Celestial Mechanics

I first got interested in celestial mechanics in 1978. I enrolled in three independent study classes at two schools, New Mexico State University, then at Lansing Community College (1981, 1982). In 1981, I met an astronomer from Michigan State University who encouraged me to get this book on algorithms for calculators. He wanted it for himself and I was working for a publisher. So I ordered two. I used the routines as outlines for some BASIC programs but never went much further with it. 

[An earlier version of this essay was posted to The Sky Searchers discussion board in the Astrophysics forum.] 

John Wiley and Sons.
(c) Aubrey Jones 1978

My wife and daughter bought me a telescope for my birthday in 2014. In the past six years, I have enjoyed going out in the backyard (often) and to star parties (a few times) and verifying for myself that the universe is pretty much as described in the books. But what’s next?

I am not facile with mechanical tasks. Things come apart a lot easier than they go back together. That can be useful for documenting physical systems, but it suggests that photography and spectroscopy are not likely to be rewarding as hobbies complementing observational astronomy.  
 

On the one hand, in order to pursue celestial mechanics you really need to love mathematics. As much as I enjoy it, I took Calculus-1 twice to get a C+. I learned integration (usually Calculus-2) by taking a computer programming class and coding up the Midpoint Rule, Simpson’s Rule, and the Trapezoid Rule. The advantage to me is that it is easier to erase a mistake than it is to drive to Home Depot to buy another part (which I have to do to finish work on the backyard gate). 

McCuskey, Addison-Wesley, 1963

In the 18th and early 19th centuries, orbit plotting was the focus of astronomy. Following Sir Isaac Newton’s Principia, and the parallel work of Gottfried Wilhelm Leibniz, Pierre-Simon Laplace developed what we recognize today as the calculus of celestial mechanics. It allowed astronomers to establish the orbits of the planets and their newly discovered moons and the two new planets, Uranus and Neptune, and their moons. It also allowed astronomers to determine the physical arrangements of binary stars. With the advent of photography and spectroscopy, orbit plotting fell out of favor with researchers as those tools revealed deep and starling new truths. However, even as radio astronomy came to the fore in the 1950s, celestial mechanics regained some importance with the space age. 

 

But if you are not the person launching a satellite to Saturn, why grind through transcendental equations? My reply is the same as for any amateur pursuit, any hobby, or sport: You do it for yourself because it is at once rewarding and edifying. And unlike most other hobbies, astronomy is a study where amateurs and professionals collaborate. 

 

How fast does the Moon go around the Earth?

How fast does the Sun go around the Earth?

How fast do the stars go around the Earth?

And when will that comet come back?

 

If you have lived any arbitrarily long time, you know that our easy estimates – the Moon travelling through 360 degrees in 28 days; the Sun circling the Earth 360 days each year (plus 5 days for a long holiday "off the books"); the fixed stars moving westward one degree per night through the year -- have errors that accumulate. Can I make more accurate predictions?

 

Not only has the hard mathematics been done already, reducing the problems to the application of formulae, but I now have a computer and a spreadsheet. All I have to do is take the measurements and reduce the data.

 

(More later.)

 

PREVIOUSLY ON NECESSARY FACTS

Newton and Leibniz

Astrophotography is a Lot like Love 

Measuring Your Universe: Alan Hirshfeld’s Activity and Laboratory Manual

In Support of the Entry-Level Telescope 

John Kemeny Knew: We Shall Have Computed 

 

 

Hail to the Spartan Victors?

I do not remember where I was driving when I saw this banner. The incongruity prompted me to stop and take a picture. I found it again in my archives but it had been edited and the date was too current now. 

We mostly lived in Michigan for about 30 years off and on from 1977 to 2011, almost 20 years continuously from 1979 to 1999. The hometown rivalries are between the Michigan State University Spartans (green and white) and the University of Michigan Wolverines (blue and maize). 

Never much for team sports and certainly not college football, the fact is that we lived in and around Lansing until 1999. My daughter and I made good use of the MSU campus. I had a community library card. We skated the grounds, rented canoes, and explored buildings when classes were out. 

