Slashdot Mirror

(I recall that the outer planets were detected before they were known this way)

Neptune was found this way, but that was likely coincidence. The early estimates of Uranus's mass (and the other planets, principally Jupiter's) were off by a few percent, which made Le Verrier's estimate for the location of Neptune essentially unjustifiable. But he got lucky, and Galle found the planet at the predicted position. Repeating Le Verrier's calculation with the revised Solar System geometry after the transits of Venus in the 1870s and 1880s just did not work - Neptune was again in the "wrong place". So ... there must be another perturbing planet out there, and off went Percival Lowell on his planet-hunt, which culminated in Clive Tombaugh's 1930 discovery of Pluto.

Come the space age, and actually putting objects of known mass through the solar system (the Mariner series, the Pioneers, the Voyagers) and we got direct measurements of the masses of the major planets, and that's when the initial errors in Uranus's position reduced to within observational uncertainty, and Neptune's too. Pluto, frankly, doesn't matter. The currently proposed PlantNine (Brown-Batygin2016) doesn't matter for Neptune and inwards ; neither does the Mars-ish proposed planet. Too small, too far away.

Intuitively the angles involved must be far smaller than typical mechanical tools could measure so how do they do it?

Well ... I'll give you a hint : they don't go down to the hardware store and buy a protractor. It's custom builds all the way, for professional "astrometry" work. There was a book on my shopping list for some years, which I never found time to buy or read, called "Dividing the Circle" ... here it is, of you've got the thick end of £100 and a couple of weeks of reading time to devote to it.

What do you consider "typical tools"? I work with steering oil wells, and for 30+ years people have been making their direction and inclination measurements to an accuracy of 0.1 degrees of arc (6 minutes of arc) ; we have to correct for how much a steel pipe 200mm outside and 75mm inside sags when suspended horizontally between two supported points 20m apart (the approximate size of the tools ; smaller tools, lower accuracy). This is utterly routine. For amateur telescope work, you get to within a half-degree (of arc) or so of your desired object, then start to "zoom in" using the patterns of relative star positions from your "finder chart". (Compiling those stellar atlases is a different kettle of fish ; Google for the technical publications on how the Hipparcos and Gaia satellites work for state-of-the art.) You measure positions on the sky relative to other stars ... and have to check for ones with known relative ("proper") motions compared to other stars. And every few decades, you have to buy a new set of star atlases. The standard (to amateur level ; professionals only work from online databases) work is Uranometria 2000 ; the "2000" part of the publication's name is the "epoch" to which the atlas was drawn ; the previous edition was done in 1950, the previous in 1900 ... it is literally never-ending. Until you use the databases, which can produce a star map accurate for your date and time of observing.

For a very lightweight text that goes surprisingly deep into the physics theory, I suggest this book: "Astrophysics With a PC - An Introduction to Computational Astrophysics". It's intended for amateur astronomers with an interest in astrophysics, source code in Basic is printed along with the text.

Take a look at the table of contents in the link I gave and see what you think, it costs only $19.95, which is a very low cost for a book these days.

Hyperion is also interesting because its rotation is chaotic. There's a project for simulating this rotation in this book (chapter 12, item 12.26)

Mass of the star can be calculated from its spectrum and brightness. We have models for star formation, based on studies of the nuclear reactions that happen at the core. These stars are all relatively near, so the distance to several of them can be measured directly from the parallax. Knowing the type of the star and the distance, the mass can be calculated from the brightness.

This book shows in an introductory way how it's done, with examples of all the calculations in BASIC. It's a very interesting book, highly recommended.

That's not entirely true. The earth rises and sets in places all around the moon's circumference as seen from the earth, not only at the equator. The effect that makes the moon's face as seen from the earth move a little bit is called "libration". There is libration both in longitude and in latitude. For some points near the poles of the moon, libration in latitude can make the earth invisible at times. Formulas for calculating librations can be found in chapter 53 of this book.

That's not how simulations are done, what you suggest would be a waste of time. You should first learn something about the mathematics of simulations, a good place to start is in this book.

Then you should learn something about the physics, I suggest chapter 1 in this book to learn how to calculate the spectrum of the radiation emitted by a body as a function of temperature.

