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 drop in the asteroid-moving bucket

 kw: science, orbital mechanics, asteroids, near-earth asteroids, dart mission

Didymos is a small asteroid, about 3/4 km in diameter, or less than half a mile. Not quite mountain-sized, more like a big hill. It has a satellite, named Dimorphos, 170m in diameter, the size of a five-story office building. Unlike an office building, which is 90+% air, it is a big rock. It weighs about five million tons.

This orbiting pair have the great good fortune to be in an orbit that is "reachable" by spacecraft. Not quite Earth-crossing, but much closer than most. As an orbiting pair, these rocks are also much easier to study dynamically. In particular, the orbit of Dimorphos about its common center of gravity with Didymos can be well-characterized, and very small changes in its orbit can be detected. Changes such as the one that will soon occur.

In a couple of weeks, a NASA spacecraft will be smashed into Dimorphos at high speed, and the collision will be watched by a companion spacecraft (the little one shown at center left in this NASA publicity image); and also from ground-based telescopes, symbolized by the icons at lower left.

How sensitive a "probe" is this little satellite? The key is its orbital velocity and period, which can be measured with great precision.

The collision, on September 26, 2022, will be made on the leading side, so it will slow Dimorphos down a tiny bit, moving it into an orbit just a bit closer to Didymos. The key parameters are these:

• Mass of Dimorphos: 4.8 billion kg, equal to 4.8 million metric tons or 5.3 million short tons.
• Mass of the DART impactor: about 500 kg on impact. It starts out weighing 610 kg, and burns propellant to ramp up to speed.
• Impact relative velocity: 6.6 km/sec, equal to 4.1 mi/sec or almost 15,000 mph. For comparison, the orbital velocity of Earth around the Sun is about 67,000 mph or 29.9 km/sec.

The minimum change in the velocity of Dimorphos is calculated by assuming a perfectly inelastic collision. It comes to 0.6875 mm/sec. 

NASA writes that they expect an orbital velocity change of 0.4 mm/sec; perhaps they are assuming lots of kinetic energy will be lost to vaporizing the DART impactor and about a desk-sized chunk of Dimorphos. NASA expects this small slowing of the moonlet to move it into a slightly smaller orbit, such that it will speed up a bit and each orbit will take about 10 minutes less than before. The orbital period is presently just under 12 hours.

It occurs to me that NASA's figure of 0.4 mm/sec must represent the expected increase in orbital velocity resulting from the shrinking of the orbit. Perhaps the instantaneous "bump" will be of the order of 0.7 mm/sec of slowing, but in the resulting, smaller orbit, Dimorphos will have an average velocity as NASA has calculated (their math whizzes are certainly much more savvy than I!).

That's as far as my amateurish figurations can take me. I'll stay tuned to the NASA webcast on the 26th! This is step 1 in figuring out what it takes to shift the orbit of any asteroid that is found to be threatening Earth.

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.