Category Archives: History

Math – How Come We Forget So Much of What We Learned in School?

27 Monday Aug 2018

Posted by in astrophysics, education, History, Math, science, teaching, Telescope Making, Uncategorized

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This was a question on  Quora. Here is an answer I wrote:

In the US, judging strictly on what I’ve seen from my time in the classroom as both a student, a teacher, and a visiting mentor of other math teachers, I find that math and science was very often taught as sort of cookbook recipes without any real depth of understanding. The recent National Council of Teachers of Mathematics prescriptions have attempted to correct that, but results have been mixed, and the Common Core has ironically fostered a weird mix of conceptual math marred by teachers being *OBLIGATED* to follow a script, word-for-word, if they want to remain employed. Obviously, if students are really trying to understand WHY a certain mathematical or scientific thing/fact/theorem/theory/law is true, they are going to have questions, and it’s obviously the teacher’s job to figure out how best to answer said questions — which are not likely to have pre-formulated scripts to follow in case they come up — and which are going to take time.

Another thing that is true is that not everything in mathematics has real-world applications in every single person’s life. I taught a good bit of computer programming (aka ‘coding’ today), geometry, arithmetic, probability, algebra, statistics, and conic sections, and in fact I use a LOT of that every week fabricating telescope mirrors to amazing levels of precision, by hand, not for a living, but because I find telescope-making to be a lot of fun and good mental, aesthetic, manual, and physical exercise. But I’m a pretty rare exception!

Most people obviously don’t dabble in math and physics and optics like I do, nor should they!

In fact, I have made it a point to ask professional scientists and engineers that I meet if they actually use, on their jobs, all the calculus that they learned back in HS and college. So far, I think my count is several dozen “Noes” and only one definite “Yes” – and the latter was an actual rocket scientist / engineer and MIT grad and pro-am astronomer (and wonderful, funny, smart person) who deals/dealt with orbital rocket trajectories. (IIRC).

In France, when I went to school there 50 years ago and in my experience tutoring some kids at the fully-French Lycee Rochambeau near Washington, DC, is that they go very deeply into various topics in math, and the sequence of topics is very carefully thought out for each year for each kid in the entire nation (with varying levels of depth depending on what sort of track that the students elected to go into (say, languages/literature, pure math, or applied sciences, etc), but the kids were essentially obligated to accept certain ideas as factual givens and then work out more and more difficult problems that dealt with those particular givens. No questions allowed on where the givens came from, except to note the name of the long-dead classical Greek, French, Italian or German savant whose name is associated with it.

As an American kid who was mostly taught in American schools, but who also took 2 full years of the French system (half a year each of neuvieme, septieme, premiere, terminale, and then passed the baccalaureat in what they called at the time mathematiques elementaires, I found the choice of topics [eg ‘casting out nines’ and barycenters and non-orthogonal coordinate systems] in France rather strange. Interesting topics perhaps, but strange. And not necessarily any more related to the real world than what we teach here in the US.

Over in France, however, intellectuals are (mostly) respected, even revered, and of all the various academic strands, pure math has the highest level of respect. So people over there tend to be proud of however far they got in mathematics, and what they remember. Discourse in French tends to be extremely logical and clear in a way that I cannot imagine happening here in the public sphere.

So to sum up:

(a) most people never learned all that much math better than what was required to pass the test;

(b) only a very few geeky students like myself were motivated to ask ‘why’;

(c) most people don’t use all that much math in their real lives in the first place.

 

 

Safer Table Saws Should Be Mandatory

14 Monday Aug 2017

Posted by in History, Safety, science, Telescope Making

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Three parts to this little essay:

  • What happened to me about a month into my retirement, with an old, nearly-free table saw that lacked SawStop safety features (and which I was using totally improperly, because I didn’t know better)
  • Table saws are one of the most commonly-used power tools both commercially and at home, and are responsible for an AMAZING number of injuries and amputations every DAY.
  • A fix for this exists — the technology included in every single SawStop table saw. The inventor tried, but failed to convince table saw manufacturers to incorporate this essential, and not-terribly-expensive feature, and they ALL turned it down, essentially saying that ‘safety doesn’t sell’. Congress has the power to make this feature mandatory and to save many a hand, finger, or eye.

