it.

Here I turn to a better authority on science history, Johnjoe McFadden. In his book Life is Simple: How Occam's Razor Set Science Free and Shapes the Universe, Professor McFadden traces the progressive simplification of science and scientific theories, based on a 14^th Century meme we call Occam's Razor. This is expressed in several ways, as it was by William of Ockham in the early 1300's. I like, "Do not multiply entities beyond necessity." This statement does not disallow complexity, it discourages unneeded complexity. Einstein's version is, "Make things as simple as needed, but no simpler," which looks at the matter from the other end.

Either way one looks at it, the principle known as Occam's Razor slices away unnecessary encrustations from scientific models. Before reading Life is Simple, that's about all I knew of the matter. I didn't even know that William, born in Ockham, lived in the early 1300's, about 700 years ago. This was just before the era of Geoffrey Chaucer (Canterbury Tales), who was born just a few years before William of Ockham died. The "English" of the day was Middle English, when the use of "thee" and "thou" and "doest" for "does", still found in the King James Bible, were at their height. But William wrote in Latin, which requires just a tad more translation than Middle English.

Neither did I know how the Razor grew and spread among the literate people of Europe and the Middle East. By the time of Kepler, 300 years later, and Newton, a generation later, simplification of theories was accepted throughout the world of the Enlightenment. The thread of the Razor through history is followed in all its excursions, leading to its dominance today.

It has become the ambition of many scientists to determine a Theory of Everything, which can be expressed on a T-shirt as a single equation that unifies not just the Weak and Strong and Electromagnetic forces, but also Gravity and Quantum Mechanics. Such a theory would not be a theory that "explains" everything, for a corollary to the Razor is, "That which explains everything explains nothing." The prolific clusters of epicycles in cosmology are an example. The more cycles you add, to account for refinements in astronomical observations, the less you actually know about them. The laws of orbital areas derived by Kepler, and the three laws of motion of Newton, as modified by Einstein, allow us to calculate exactly where each planet, moon, asteroid, comet, and artificial satellite is going, for decades or centuries into the future, and where they were at any time in the past. The calculations are tedious, but not difficult, and modern computing machinery shoulders the load of the tedious part.

Sadly, many (most?) modern theorists have gotten bogged down in String Theory. Somehow, these mathematical models require calculations in at least 10 or 11 dimensions (some versions, as many as 26 dimensions). None of the string theories so far proffered can be tested experimentally, and the number of possible string theories is a gigantic number with about 500 digits. And we thought 80 epicycles are too many! At the moment, this is a lot more "hair" than the Razor can manage to tame.

I was quite enthralled by the stories, the history, of how modern science developed once it was freed from the cosmogony of Aristotle and Ptolemy, which somehow became the foundation of Roman Catholic cosmology (for the curious: cosmogony is about "what is there", and cosmology is about "how it goes"). In effect, the Razor removed God's hand from the tiller of the Universe, at least so far as science is concerned. William of Ockham was also far ahead of his time in political understanding, which is probably a consequence of his revolutionary understanding of nature: he insisted that rulers' legitimate power came through the consent of everyone. His understanding of natural rights is an embryo of the Bill of Rights in our Constitution.

While I recommend this book for its historical perspective, I have a few quibbles about statements made by the author when he stepped outside his area of expertise, which is molecular genetics. Those who think my objections are TMI can stop here. What follows touches on three items that surprised me the most:

• On p 271, discussing the Planck Law for the spectrum of a heated blackbody, he writes that such bodies "emit light in a narrow band that depends only on the black body's temperature." Not quite. The actual spectrum of a blackbody (note the absence of a space) covers all wavelengths, and the width-at-half-height of the spectrum is about 2.8:1. For example, for a blackbody at a temperature of 7,250K (~12,600°F), the half-height spectrum ranges from 240 nm to 680 nm. The peak of the spectrum for this temperature is at 400 nm. The location of peak radiation depends on temperature, and the relative shape of the spectrum follows. An analogy about whacking a piano and somehow getting only a single note is quite bogus. The range of "notes" so emitted is strongest over more than an octave (18 half-tones), and there is some resonance from every string on the "piano".
• On p 293, about symmetry, "…time symmetry implies energy conservation, translational symmetry implies conservation of momentum, and Newton's third law, that every action has an equal and opposite reaction, is a consequence of rotational symmetry." About the last phrase: Where did that come from? Newton's third law is equivalent to time symmetry, and has nothing specific to do with rotation.
• On p 327, regarding the Bayesian likelihood of a particular combination of numbers being thrown in ten tosses of a 60-sided die, he states correctly that this is the tenth power of 60, or 60¹⁰, but then he evaluates it as 600 million to one. Hardly! 60¹⁰ = 6.05 x 10¹⁷, or 600 million times about a billion, or 600 quadrillion. Really! Don't any of his editors and readers know enough math to punch this out on a calculator?

That's enough of that. I can't blame him too much. Although I strive to be a generalist, I admit I know woefully little about molecular genetics, at least compared to Prof. McFadden. So, if I ever write a book that happens to wander into that arena, I'll see if he's willing to give it a read, and after he stops laughing, make the odd correction here or there.