Knowing all that, it's a simple matter to realize that sunlight is emitted by the sun at a shorter wavelength than heat radiated by the earth, because the sun is hotter than the earth. It just happens that CO2 absorbs less radiation at shorter wavelengths than at longer wavelengths, therefore heat from the sun reaches the earth surface, but heat radiated by the earth surface gets absorbed by the CO2 in the atmosphere.

The rise in the temperature isn't programmed into the simulations, it's a result of the calculations, which use data that has been verified many times.

Look in the 'dead tree file' "Astrophysics with a PC", by Paul Hellings.

Item 4.7.3. "The case of Pluto and Neptune" explains why they will never collide, and gives the source code for implementing the simulation. Sorry, it's in BASIC, but you can easily reimplement it in Perl or Python, or whatever your favourite langage is, it's just one page of code.

If your interest is purely academic, you might check out the CCD Camera Cookbook Webpage. The CCD Camera Cookbook is a book covering the design of two CCD cameras for Astrophotography. The resolution of these cameras is not high, and they do not come out being cheap. I am currently reading the book and will probably build the TC245 camera as a prelude to trying to design my own higher resolution CCD camera for Astrophotography. I think the book alone would be a good start in an attempt to understand CCDs.

The most useful thing anyone who owns a telescope should know is how to perform and analyze a star test. A very thorough treatment can be found in this book.

By the way, the Willmann-Bell web site has a number of outstanding amateur astronomer books at very good prices.

The most useful thing anyone who owns a telescope should know is how to perform and analyze a star test. A very thorough treatment can be found in this book.

By the way, the Willmann-Bell web site has a number of outstanding amateur astronomer books at very good prices.

Build the scope yourself, don't spend all that much money on the focuser (better yet make your own focuser) and spend the saved dough on additional eyepieces. You can get a "better" focuser later.

A 6-inch f/8 scope is a wonderful starter - much better then the junk you find in stores. Hundreds of deep sky objects, craters on the moon, moons of Jupiter and rings are Saturn are all easy to see.

Final advise. Locate and join your local astronomy club, go to a regional star party (can you find both here and get out under dark skies.. sorry, this requires getting out of the city.

I've been an avid avid amateur telescope maker since I was twelve years old. It led to me studying astronomy for a time at Caltech. While I'm a programmer now, it's still a very enjoyable and intellectually stimulating hobby.

While a basic newtonian is a straightforward instrument that can be built by anyone who's good with their hands, telescope making can get as complicated as you want if you're really looking for a challenge. Optical design is still a wide open area of research in mathematics, software engineering, and physics, and some of the more interesting designs take quite a bit of skill to fabricate. That means anyone can make a satisfying telescope, but the hobby will yield a lifetime of interest because there's always new things to learn.

You can construct your own telescope with a primary mirror of 8 inches in diameter for less than $200. It will take quite a bit of work, but it is enjoyable and meditative work. Grinding mirrors is one of the things I do to relax and relieve the strain of coding all day.

A good place to start looking for information is the ATM FAQ. The procedures for grinding, polishing and figuring are pretty involved - you should buy one of the books from astronomy publisher Willman-Bell.

There are a number of people and business who sell inexpensive mirror grinding kits. They will come with a glass mirror blank and an assortment of different sizes of abrasive grits. I would recommend asking on the ATM mailing list (that you can find in the FAQ) when you're ready to order your first kit.

The 8" plate glass kit I bought from Dan Cassaro for my current project set me back $64. When I get done working on the mirror, it will cost me about $35 to have a vacuum coating laboratory aluminize it. Good quality eyepieces cost about $50 - just one will do to start with but it helps to have more.

While fancy equatorial mountings can be expensive to make, it's possible to make a quite servicable altazimuth mount out of common materials like plywood and a few hand tools.

Jean Meeus' classic Astronomical Algorithms has some formulae for compensating for this factor. However, they are empirical (i.e. derived from fitting formulae to data as opposed to derived from an established theory), so they have to be updated frequently.

There are more manufacturers out there, now. That's a good thing since people who don't have the time can at least get in the hobby and even contribute to science.

And anyone who complains they aren't into astronomy because they live in the city and have to deal with light pollution, doesn't understand the hobby, the science and the technology completely.