Part One

These are not trick shots. It’s just my left hand, imaged poorly just now with my smart phone. I was really ashamed, embarrassed, and sad when this injury occurred, roughly a month after I retired from teaching, for several reasons:

(1) It turned out that I was using the table saw totally improperly, holding a very small piece of wood as I fed it into the blade

(2) I literally did not know that was an improper way of feeding wood into a table saw; I was treating it like a band saw

(3) I should have read up on safety rules for table saws, even though I had used them without incident quite a few times earlier, and thought that I was safe enough (and I wasn’t)

(4) While I am right-handed, losing part of one’s left-hand index finger and having the adjacent finger be mauled so that it lacks feeling on one side, and doesn’t bend properly, and is crooked, means that there are many things one can never do again – for example typing quickly and efficiently. The letters e, r, t, d, f, g, c, v, and b (look at your keyboard and if you ever learned touch typing, you’ll see why) are all now much harder for me to type. And unfortunately for me, E and T are the two most common letters in the alphabet. (I’m not asking for sympathy! Just don’t do this to yourself!! Wear safety equipment and read the fri&&14& manuals!)

 

On the good side, I am extremely grateful and amazed at the skill of Dr. Reisin, my hand surgeon. Without any warning that I could see, my hand got dragged into the blade by the tiny piece of wood. My two fingers looked like very fresh hamburger, and I thought I had lost them down to stumps. I was amazed that when I got my first view of the damage, I still had most of them! Yay Dr. Reisin! Really, amazing job!

In addition, we have Kaiser Permanente family high option insurance. It’s not cheap, something like $400 a month that I pay, plus I have a wonderful subsidy from the DC government, which pays something like $1000 a month. All of that adds up to just about 1/3 of my gross retirement pay, but at least I was never asked to liquidate my retirement savings or sell our house to pay for the astronomically huge bills for all of the doctors’ fees (think anaesthesiologist, primary care physician, ER physicians, surgeon, just to name a few) and the hospital stay and the several months of careful and skillful rehabilitation. It was tens of thousands of dollars, though I certainly don’t know the exact total. If we did not have medical insurance, it would have been very, very tough, but we had minimal co-pays for each visit and for the various antibiotics and painkillers. EVERYBODY SHOULD HAVE THAT!

Again, I was really embarrassed at my own stupidity. For the first few months, I labored under the misapprehension that the wood had been thrown INTO my hand by kickback. But a more knowledgeable friend (WHR) convinced me otherwise; plus I looked at the sawblade scars on the underside of the other pieces that I had fed through – in each case, the saw had started grabbing the wood and had left its marks on the pieces of plywood — and I was too stupid and ignorant to notice. This video shows how dangerous table saws can be – it’s pretty similar to what happened to me: the blade catches the wood, AND the author’s pushing block, AND just barely misses taking off his finger(s).

SECOND PART:

It took me a while to realize that I was far from the only person who had suffered this sort of injury. I was quite aware that the workers at my college (Dartmouth) were almost ALL missing a finger or two or five – but that was from industrial accidents in the textile mills that used to exist all over New England, but had moved on to other places, probably because the owners could get labor for even less and spend even less on safety than before… I wish now I had asked them more about those injuries… But I’m pretty sure that they were not operating table saws.

I did not know that anywhere from SCORES to HUNDREDS of Americans have some sort of an injury with a table saw not per year, not per month, not per week, but EVERY SINGLE DAY.

Let that sink in. Somewhere between 40 and 400 people in the USA have an accident with a table saw, EVERY SINGLE DAY. Some of these accidents were worse than mine, some were less so (two sources on numbers: here,  here and here, each with links pointing elsewhere. It seems to me reprehensible that Robert Lang, the author of the Popular Woodworking magazine (the second link), belittles the number of injuries, comparing them to the number of kids who are hurt by doors everyday.