But Laurel’s freshman year was at the U of M before we met. She returned to work at the University and take a graduate class when we were living in Ann Arbor and attending Eastern Michigan University 2005-2010. So, our loyalties are somewhat conflicted.

 

But, as I said, I don’t follow sports. So, there was one time I was working for a software firm in Lansing and some of the programmers were MSU graduates; everyone else was an MSU fan. I caught a cold the week of Thanksgiving and missed a day of work that Wednesday and spent the weekend in bed recuperating. The Michigan-Michigan State game was televised (oddly) and I caught snatches of the last quarter as I surfed the channels. When the game was over, the Green and White band came out and played “Hail to the Victors.” 

 The next Monday, they were talking about the game, and going to school, and learning the MSU fight song at orientation. And I said, “Hail to the Victors” and they said, “WHAT?!?!” And I explained that I caught the end of the game and the Spartan band played “Hail to the Victors.” And they said, “That’s because we lost. The band salutes the winner by playing their song.” Oh…

PREVIOUSLY ON NECESSARY FACTS

Hook ‘em Horns! 

Good-Bye Redskins 

Why a Level Playing Field? 

Big Bang Theory: More Friends than Seinfeld 

 

Pencil Notes: Reflections on Henry Petroski’s "The Pencil"

“Yet, perhaps in part because specialization was no doubt as common in ancient times as it is today, the written history of engineering is sparse. Even the most able and articulate of ancient engineers, whether they were known as artisans, craftsmen, architects, or master builders, might have had no more time or inclination or reason to articulate what it is they did and how they did it than do some of the most able of today’s engineers.” – page 17

That is why they hire technical writers. To me, it is a right-brain/left-brain situation. Engineers tend to be right brain thinkers. Technical writers bring that with them, also, the ability to read, edit, and create drawings, whether architectural plans or software flowcharts. Ultimately, though, the images get verbal explanations. That may explain why so many technical writers are women: the left and right hemispheres of the brain are connected by the corpus collosum, which tends to be more highly developed in females than in males.

 

It is difficult to be certain how this or that better design for a brush, plow, house, or sword evolved from its predecessors, for the process was at best sketched metaphorically in pencil and seldom if ever copied in pen. It is because of this that the ideas and artifacts of technology—the processes and products of engineering—are so very different from the creations and theories of literature, philosophy, and science. … The classics, even if superseded in factual or theoretical sophistication are considered models of thinking from which one can today still benefit by emulation, or at least inspiration. […] Curators of technological artifacts, industrial archaeologists, and historians of technology represent rather new careers…” – pages 20-21

1. First, that is why we have industrial archaeology now, to recover and understand those earlier activities and artifacts. 
2. Second, we have lost some mathematics. Richard P. Feynman wanted to demonstrate to his class how Newton proved Kepler’s laws, and he wanted to do it in Newton’s own language. He could not. Feynman could not recreate the geometry that was fundamental to the Principia. We have become so dependent on algebra and calculus that we have forgotten the admittedly more cumbersome tools of earlier mathematics.
3. We also lost the machinery of the Antikythera Mechanism. It would be almost 1500 years before clocks were again so complicated, accurate, and precise.
4. Fourth, and to Petroski’s point, antiquarians do inform the present. Though we had advanced past the hand-hammered methods of coinage, it is famous that President Theodore Roosevelt commissioned Augustus Saint-Gaudens to give America coinage as compelling as that of the ancient Greeks. 

Professional Coin Grading Service "Coin Facts" website
TOP: Half Dollar of Charles Barber imitating the work
of Oscar Roty for France. BOTTOM: Something better. 

“[Sir Isaac Newton’s] seashore metaphor allows that one shell (theory) may be prettier (more elegant) than another, and perhaps the searcher becomes less fond of the old shells as prettier ones are found, but the implication is still that the truths are whole in the ocean and it is just a matter of time before they are found thrown up on the shore.

“While pencils may be helpful in formulating abstract theories of motion and gravitation, abstract theories do not make pencils.” – page 74.

 

The history of modern physics may refute that. The mathematics describing atomic and nuclear processes energy became the design specifications. We did not tinker our way to nuclear power.

