A note on Ptolemy and Copernicus

Copernicus was the 16th-century astronomer who convinced everyone that the planets orbit the sun, not the earth. Ptolemy is the ancient astronomer whose earth-centered system of orbits was used until that time. Fifty years ago I spent much of the year doing a science fair project on the relation between the two, and recently I've been reading up on the subject again. Many excellent studies have come out since the last time I looked, and general reference books are much more accurate.

Back at mid-century, many books gave the impression that Ptolemy's and Copernicus' systems were more alike than they were, and that both of them piled up large numbers of epicycles to deal with trivial inaccuracies. Not so.

It is true that both of them described orbits in terms of a main circle (the deferent) which carries the center of a smaller circle (an epicycle) which carries the planet itself, and there could be further layers of epicycles. This is because they believed non-circular orbits were only physically sustainable as combinations of perfect circles. But there the similarity ends.

The problem to be solved, for both of them, is this:

(0) As seen from the earth, relative to the distant stars, the sun, moon, and planets go around the earth eastward, each with its own orbital period, staying close to a line in the sky called the ecliptic.

(1) The orbital motion is not uniform; it is faster on one side of each orbit than the other side. We see this with all 7 objects (sun, moon, and planets).

(2) What's worse, the motion of the planets is not always eastward. The inner planets (Mercury and Venus) follow the sun and swing back and forth east and west of it, moving westward a substantial amount of time. The outer planets briefly reverse course and move westward for a short time when opposite the sun.

On (0) everyone agrees. Ptolemy deals with (1) by putting the orbits off-center and deals with (2) by adding epicycles. For him, Mercury and Venus each follow a main orbit synchronized with the sun-earth orbit and have an epicycle to account for the east-west swings. The outer planets have main orbits that are independent of each other, but each has an epicycle synchronized with the sun-earth orbit.

Copernicus did things quite differently. He dealt with (1) using a small epicycle so that nothing needed to be off center. More importantly, he made problem (2) disappear by making the earth move. Then all those other orbits don't need to contain anything synchronized with the sun-earth orbit. We are simply looking at the effect of the earth's motion.

It's true that Copernicus clung to the ancient and medieval belief that only circular motions could be sustained eternally. But at least he made his system actually work that way, getting rid of Ptolemy's clumsy off-center mechanism (where not only the sun but also the center of uniform motion were not at the center of the circle).

And neither one of them "piled up epicycles" to make minor adjustments. Each epicycle expressed an important empirical generalization.

I am still researching this subject, and if there are inaccuracies in this entry, I plan to revise it. Seemingly reliable sources contradict each other, I think partly because the number of people who have ever actually understood Ptolemy and Copernicus is small.

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Colorful pencils

This picture has been hanging in my home office area for a very long time. I took it on film (in the late 1990s, I think), and then digitized it and made a color inkjet print, one of the first good inkjet prints I made. The pencils are, of course, Melody's.

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What the law calls "irreparable damage"

I've written some time ago about how, if you disrupt someone's educational or career progress, there may be no way to make things right again. It's not like just paying for something you failed to pay for. Even if you give the person time and funding to do the thing they missed, by then time has passed, and the person is older, has new opportunities, and needs to be doing something else.

If you've destroyed something like an artist's masterpiece, a writer's manuscript, or a scholar's research notes, it's even worse. Even with time and funding, a do-over of a creative work is not the same as the original. It's not eligible for the same awards and recognition. The original may have been recognized for how well it was done with limited time and resources, or at a specific stage of education; giving extra time changes the whole game. (Now you have to show what you could do in two years instead of one, and you can never catch up.) The work may have involved gathering material or having experiences that aren't going to come again, or the results may be obsolete, or no longer competitive, by the time the do-over is finished. And the creative person is burdened with having to do the whole thing again. The do-over isn't what he was planning, wanting, or feeling inspired to do. It probably prevents him from doing something new that was coming next.