‘Back in January 2005, the Consumer Product Safety Commission (CPSC) required that new tablesaw models include a riving knife and modular guard to prevent these injuries. Since that time injury rates have remained virtually unchanged, which begs the question: “Why are so many people hurt while using tablesaws, despite improvements in guards and splitters?”’ (source)

As soon as I could use my arm again, I supervised getting rid of that old table saw. I think we sold it for scrap iron. (It had been sold to us for a pittance by a friend — who passed away from a heart attack at a very early age, as it happened. I never had the chance to mention to him what happened to me.)

Fortunately, after this event, the same friend (WHB) got wind of someone who wanted to donate funds so that we at the NCA Amateur Telescope Making workshop could actually get a decent, SAFE table saw. We also used the monies to purchase a very nice H-Alpha solar telescope for the astronomy club under whose auspices we operate, as well as a nearly-unused Grizzly milling machine… And while it doesn’t have lots of fancy features, that SawStop table saw will immediately (in 0.003 seconds) if it senses anything like your finger touching the blade while in operation; if it does, it slams the blade down into an aluminum chunk and stops it immediately and OUT OF THE WAY. (Have you seen any of those hot-dog table-saw videos? or ) Sure, it kills the blade and the chunk of aluminum (roughly $60)  but that’s way better than cutting off your finger!

In fact, the inventor agrees to put HIS OWN finger into a SawStop table saw, under a high-speed camera and very bright lighting, here. He does so, and the sawblade stops instantly, you can see that no damage to his finger at all: no blood, no bruising, no nothing. The inventor says it felt a little like a buzzing insect or a tickle. Absolutely amazing!

Plus, the saws are really, really well made and easy to put together, and have a very good manual that comes with a spiral-bound notebook with laminated pages and very clear instuctions in English, that you can lay flat at any page you want.  In other words, not the incomprehensible hieroglyphics, printed on flimsy paper, that is so common with manuals today. (Think IKEA…) And the prices are well within range of the prices of other table saws with comparable features.

The original inventor has recently testified at the Consumer Product Safety Commission, and was interviewed by NPR. He could not get manufacturers to agree to put his device (or one just like it) into their saws, EVEN AS AN OPTION. So he set up his own company to make them.

It’s also reprehensible that something like the Power Tool Institute wants to prevent the government from making this electronic safety feature mandatory, as you can see here. 

It’s the usual crapload of hysterical propaganda: higher unemployment, making companies go bankrupt — the same lies that the Big Three carmakers said when they resisted putting in seat belts, antilock brakes, turn signals, doors that have hinges at the front and not the back, unleaded gas, airbags, and so on. But those inventions (and others) have saved untold millions of lives, despite the resistance of the rich and powerful. It’s disgraceful.

Yes, we ordinary humans do make mistakes, each and every single day. People are going to lose focus, or get distracted, or make stupid errors of judgement, like me. It doesn’t matter if you drive (or use a table saw) correctly 99.9% of the time: that still leaves that one time in a thousand where you don’t, AND IT CAN KILL YOU OR MAIM YOU FOR LIFE.

If the fix for that is simple — and even if it costs something — it should be done.

We are only human.

Religions based on … well … myths, or alternative facts. Or lies.

14 Friday Apr 2017

Posted by in History, nature, science

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Every single religion that I can think of seems to be based on totally unreliable witnesses and stories that are mis-remembered (at best) or deliberately distorted.

Judaism just celebrated one of its most important rituals, the Passover seder, in which I have participated about six times. If you’ve forgotten, the story is supposedly recorded in the Old Testament (or Tanakh) and the event celebrates the freeing of a large group of Hebrew people from Egypt. They then wandered the Sinai desert (a very, very hot and dry place – I lived next to it for about 9 months).