You can build your own telescope, your own CCD camera, and a cheap PC to run it and do some great science and take some great pretty pictures all from a very light polluted area.

I first played with CCD's on telescopes in 1987. It has come along way since then; in fact some early amateur astronomers turned image processing software developers have even contributed serious advances in image processing.

If you want to hack a really cool system, see how to build your own "Cookbook" cooled CCD camera and the related Cookbook camera website.

I first played with CCD's on telescopes in 1987. It has come along way since then; in fact some early amateur astronomers turned image processing software developers have even contributed serious advances in image processing.

If you want to hack a really cool system, see how to build your own "Cookbook" cooled CCD camera and the related Cookbook camera website.

Personally when I got into star gazing my grandfather gave me a book on grinding and building my own reflector telescope. So for the next few months I did, looking back now it wasn't the greatest telescope, but it meant a lot to me to be seeing Saturns Rings with something I built with my own hands.

It really isn't that diffucult to do, just takes time, and it is pretty cheap too, least compared to shelling out 500 bucks for a 3.5 inch reflector.

Here are some links for books and stuff:

http://www.willbell.com/tm/tm2.htm

http://www.hickorytech.net/~landsg/

You can get books telling how to make telescopes from Willman-Bell and ask for help on the Amateur Telescope Maker's mailing list. Dan Cassaro can sell you a reasonably priced mirror grinding kit.

You can find many products for amateur astronomers at the Astronomy Mall.

Clear Skies!

It helps to be under dark skies, as that will allow longer exposures and increase the chance you will catch a meteor. Exposures of 45 seconds to 20 minutes work well, but if you are light polluted, your exposure time will limited because the film will get fogged by the light pollution.

CCD's aren't normally used for meteor imaging unless you are trying to do some sort of movie. The key here is that the shutter needs to be open for more than a few seconds... most webcams not only don't support this with the software out of the box, but many of them aren't capable of doing it at all.

CCD's also get "noisy" over time and need to be cooled if used for long exposures. This can be done with a peltier cooler, water/air/ice/whatever. This also greatly increases the senstivity of the CCD. For a collection of good books about this, see this page and this one about building your own CCD.

Using a telescope to image meteors costs you more than not. A telescope - in this case, you are using it as a telephoto lense - sees a smaller piece of sky and greatly reduces the chance a meteor will pass in front of the detector/film.

It helps to be under dark skies, as that will allow longer exposures and increase the chance you will catch a meteor. Exposures of 45 seconds to 20 minutes work well, but if you are light polluted, your exposure time will limited because the film will get fogged by the light pollution.

CCD's aren't normally used for meteor imaging unless you are trying to do some sort of movie. The key here is that the shutter needs to be open for more than a few seconds... most webcams not only don't support this with the software out of the box, but many of them aren't capable of doing it at all.

CCD's also get "noisy" over time and need to be cooled if used for long exposures. This can be done with a peltier cooler, water/air/ice/whatever. This also greatly increases the senstivity of the CCD. For a collection of good books about this, see this page and this one about building your own CCD.

Using a telescope to image meteors costs you more than not. A telescope - in this case, you are using it as a telephoto lense - sees a smaller piece of sky and greatly reduces the chance a meteor will pass in front of the detector/film.

The reason they are called the Leonids is that the main orbital path the meteroids are on before they strike the earth is such that it points back in the general direction of the constellation Leo at the point where the earth crosses the comet's orbit each year (meteor showers come from debris broken off a comet).

If you make a black-on-white copy of a starchart, and draw a line on it for each meteor you see when it happens, with an arrowhead in the direction of travel, at the end of the night you will see the most of the paths generally radiating away from Leo, like spokes radiating from the hub of a bicycle wheel. This is like what you'd see if you stood in the middle of a multilane highway as cars sped past you, facing where they come from - you'd see the cars angling to the right and left, but "radiating" from one spot in the distance.

If a meteor's path is very short, it is headed in your general direction. If it just a bright spot, then it is headed straight for you, so you know when to duck. If it is very long, it is headed away from you.

I don't know if it is still practiced, but there used to be organized efforts among amateur astronomers to map meteor paths during showers so their orbits could be calculated. Now I guess it would be more practical and accurate to do it with radar. To do make such a calculation, the observers also need to write down the time they saw each meteor.