 

Of all the revelations and insights here, I was captivated by the story of Henry David Thoreau (Chapter 9: An American Pencil-Making Family). We recently watched the most recent remake of Little Women (Greta Gerwig director). We see Jo March’s ink-stained fingers and we watch her on the floor, scribbling in pen. But we all also know that the family was connected with the Transcendentalists, among them Henry David Thoreau. But who knew that his family made pencils? In his list of supplies taken to Walden Pond, mostly likely written with the pencil he carried, Thoreau omitted the pencil. Thoreau also billed himself as a surveyor and civil engineer, two professions that even in 1840 depended on good, reliable graphite pencils. 

 

I wrote here last week about the passage on pages 223-225 describing how engineers often were trained to draw by copying architectural treatments. It is, of course, how architects learned to draw. That opened up a new vista on an early passage in The Fountainhead. That being as it may, it is nonetheless true that to learn science, we recreate the important experiments of the past. We just do not slavishly recreate them with archaic beakers, wires, and flyball governors. I believe that it is a valid criticism of physics in particular, stated in Thomas Kuhn’s Structure of Scientific Revolutions, that we are handed science as a completed artifact and do not trouble ourselves much with discarded paradigms—or why we discarded them. (My review for this blog is here.)

 

“One desirable quality is often gained at the expense of another, for how the properties of complicated materials will change with changing ingredients and methods of preparation, whether they be pencil leads or concrete, is not always easily predictable. While a new mixture might give a stronger material, it might also give a more brittle one that will be greatly weakened by a small crack.”—page 236

 

“The stories of the Munroes and the Thoreaus and their pencils illustrate in microcosm the often conflicting objectives of real-world engineering and business: making pencils as fine as possible as an end in itself; making pencils better in quality or price than other pencil makers; making pencils secretly in order to have an advantage over the competition; making pencils overtly to conceal a more profitable business; making pencils for the social and cultural good of artists, engineers, and writers of all kinds. There is no such thing as pure engineering, whether in the artifact or in the abstract—for that would be nothing but irresponsibility or a mere hobby. Engineering, far from being applied science is scientific business.” – page 276-277.

It reminded me of the discussions among Austrian economists over what entrepreneurship essentially is. (See NecessaryFacts here.) Being rationalists  they seek one or a few axioms from which all of the remainder can be derived by pure reason. Do entrepreneurs bring new inventions to market? Do they arbitrage risk? Do they carry goods from where they have lower value to where they are valued more? Do they drive each other out of business by any means possible? Do they find cooperation where others find conflict? Do they take advantage of the unwary or do they profit from intelligent decisions? Mises pointed out at some length that the entrepreneur can be so self-centered that they invest all of their resources in a lost cause when a rational person would just get any good-paying job and keep it. There is no such thing as pure entrepreneurship unless it is a hobby. 

 

In 1933 [the Lead Pencil Institute] has ten members who together manufactured 90 percent of all American pencils. Thus the institute effectively represented the entire industry, which at that time included thirteen firms. They were roughly in order of size: Eagle Pencil Company, New York, N.Y.

Eberhard Faber Pencil Company, Brooklyn, N.Y.

American Lead Pencil Company, Hoboken, N.J.

Joseph Dixon Crucible Company, Jersey City, N.J.

Wallace Pencil Company. Brentwood, Mo.

General Pencil Company, Jersey City, N.J.

Musgrave Pencil Company, Shelbyville, Tenn.

Red Cedar Pencil Company. Lewisburg, Tenn.

Mohican Pencil Company, Philadelphia, Pa.

Blaisdell Pencil Company, Philadelphia, Pa.

Richard Best Pencil Company, Irvington, N.J.

Empire Pencil Company, New York, N.Y.

National Pencil Company, Shelbyville, Tenn.

(Page 293)

 

I found it disappointing that Petroski quoted John Middleton Murray at length on the poetry of being a pencil, but never mentions “I Pencil” by Leonard E. Reed.