The problem is, there is absolutely nothing in the historical record that corroborates any of this story. The Egyptians kept a lot of records, and much of it is still readable — no mention of any such tribe fleeing, no first-borns murdered, no special heavenly plagues, yadda, yadda. No archaeological evidence whatsoever of any tribe of Hebrews wandering in the Sinai desert for any such expedition.

(Stuff like that gets preserved there! In fact, at the famous fort and palace known as Masada, near the Dead Sea, you can clearly see the streets and walls of the camp built by the legions of the Roman Army that besieged and eventually captured the fort, from roughly 2000 years ago! Now THAT incident and war is definitely mentioned — in Josephus, among other places…)

That story of Abraham getting ready to slit his son’s throat and god providing a lamb instead? Really? Inscribed tablets from Mount Sinai – really? How do we know any of this? We don’t. And in any case, if God tells you to commit genocide (it’s spelled out in Genesis / BeReshit), is that a wonderful thing? I don’t think so.

If we get to Jesus, well, again, the evidence that he produced any miracles or was somehow resurrected and became one with God (or didn’t) is pretty darned thin. Today is supposedly the day that he got crucified (the Romans were NOT nice people!!!), which was a shame. The Romans killed and tortured and enslaved a LOT of people. I’m not so sure that they should be held in such high esteem…

But I can think of many ways that a body can be taken out of a tomb, and none of them involve miracles or angels. Then, if you read all of the various Gospels, canonical or not, you realize that their outlooks and details are all profoundly at odds with each other.

If you come to Mohammed, I can think of many ways that somebody could appear to be possessed and to recite various lines of poetry (see Mormons, below) — although that would certainly explain why he would have prophecies that justified what he wanted to do (such as marry little girls) or needed to be amended (see Satanic Verses…)

Now both Jesus and Mohammed said some stuff about equality and supporting the poor, nonetheless the leaders of both religions (Popes, Kings, Emperors, Califs and so on) ended up being wealthy beyond anybody’s dreams, while the majority of people lived in pretty base poverty….

If you go back to the founding of Buddhism, what does that mean that someone is ‘enlightened’? How do we know if someone is in fact in that state? Is it even a good thing to attempt to achieve it? It seems to me that it’s more worth while to try to be good to other people (without endangering your own welfare unless absolutely necessary) and to try to leave the entire planet (and solar system) a better place for your descendants — by not driving species to extinction, not raising the global temperature if at all possible, and by helping so many billions of our kin to avoid lives of infernal poverty and oppression.

Hinduism seems to blame the poor and lowest classes for having been wicked people in a past life, and therefore should be not permitted equality with the upper castes. Sounds great if you are a Brahmin, but what an oppressive religion, really! And how can anybody with an ounce of skepticism believe any of those stories?

Going back to 2000+ years ago — All those stories that the Romans, the Greeksm the Babylonians, Persians and Egyptians made up about their gods — are you serious? They actually believed that? Well, you may as well believe in the Tooth Fairy or the Easter Bunny or the Flying Spaghetti Monster!

Oh, can’t leave out the Mormons. Golden plates buried in upstate New York but only viewable and translatable by someone talking through his hat, writing pseudo-king-James-English and talking about lots of animals and plants and metals that supposedly were used by warring tribes of American Indians — and nobody has ever found figs, wheat, camels, sheep, goats, or horses, or the use of iron or wheeled vehicles of any sort anywhere in the Americas for the entire period of say 500 BC to 1491. So that’s all a lie, too.

Sorry if I offend you, but while I know I’m not perfect (far from it) I don’t need fairy tales to try to be a better human being. I prefer to know things that are true and verifiable. And I really don’t like it when people try to kill each other to support ideas that are really just hoaxes.

 

How Britain Became an Island

06 Thursday Apr 2017

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Interesting report with pretty geological maps indicate that the Island we call Britain got cut off from what we know as France and Belgium by a catastrophic waterfall and flood that broke through what we now call the Straits of Dover as the ice that covered Northern Europe was beginning to melt, and sea levels were much lower than today.