Even so, the meteors won't all be radiating from a single point. There will be a lot of randomness. Part of this will be because the meteoroids are spread out in space, to either side of the comets orbit, each on its own slightly different orbit.

Also, as it approaches the earth, the earth's gravity will disturb the orbit of the meteoroid. If the meteoroid is heading straight to the center of the earth just before it hits, then it will just go faster. If it's heading a ways to one side of the earth, then its path will be deflected in towards the earth, and when it hits it will be at a highly deflected path. If it's even farther to the side, it won't hit the earth but it's orbit will be disturbed, and many orbits of a planet through a comet's path will introduce a lot of scatter in future showers.

Now let me shill for amateur astronomy. I'm grinding my own telescope mirror. You can join the Amateur Telescope Maker's mailing list and they'll tell you how - read the FAQ. Dan Cassaro can sell you a mirror grinding kit. You can get books with instructions (you need a whole book, it's pretty involved) from Willman-Bell. You can find lots of tips on the Telescope Making WebRing.

Or you can buy telescopes from Meade and Celestron or shop at the shop at the astronomy mall. Finally, there's a new ATM portal at www.telescopemaking.com.

I made several telescopes when I was a teenager, and have recently taken up grinding glass again after a long hiatus. I was also pleased to find the Central Maine Astronomical Society is in my area and joined last night while visiting their new observatory.

Telescope mirrors can be made by hand with suprisingly simple equipment. An eight-inch diameter telescope will run you about $250, maybe less if you're creative, for the mirror kit, eyepiece, aluminizing, and mounting.

There may be a telescope making or astronomy club in your area. A good way to find out is to subscribe to the ATM mailing list. Another way is to follow some of these links:

• Chabot Telescope Maker's Workshop (Oakland, California)
• Sidewalk Astronomers (Los Angeles and San Francisco)
• Amateur Telescope Makers of Boston
• Stellafane - Springfield Vermont, where the hobby was started in the USA

If you don't want to build a telescope, you can buy one. The telescopes made by Meade and Celestron are well known. You can find ads for dealers in the pages of Sky and Telescope Magazine, which you'll find in many bookstores.

A large number of astronomy products may be found through the Astronomy Mall.

Although the price differential for small telescopes like 6 or 8 inches is not that great between making it oneself and purchasing, the cost of purchasing really large instruments is really prohibitive, while large ones are actually affordable to make, comparable to purchasing a computer. If you start off making an 8 inch mirror, your next mirror can be much larger, say 16 inches, and amateurs commonly make mirrors from 20 to 30 inches, and I think there is a 72 inch mirror nearly complete made by some amateurs. My goal is to have a 40 inch observatory in my backyard.

Although I've listed U.S. organizations and companies, telescope making is practiced world-wide. A while back someone from Iraq subscribed to the ATM list and asked for help obtaining a kit. There are lots of subscribers from Europe and a number from Asia and Africa. Follow the links, and maybe you'll find a club in your home town, or at least within a reasonable distance!

I cannot describe the awe that comes from beholding the wonders of the heavens through a telescope made with one's own hands.

• Amateur Telescope Making by Albert Ingalls
• How to Make a Telescope by Jean Texerau

The stubby Celestron and Meade telescopes that are popular with amateur astronomers who prefer to purchase their instruments are of a type called a "schmidt-cassegrain". This has a nearly flat corrector plate in the front, that actually has a shallow fourth-order curve ground into it to correct spherical aberration, a deep prolate spheroidal primary mirror, and a convex secondary mirror mounted on the back of the center of the corrector plate.

It's the convex secondary that makes the telescope a cassegrain. The 200 inch on Palomar is a cassegrain. I don't have a schmidt-cassegrain to show you but here's how an ordinary cassegrain is laid out.

The use of the schmidt corrector plate allows one to make the telescope very short, with a small ratio of focal length of the primary to its diameter, without making images away from the center of the field blurry.

This is an advanced kind of design for an amateur to make oneself, although many amateurs have. Here's how one guy made a schmidt corrector plate.