 

The old meets the new. These pencil extenders are built
from STL files provided to 3-D printers

“Who today but a frugal draftsman would use a pencil down to such a stub? But our pencils, unlike many of those of the Victorians, have lead from end to end, and some engineers and draftsmen, when a good pencil’s stub is too small to hold even in a pencil extender, have been known to cut away the last of the wood case and use the left in their compasses.” – page 354

 

Previously on NecessaryFacts

Imaginary Numbers are Real but Pegasus is not 

Forbidden Planet 

Spoken American Grammar 

The Map that Changed the World 

The Pencil: History, Design, and Circumstance

The book opens and closes with the fact that the pencil’s ubiquity rendered it invisible. On pages 5 and 346 the author tells of being unable to find old pencils in antique stores or museums. Shops that specialize in classic craftsman’s tools keep the compasses, but throw out the pencils. They value the carpenter’s levels, but discard the trade’s signature pencils. They curate the surveyor’s drafting pens, but not the pencils that laid out the guidelines that made inking possible. If that is received as incongruous, then consider that very little engineering is ever recorded. The work is the story. How it came to be is locked and lost in the mind of the inventor. The engineering drawing delivers its thousands of words. The engineer seldom records any of the words that gave birth to the plans and procedures. And as central as is the precision drawing, the pencil that made it has been ignored.

The Pencil: A History of Design and Circumstance by Henry Petroski (Alfred A. Knopf, 1990) is a paean to engineering with the pencil as its metonym. Being a professor of civil engineering, the author frequently compares the creation of pencils with the development of bridges. The allusion is not deep. The focus is the pencil, not the truss or suspension, though both are mentioned as needed for context.

  

We are told too easily that scientific theories become applied as engineered structures or machines. In truth, it is the other way around: theories explain what engineers develop by intuition, insight, trial and error, craft, and trade secret. When those are formalized into mathematics, then engineering science can improve the product or the process by analysis, seeking and eliminating limitations, flaws, defects, and oversights.

 

People were happy with metallic scribers made of lead, tin, or silver, and pens cut from reeds or feathers. The discovery in the 16^th century of “black lead” or “plumbago” or “British lead” that we now call “graphite” radically altered writing and drawing, both for fine art and engineering. For three hundred years, the best graphite came from a single district in England. France’s wars with England led to the Conté crayon, a secret mixture of clay and graphite. Closed out of France, German firms developed their own secret formulas with graphite from Bavaria and Bohemia. Suitable graphite was found in New England and pencils were the family business for Henry David Thoreau. A new lode was discovered in China, giving rise to the yellow color we assume for the default and trade names such as “Mongol.” 

Alongside the rapid successive innovations of the 19^th and 20^th centuries, pencils were still sharpened with penknives. The first pencil sharpeners date to the 1890s and did not achieve the forms we accept today until after the 1930s. (Wikipedia has more to say about their development.) Into the 1980s, if not still a practice today, drafters at their drawing boards sharpened their pencils with sandpaper. I had mechanical drawing classes in junior high school (1962) and college (1978 and 1984) and that is how I was taught. 

 

Through all of that and into our time, the challenges have been to make consistent pencil leads in predictable grades, tough, strong, resilient, pliant, black (or other colors), and cheap; and do so by the millions, eventually billions. Graphite mixed with clay will not make a pencil. Only a few species of trees—mostly cedars—will do. The wood must be treated. The leads must be prepared. They are both in their ways shaped, formed, baked, boiled, heated, coated, stripped, and glued. While mechanical pencils—known since the 18^thcentury—solve the problem of the wooden casing, they bring their own limitations. 

As a result of this book, I have been buying pencils, driving to office supply and art supply stores, giving long minutes to reading the pencils themselves, comparing their imprinted names and grades with the notecard I made for the purpose. I think that for myself, a 2-½ H or F would be best, but I cannot find them locally. Amazon has two brands, Mirado and Ticonderoga. I may have to give in and buy there.

 

PREVIOUSLY ON NECESSARY FACTS

Start the Presses! 

Art & Copy 

For the Glory of Old Lincoln High 

Dealers Make the Show: Armadillocon 41 Day 3 Part 2