Gupta_NCOMMS-16-16909A_Fig2_rev2

Here is the link. 

By the way, if the weather is fairly clear, it’s easy to see the famous White Cliffs of Dover from the French side (for example, at Cap Gris-Nez).

The Mathematics of George Washington

24 Friday Feb 2017

Posted by in History, Math, Uncategorized

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I recently learned some things about how the young George Washington did math, including surveying. Mathematician and historian V. Frederick  Rickey gave a talk 2 nights ago at the Mathematical Association of America here in DC, based on his study of GW’s “cypher books”, and I’d like to share a few things I learned.

(1) The young George appears to have used no trigonometry at all when finding areas of plots of land that he surveyed. Instead, he would ‘plat’ it very carefully, on paper, making an accurate scale drawing with the correct angles and lengths, and then would divide it up into triangles on the paper. To find the areas of those triangles, he would use some sort of a right-angle device, found and drew the altitude, and then multiplied half the base times the height (or altitude). No law of cosines or sines as we teach students today.

(2) He was given formulas for the volumes of spheroids and barrels, apparently without any derivation or justification that they were correct, to hold so many gallons of wine or of beer. (You probably wouldn’t guess that you had to leave extra room for the ‘head’ on the beer.) Rickey has not found the original source for those formulas, but using calculus and the identity pi = 22/7, he showed that they were absolutely correct.

(3) GW was a very early adopter of decimals in America.

(4 ) This last one puzzled me quite a bit. It’s supposed to be a protractor, but it only gives approximations to those angles. The results are within 1 degree, which I guess might be OK for some uses. I used the law of cosines to convince myself that they were almost all a little off. Here’s an accurate diagram, with angle measurements, that I made with Geometer’s Sketchpad.

His method was to lay out on paper a segment 60 units long (OB) and then to construct a sixth-of-a-circle with center B, passing through O and G (in green). Then he drew five more arcs, each with its center at O, going through the poitns marked as 10, 20, 30, 40, and 50 units from O. The claim is then that angle ABO would be 10 degrees. It’s not. It’s only 9.56 degrees.

A Talk at AHSP on Telescope Making

16 Friday Sep 2016

Posted by in astronomy, History, Telescope Making

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Two weeks ago was the Almost Heaven Star Party on the slopes of Spruce Knob, West Virginia, sponsored and organized by the Northern Virginia Astronomy Club (NOVAC). The weather was wonderful, and we could see the Milky Way and lots of Messier objects with our naked eyes, every single night for four nights. This is by far the longest stretch of good weather I’ve ever experienced up there at The Mountain Institute.

(Friday and Saturday, it was only clear for a few hours, but Sunday and Monday nights were clear all night, AND there was NO DEW to speak of!! Wow!!)

During the daytime, there were lots of talks and also activities and expeditions such as hiking, spelunking, visiting the National Radio Astronomy Observatory at Green Bank, canoeing, and Phun With Physics and arts & crafts for kids. I particularly enjoyed the talks on Russell Porter (the founder of amateur telescope making in the US and one of the major designers of the 200-inch telescope at Palomar), LIGO (detection of gravity waves), and Rod Molisse’s talk on 50 years of mostly-commercial telescopes as seen in the pages of various astronomy regime.

I was one of the speakers and gave a little talk on telescope-making. If you care to sit through it, you can find it along with all of the other talks (many of which I missed for various reasons) at this web-page.