The typical amateur starter scope is the "newtonian reflector". This has a concave parabolic mirror at the back end of the tube, and a few inches inside its focus is an optically flat mirror at 45 degrees. The optical path shown in the diagram is for the light from a single star, an image is formed from light sources spread across a small angle, and a small image is formed at the focal plane where it's examined by the eyepiece (a high-power magnifier) or photographed with film, a CCD or I guess even a webcam.

If you make a parabolic mirror with too short a ratio of focal length to diameter (the f-number, like the f ratio on a camera lens), then the images away from the center are blurred. This is called "coma". A parabola only focuses light perfectly if it's parallel to its axis and tilting the beam introduces coma. A ratio of 1 to 4 is about the shortest you can make it - f/4. My 6 inch is f/8, my 10 inch is f/3.5, and my 8 inch is f/6.

Having a longer focal length gives you greater magnification. Having a shorter one gives you a wider field of view, within the limits of the coma. Having a shorter focal ratio also makes it easier to fit in a car, an important consideration for making the scope enjoyable. Those Celestrons are nice because they'll easy fit in the trunk of a car or even in airline luggage (with a hard case) but it comes at the expense of a fancier design.

For the first homebuilt scope one usually grinds the primary and buys the flat diagonal mirror from a vendor. More advanced amateurs make their flats too but again optically flat surfaces are hard to make.

Making a primary that doesn't have too short a focal ratio is not too bad because the grinding process naturally makes a sphere. You grind a sphere of the right radius of curvature, fine grind through successively finer grits, then polish. You then use an optical test to get the mirror perfectly spherical, then deepen the center to move from a sphere to a parabola of revolution, testing carefully as you go.

The way I ground my mirrors was with pyrex mirror blanks on plate glass tools. Initially each is flat. They are both pretty thick, my 8 inch is about 1.25 inches thick, to stiffen them so they don't lose their figure. You have to have a figure that is perfect to about 1/8 of a wavelength of visible light in variation across the whole face of the glass, so any bending is disastrous. The 1/8 wave limit is the same for mirrors of all sizes so it's much harder to figure larger ones - best to start small. I would recommend an 8 inch for a first mirror. I have heard of people doing much larger first telescopes though.

What you do is sprinkle some granulated silicon carbide and water on the tool, place the mirror blank face down on it and push it back and forth until the silicon carbide ("carborundum") breaks down. (This is the same abrasive as you find on black wet-or-dry sandpaper, only in free-flowing powdered form). Then you add more abrasive and water and repeat. When too much mud builds up you wash it off and add more abrasive again.

To grind a concave curve into the mirror blank you place it on top, face down, grind with long strokes and have it hanging mostly off the side. Also you put pressure on it, either pushing hard or putting weights on it. This concentrates the grinding action in the middle and a shallow sphere develops.

Every few strokes you rotate the mirror a little, and once a minute or so you rotate the tool a little, with the idea that every part of the mirror gets ground over every part of the tool in every direction.

These days it has become popular to "hog out" a mirror with a metal ring tool, like a pipe cap as I'm about to try, then after rough grinding you make a fine-grinding tool out of small bathroom tiles mounted in dental stone or portland cement. This is in part because it's getting harder to get telescope making kits, unfortunately because it's so easy to buy a Celestron people don't make their own as much anymore. So people conserve the glass just for the mirrors and make the tile tools instead.

Be aware, before you say "well it's easier to buy a Celestron", that the price of a telescope goes up astronomically with increasing diameter - my 8 inch kit was $78 including shipping, I'll probably spend a few hundred to make a nice clock-driven mount, but the 10 meter telescope on Mauna Kea cost $90 million! If you know how to make your own, it is within your reach to grind your own 20 inch, which will have astounding views, but few of us could hope to afford to purchase a twenty inch commercial scope.

I know people who have ground 30 inch scopes and I know of some amateurs who are now figuring a 67 inch mirror!

Anyway it takes several hours of work to rough grind your mirror, more if you're doing a short f/number, less if you have a higher one, also less for smaller mirrors and more for larger ones. My 6" f/8 was about as deep as the thickness of an american dime, I don't know a little more than a millimeter.

Then you fine grind, grinding for a few hours with successively finer grades of abrasive. Usually you rough grind with 80 mesh silicon carbide - it is graded by sieving it through a mesh with 80 wires in it (same as the sandpaper sizes). Then you grind with #120, #220, #320, #400 and then several very fine grades of aluminum oxide whose sizes are given in microns.