I brought my home-made 12.5″ Dob-Newt [shown to the left in the picture below] and added about a dozen items to my formal list of Messier objects. (I had already seen all 100+ objects, but hadn’t recorded enough details on them to be able to earn one of the ‘merit badge’ pins from the Astronomical League, so I’m going through the list again

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(If you didn’t know: Charles Messier loved hunting comets about 220 years ago, with what we would consider today to be a fairly small (4″ diameter) refractor that he used from downtown Paris, not far from where I lived back in 1959. Comets look like fuzzy patches in the sky, and so do galaxies, star clusters, and illuminated clouds of gas, all of which are MUCH farther away and MUCH larger. Comets are part of our own solar system, and move noticeably from one night to the next against the apparently fixed background of stars. Messier is credited with discovering 13 comets. But when he discovered a fuzzy item in the sky that did NOT move, he would record its location and its appearance, so as to avoid looking at it again. He published and updated this list a few times before he died, 199 years ago. Nowadays, his list of things-to-be-avoided are some of the most amazing and beautiful things you can see in the night sky. I’ve tried imaging a few of them, but am very, very far from being proficient at it. I attach my best one so far, of something called the Dumbbell Nebula. No, it’s not named after me. And thanks to Mike Laugherty for helping with the color balance!)

dumbbell-processed-november-1-2015

Movie about Ramanujan

19 Thursday May 2016

Posted by in History, Math

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I recommend going to see ‘The Man Who Knew Infinity’, about the famous Indian mathematician Srinivasa Ramanujan, whose originality astonished the greatest mathematicians of his day, G H Hardy and Littlewood.

It’s a historical romance rather than a documentary, so there are parts that are completely made up — like German Zeppelins bombing Cambridge University during World War 1, and off-duty British soldiers beating up Ramanujan for being a foreign draft dodger. A weird aspect is that the actors and directors don’t seem to be on the same page about the correct pronunciation of Ramanujan’s name. They mostly put the accent on the third syllable, where as far as I can tell it should be more like ruh – MAHN – uh – jahn.

However, there was such a bombing near-by during the war, and the British army did have temporary hospitals for wounded soldiers during that war, and Ramanujan did contract tuberculosis and die at the sadly early age of 32, after he had gone back home. And apparently his mother had indeed been intercepting letters to and from his wife, so they were completely cut off from each other, as the movie states.

And of course, they can’t really explain much of the mathematics – heck, I can’t understand much of anything that Ramanujan did! Even his simplest formulas are way, way over my head! Dramatizing partitions of a number was probably a wise move, since it’s one of the few things that an ordinary person might understand.

 

 

 

 

On Making an Artificial Star for an Indoor Star Tester

04 Sunday Jan 2015

Posted by in History, Telescope Making

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I help run the amateur telescope-making workshop at the Chevy Chase Community Center in Washington, DC, sponsored and under the auspices of the National Capital Astronomers. Both the NCA and its ATM group have been on-going since the 1930’s, well before I was born. In our ATM group, have the somewhat esoteric thrill of manufacturing incredibly accurate scientific devices (telescopes), from scratch, with not much more than our bare hands and a few tools. And then we go and use them to observe the incredible universe we come from.

Since these telescope mirrors are required to be insanely accurate, we need extremely high-precision ways of testing them. However, we don’t have the tens or hundreds of thousands of dollars needed to purchase something like a professional Zygo Interferometer, so we use much cheaper ways of testing our mirror surfaces.

Some of those methods are associated with the names Foucault, Couder, Bath, Ronchi, Ross, Everest, and Mobsby, or are described with words like “knife-edge”, “double-pass” and “wire”. They all require some relatively simple apparatus and skill and practice in measurement and observation.

We are of the opinion that no one single test should be trusted: it’s easy to make some sort of error. (I’ve made plenty.) You may perhaps recall the disaster that happened when the Hubble Space Telescope mirror passed one test with flying colors, and other tests that weren’t so good were ignored. When the HST finally flew in orbit, it was discovered that the mirror was seriously messed up: the test that was trusted was flawed, so the mirror was also flawed.

We don’t want to do that. So, at a minimum, we do the Ronchi and Foucault/Couder knife-edge tests before we say that a mirror is ready to coat.

But the ultimate test of an entire telescope is the star test.

In principle, all you need for that is a steady star, your telescope, a short-focal-length eyepiece, and a copy of Richard Suiter’s book on star-testing optical telescopes.