The idea is that each finer grade erases the pits left by the previous grade. Between each grade you must scrupulously clean yourself, the mirror and tool and your work environment lest a coarse particle get into a finer stage and cause a scratch.

With each grade the mirror and tool surfaces will become more and more accurately spheres, within the limits of the sizes of the grits. This is because a sphere is the only shape that allows two surfaces to be placed anywhere against each other in any position or rotation (a flat surface is the limit of this as the radius goes to infinity). If there are any high spots, they will get more pressure and grind off quickly; any low spots will miss out on grinding and the surrounding surface will come down to match.

Then you polish. You make a "pitch lap", using either another dental stone base or the glass grinding tool, covered with refined, thickened pine pitch. You cut channels in the pitch with a knife or mold them in with a silicone mold. Then you cover the pitch lap with a suspension of cerium oxide in water, or else ferrous oxide (same as rust but finely powdered - "jeweler's rouge"). Then again you stroke the mirror on the pitch lap.

During fine grinding and polishing you use shorter strokes, and alternate which is on top, the mirror or the tool, to keep the depth constant. You also stroke a little side-to-side, in a W pattern. This evens everything out.

To test the mirror you use the Foucault test or the Ronchi Test. The foucault test appatatus I link to is much fancier than you need, although nicer to use - you can do it all with your naked eye and the tester, you don't need a camera.

In each test you use a light emanating from a pinhole or narror slit just to the side of the center of curvature of the mirror. The image of the pinhole or slit will form an equal distance to the other side, where you can place a knife edge (Foucault) or screen (Ronchi) across it and hold your eye there and look at the mirror.

It's kind of hard to explain but each of these has the effect of dramatically magnifying deviations from spherical surfaces in the mirror. A dramatic demonstration is to have someone hold their hand in the beam - you can see the distortion in the beam caused by the warm air rising from their hand.

You can easily make out a bump or hollow that's a fraction of a wavelength high on the glass.

Then you make your mirror perfectly spherical by preferentially polishing off the high spots. If you did the fine grinding and polishing well you won't have to work hard to do this.

Unfortunately what we want is a parabola, not a sphere. This must have a precisely controlled error in each test. This is a little more than I want to get into, but basically your preferentially polish out the center of the mirror so it's deeper in the middle than appropriate for a sphere by a little bit. Get it just right and you have a parabola, and your mirror will focus perfectly.

Then you package it securely and send it off to one of the people who does vacuum aluminization. They clean the mirror extremely well, place it in a high vacuum, and evaporate aluminum off of tungsten wires. The aluminum vapor sticks to your glass and you have a telescope mirror.

Mike

• Amateur Telescope Making by Albert Ingalls
• How to Make a Telescope by Jean Texerau

The stubby Celestron and Meade telescopes that are popular with amateur astronomers who prefer to purchase their instruments are of a type called a "schmidt-cassegrain". This has a nearly flat corrector plate in the front, that actually has a shallow fourth-order curve ground into it to correct spherical aberration, a deep prolate spheroidal primary mirror, and a convex secondary mirror mounted on the back of the center of the corrector plate.

It's the convex secondary that makes the telescope a cassegrain. The 200 inch on Palomar is a cassegrain. I don't have a schmidt-cassegrain to show you but here's how an ordinary cassegrain is laid out.

The use of the schmidt corrector plate allows one to make the telescope very short, with a small ratio of focal length of the primary to its diameter, without making images away from the center of the field blurry.

This is an advanced kind of design for an amateur to make oneself, although many amateurs have. Here's how one guy made a schmidt corrector plate.

The typical amateur starter scope is the "newtonian reflector". This has a concave parabolic mirror at the back end of the tube, and a few inches inside its focus is an optically flat mirror at 45 degrees. The optical path shown in the diagram is for the light from a single star, an image is formed from light sources spread across a small angle, and a small image is formed at the focal plane where it's examined by the eyepiece (a high-power magnifier) or photographed with film, a CCD or I guess even a webcam.