Unfortunately, around here, it’s often cloudy at night, and if it’s clear, it might be windy, and around the CCCC building there are lots of lights — all of which make star-testing a scope on the two evenings a week that we are open, virtually impossible. We aren’t open in the daytime, and even if we were, I don’t see any ceramic insulators on any telephone poles that are both small enough and far enough away to use as artificial stars in the manner that Suiter describes. (There are a few radio towers visible, but I doubt that their owners would let us climb up one of them and hang up a Christmas tree ornament near the top!)

So, that means we need to make an artificial star.

I’ve been reading a few websites written by folks who have done just that, and it seems to be a bit easier than I thought. The key is to get a source of light that acts like a star at astronomical distances — but close enough that we can fit it inside the basement of the CCCC, probably not in the woodshop where we make the scopes, but more likely out in the hallway or in the large activity room next door, both of which are about 40 or 50 feet long.

So here are my preliminary calculations.

First off, it appears that the resolving power of a telescope equals the wavelength being used, divided by the diameter of the objective lens or mirror, both expressed in the same units. The result is in radians, which you can then turn into degrees, arc-minutes, arc-seconds, or whatever you like, but it’s perhaps easier to leave in radians. In any case, the larger the diameter, the tinier the angle that your telescope can resolve if it’s working properly.

I am going to use a 16-inch mirror diameter, or about 0.4 meters, as an example, and I will use green light at about 560 nanometers (560 x 10^-9 m) because that’s pretty close to the green mercury line we have in our monochromatic light box. I then get that the resolution is 1.4×10^-6 radians.

resolution of lens or mirror

(We can convert that into arc-seconds by multiply that by 180 degrees per PI radians  and by 60 arc-minutes per degree  and by 60 arc-seconds per arc-minute; we then get about 0.289 arc-seconds. If we were to use an 8-inch mirror, the resolution would be half as good, meaning the object would need to be twice as big to be resolved, or about 0.578 arc-seconds.)

resolution in arc seconds

I read that one can make an artificial star by using an ordinary eyepiece and a small illuminated hole that is put some distance away from the eyepiece. The entire setup is aimed at the telescope, and then you have an artificial star. Here is the general idea:

artificial star setup

Supposedly, the equations go as follows, with all of the dimensions in the same units. I think I will use millimeters.

Star Size of artificial rigWe want to make it so that the size of the artificial star will be small enough to be below the limit of resolution of any telescope we are making. I am pretty sure that we can set things up so that there is 40 feet (13 meters) between our telescope rig and the table or tripod on which we sill set up this artificial star.

I also know that I can find an eyepiece with a focal length of 12 mm that I’m willing to use for this purpose, and I also purchased some tiny little holes from “Hubble Optics” that are of the following sizes: 50, 100, 150, 200, and 250 microns, or millionths of a meter. Those holes are TINY!!! So that takes care of H and F. I still need to figure out what SS should be.

A few lines ago, I found that for a 16-inch telescope, I need a resolution of about 1.4×10^-6 radians. The nice thing about radians is that if you want to find the length of the arc at a certain radius, you don’t need to do any conversions at all: the length of the arc is simply the angle (expressed in radians) times the length of the radius, as shown here:

angle arc radius

c=theta times Radius

So if our artificial star is going to be 13 meters away, and we know that the largest angle allowed is roughly 1.4×10^-6 radians, I just multiply and I get 1.82×10^-5 meters, or 1.82 x 10^-2 millimeters, or 18.2 microns.

Which means that I already have holes that are NOT small enough: the 150-micron holes are about 10 times too big at a distance of 13 meters, so my premature rejoicing of a few minutes ago, was, in fact, wrong.  So, when I make the artificial star gizmo, I’ll need to figure out how to make the ‘star size’ to be roughly one-tenth the size of the holes in the Hubble Optics micro-hole flashlight.