If you make a parabolic mirror with too short a ratio of focal length to diameter (the f-number, like the f ratio on a camera lens), then the images away from the center are blurred. This is called "coma". A parabola only focuses light perfectly if it's parallel to its axis and tilting the beam introduces coma. A ratio of 1 to 4 is about the shortest you can make it - f/4. My 6 inch is f/8, my 10 inch is f/3.5, and my 8 inch is f/6.

Having a longer focal length gives you greater magnification. Having a shorter one gives you a wider field of view, within the limits of the coma. Having a shorter focal ratio also makes it easier to fit in a car, an important consideration for making the scope enjoyable. Those Celestrons are nice because they'll easy fit in the trunk of a car or even in airline luggage (with a hard case) but it comes at the expense of a fancier design.

For the first homebuilt scope one usually grinds the primary and buys the flat diagonal mirror from a vendor. More advanced amateurs make their flats too but again optically flat surfaces are hard to make.

Making a primary that doesn't have too short a focal ratio is not too bad because the grinding process naturally makes a sphere. You grind a sphere of the right radius of curvature, fine grind through successively finer grits, then polish. You then use an optical test to get the mirror perfectly spherical, then deepen the center to move from a sphere to a parabola of revolution, testing carefully as you go.

The way I ground my mirrors was with pyrex mirror blanks on plate glass tools. Initially each is flat. They are both pretty thick, my 8 inch is about 1.25 inches thick, to stiffen them so they don't lose their figure. You have to have a figure that is perfect to about 1/8 of a wavelength of visible light in variation across the whole face of the glass, so any bending is disastrous. The 1/8 wave limit is the same for mirrors of all sizes so it's much harder to figure larger ones - best to start small. I would recommend an 8 inch for a first mirror. I have heard of people doing much larger first telescopes though.

What you do is sprinkle some granulated silicon carbide and water on the tool, place the mirror blank face down on it and push it back and forth until the silicon carbide ("carborundum") breaks down. (This is the same abrasive as you find on black wet-or-dry sandpaper, only in free-flowing powdered form). Then you add more abrasive and water and repeat. When too much mud builds up you wash it off and add more abrasive again.

To grind a concave curve into the mirror blank you place it on top, face down, grind with long strokes and have it hanging mostly off the side. Also you put pressure on it, either pushing hard or putting weights on it. This concentrates the grinding action in the middle and a shallow sphere develops.

Every few strokes you rotate the mirror a little, and once a minute or so you rotate the tool a little, with the idea that every part of the mirror gets ground over every part of the tool in every direction.

These days it has become popular to "hog out" a mirror with a metal ring tool, like a pipe cap as I'm about to try, then after rough grinding you make a fine-grinding tool out of small bathroom tiles mounted in dental stone or portland cement. This is in part because it's getting harder to get telescope making kits, unfortunately because it's so easy to buy a Celestron people don't make their own as much anymore. So people conserve the glass just for the mirrors and make the tile tools instead.

Be aware, before you say "well it's easier to buy a Celestron", that the price of a telescope goes up astronomically with increasing diameter - my 8 inch kit was $78 including shipping, I'll probably spend a few hundred to make a nice clock-driven mount, but the 10 meter telescope on Mauna Kea cost $90 million! If you know how to make your own, it is within your reach to grind your own 20 inch, which will have astounding views, but few of us could hope to afford to purchase a twenty inch commercial scope.

I know people who have ground 30 inch scopes and I know of some amateurs who are now figuring a 67 inch mirror!

Anyway it takes several hours of work to rough grind your mirror, more if you're doing a short f/number, less if you have a higher one, also less for smaller mirrors and more for larger ones. My 6" f/8 was about as deep as the thickness of an american dime, I don't know a little more than a millimeter.

Then you fine grind, grinding for a few hours with successively finer grades of abrasive. Usually you rough grind with 80 mesh silicon carbide - it is graded by sieving it through a mesh with 80 wires in it (same as the sandpaper sizes). Then you grind with #120, #220, #320, #400 and then several very fine grades of aluminum oxide whose sizes are given in microns.

The idea is that each finer grade erases the pits left by the previous grade. Between each grade you must scrupulously clean yourself, the mirror and tool and your work environment lest a coarse particle get into a finer stage and cause a scratch.

With each grade the mirror and tool surfaces will become more and more accurately spheres, within the limits of the sizes of the grits. This is because a sphere is the only shape that allows two surfaces to be placed anywhere against each other in any position or rotation (a flat surface is the limit of this as the radius goes to infinity). If there are any high spots, they will get more pressure and grind off quickly; any low spots will miss out on grinding and the surrounding surface will come down to match.

Then you polish. You make a "pitch lap", using either another dental stone base or the glass grinding tool, covered with refined, thickened pine pitch. You cut channels in the pitch with a knife or mold them in with a silicone mold. Then you cover the pitch lap with a suspension of cerium oxide in water, or else ferrous oxide (same as rust but finely powdered - "jeweler's rouge"). Then again you stroke the mirror on the pitch lap.

During fine grinding and polishing you use shorter strokes, and alternate which is on top, the mirror or the tool, to keep the depth constant. You also stroke a little side-to-side, in a W pattern. This evens everything out.

To test the mirror you use the Foucault test or the Ronchi Test. The foucault test appatatus I link to is much fancier than you need, although nicer to use - you can do it all with your naked eye and the tester, you don't need a camera.

In each test you use a light emanating from a pinhole or narror slit just to the side of the center of curvature of the mirror. The image of the pinhole or slit will form an equal distance to the other side, where you can place a knife edge (Foucault) or screen (Ronchi) across it and hold your eye there and look at the mirror.

It's kind of hard to explain but each of these has the effect of dramatically magnifying deviations from spherical surfaces in the mirror. A dramatic demonstration is to have someone hold their hand in the beam - you can see the distortion in the beam caused by the warm air rising from their hand.

You can easily make out a bump or hollow that's a fraction of a wavelength high on the glass.

Then you make your mirror perfectly spherical by preferentially polishing off the high spots. If you did the fine grinding and polishing well you won't have to work hard to do this.

Unfortunately what we want is a parabola, not a sphere. This must have a precisely controlled error in each test. This is a little more than I want to get into, but basically your preferentially polish out the center of the mirror so it's deeper in the middle than appropriate for a sphere by a little bit. Get it just right and you have a parabola, and your mirror will focus perfectly.

Then you package it securely and send it off to one of the people who does vacuum aluminization. They clean the mirror extremely well, place it in a high vacuum, and evaporate aluminum off of tungsten wires. The aluminum vapor sticks to your glass and you have a telescope mirror.

Mike

The 6 inch had a decent figure but I didn't know I could send it away to be vacuum aluminized, so I chemically deposited silver on it using chemicals I bought at the University of Idaho chemistry stockroom. Take my advice, it's much better to get a mirror aluminized.

I hurried a bit too much on fine grinding the 10 inch and wasn't happy with it, so I tried again with my 8 inch and was much more patient, and got excellent results from it (1/10 wave according to Chabot Amateur Telescope Maker's Workshop's Paul Zurakowski).

Grinding telescopes and being a sciency kind of guy led me to study astronomy at CalTech where I assisted CalTech astronomer Jeremy Mould in observing the the Palomar 60 inch and 200 inch telescopes - the experience of a lifetime for an amateur astronomer.

It's been about 18 years since I last worked any glass but I just bought an 8 inch plate glass kit from Dan Cassaro. You can buy Pyrex kits and optical glass (suitable for lenses) from Newport Glass.

I'm starting to write about the telescope I'm about to work on here.

If you are in the San Francisco Bay Area check out the Eastbay Astronomical Society's Chabot Amateur Telescope Maker's Workshop (there's an observatory there too, it's in Oakland), Fremont Peak Observatory, which has a 30 inch reflector that's open to the public, with regular gatherings of amateurs who bring their telescopes up there, and the San Francisco Sidewalk Astronomers - the Sidewalk Astronomers set up telescopes on city sidewalks and introduce people to astronomy by inviting them to look through their scopes.

You can get books on astronomy, and importantly, the specifics of how to actually grind and polish a telescope from Willman-Bell and Newport Glass.

Check out this guy who made a ribbed mirror blank by cutting out a pattern from one disk of glass with a water jet and fusing it to a solid sheet in a furnace.

Visit Google's index of Amateur Telescope Making, particularly http://www.atmpage.com.

If you want to get into amateur telescope making, take advantage of an immensely valuable resource that wasn't available to me when I was a kid - subscribe to the ATM List - here's the FAQ.

Mike