Or, if I rearrange the equation with the L, H, F and SS, I get that L = H * F / SS. The only unknown is L, the distance between the hole and the eyepiece/lens. For H, I have several choices (50, 100, 150, 200 and 250 microns), SS is now known to be 18 microns or so (36 if I want to test an 8-incher), and I plan on using a 12.5 mm eyepiece. If I plug in the 150 micron hole, then I get that L needs to be about 104 millimeters, or only about 4 inches. Note that the longer L is, the smaller the artificial star becomes. Also, if I replace the 12.5 mm eyepiece with a shorter one, then the artificial star will become smaller; similarly, the smaller the Hubble Optics hole, the smaller the artificial star. This all sounds quite doable indeed.

Build Your Telescope Tube and Mount

16 Tuesday Dec 2014

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7. Build the scope

A. There are many, many books and articles and websites devoted to the many, many ways of building your telescope tube and mount. We have quite a few of these books in our library, and you should definitely study them! In addition, public star parties put on by NOVAC, NCA and other local clubs often have home-made telescopes on the field, and you can ask the makers of those scopes how they did it. Fortunately for us, John Dobson came up with an excellent way of making inexpensive, easy-to-build and easy-to-use telescopes of the Newtonian model, even if he was a nut-case. Willmann-Bell publishes quite a few such books.

B. I strongly recommend an alt-az telescope mount for visual use, rather than an equatorial mount on a pier made of plumbing parts, as people used to make in the 1940s through the 1990s. (As noted earlier, if you want to do astrophotography, you will need a much more complicated and much more expensive mount that tracks the stars precisely. Building such a mount yourself is exceedingly difficult and requires precision machining and electronics!) Most important: plan to make a telescope that is easy to use and not too complicated to build! Using slight modifications of existing plans is much easier than trying something completely novel in design. If you strive for originality, you can be sure that you will need to modify and re-build parts of your invention, perhaps several times, because of problems that you didn’t consider or notice originally. (Think about what a nightmare it would be to drive a Model-T Ford automobile, the first real mass-production car, with all of its nutty and dangerous defects, compared to the comfortable and safe and reliable car that people drive today!)

C. I have a set of plans for a simple 6” Dob on this very blog. (Click for link)

D. At the CCCC, we also have a fairly decent set of hand and power tools for working with wood and metal, so you can make the rest of the telescope here if you like. Be careful, and follow safety directions!

E. We even have a wonderful assortment of ‘oops’ paints from hardware and paint stores, if you don’t mind the ghastly colors.

F. You will need at least half of a sheet of 4’ by 8’ plywood for the scope. The plywood can be any type you like, but don’t get a sheet that is warped or wet or too thin. Nice plywood like Appleply or Baltic Birch can be expensive, but it is strong and looks quite beautiful when varnished. Three-quarter inch thickness is standard, but it’s generally sold as a weird number like 23/32”.

G. You will also need the following commercially available items, some of which we usually have on hand, marked by “UOH”.

  1. Diagonal secondary flat elliptical mirror (we have a few)
  2. Secondary mirror holder
  3. Spider
  4. Focuser
  5. Eyepieces
  6. Finder scope(s) (I recommend a 1-power finder like a Telrad or a Red Dot finder, as well as another finder scope that magnifies about 5 to 10 times)
  7. Possibly a Barlow
  8. A few pieces of Teflon UOH
  9. A few square feet of Formica or the equivalent UOH
  10. Miscellaneous screws, nuts, bolts, screws, glue UOH
  11. Guidance UOH
  12. Paint UOH
  13. Random wood scraps, including a short 2-by-4 UOH
  14. For the mirror holder, you need: Three compression springs; 3 flat-headed machine screws; 9 washers; 3 wingnuts; and a small fresh tube of pure-silicone caulk or aquarium cement

H. We are very fortunate to have a local specialty store that sells telescopes and accessories to the public, called Company 7 . It’s located near Laurel, MD and has an amazing display of rare telescopes. Please shop there! (In other words, don’t talk their ears off getting their advice, and then order an item online because it’s a few dollars cheaper!)

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