One day I may tell you what brought this to mind. A piece of my own early scholarly work was lost, not by accident, but through a blunder that I wasn't involved in making and am still trying to figure out.

Now that we can easily make digital backups and photograph works of art in progress, there's much less risk of losing creative work than there used to be. Decades ago, even Xeroxing was not widely available, and it was much easier to lose the only copy of valuable work.

[Added:] Some years ago I read about a UGA art student whose master's degree project, a sculpture, was destroyed by vandals after a football game. Fortunately, it had been photographed, and he got the degree. But I wonder what else was done or should have been done. He was, after all, entitled not only to get credit for the artwork, but also to possess it. The University also probably wanted to exhibit it.

In recent years the University has been more insistent that the Athletic Association must cover the damage done by football crowds. But even if he could be paid for his labor, would this art student have wanted to rebuild it himself? He had other things to do. I don't know whether he planned to keep the sculpture or sell it. If the latter, well, he's just sold it to the Athletic Association's insurance company, hopefully for a good price.

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How to keep perfume from drying up in the bottle

Today on Melody and Michael's Household Hints...

In the continuing saga of the rare, no-longer-available perfume that I tracked down for Melody recently...

Here is how to keep it from evaporating and drying up in the bottle.

This particular one had an inner stopper, which we did not realize needed to be kept. The screw-on cap does not make a tight seal, and we could tell that the level was going down a little from day to day. (Not all the way down from a full bottle to what you see in the picture; she has used a fair bit of it.) We also could smell the perfume outside the bottle even after allowing a day or two for any that had gotten on the outside to evaporate. Incidentally, you'll see that the black ink on the label was smudged by tiny amounts of the perfume itself; they lose points for that!

The cure is to use Teflon plumber's tape (pipe-sealing tape). This is not sticky tape; it is a soft, clean material, and layers of it join when pressed together.

In this case we folded it in half lengthwise and then wrapped several turns around the threads on the bottle. Just as with plumbing, always use a good bit more than you think there's room for. Applied once, it can survive having the cap on and off several times, but eventually you'll have to replace it. If any shows from outside the cap, and you don't want it to, you can trim it off.

Now what do you add to perfume that has started to dry up, to restore a few drops of lost liquid? We haven't tried this, but here's what I'm told:

• Not water, which might make it cloudy.
• Not ethyl rubbing alcohol, which contains too much water.
• Not denatured ethyl alcohol from the hardware store, because it is not safe to put on your skin.
• Not pure isopropyl alcohol, which is safe but might smell wrong (opinions differ).

You're supposed to use pure ethyl alcohol (Everclear from the liquor store) or "perfumers' alcohol," which is ethyl alcohol rendered undrinkable (hence exempt from liquor laws) by adding a bitter flavoring that is odorless and non-toxic. That is a specialty item from perfume makers but an interesting thing has just happened: thanks to the COVID epidemic, the same stuff is on the market, cheap in large quantities, as hand-sanitizer-grade ethanol, nearly pure ethyl alcohol that is safe for skin. Given the very low price, that stuff probably also has some uses as a cleaner and, of course, hand sanitizer.

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Not to overlook...

Far be it from me to leave unmentioned the national football championship that my alma mater won last night...

Embroidery by our college friend Keena Lowe, whom we haven't heard from in decades, but would like to! It's Latin for "Win, O dogs." We decided not to say "Go" because in that language, it might be taken as meaning "Go away."

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Farmington scenery

For our country drive today, Melody and I went to Farmington, south of Athens, and then headed back toward town on the Old Farmington Road. Let the scenery speak for itself.

Christmas music for Epiphany

(From Facebook.)

Songs of the day (for Jan. 6, which is Epiphany). First, a philosophical Christmas carol by the late Dan Fogelberg. The first line sounds like a nonbeliever's solstice celebration — but keep listening to how it progresses through a series of points. And if you're not sure he's going to give the complete Christian message, that's what the second song is for. Look at how precisely the lyrics express things.

Dan Fogelberg, "At Christmas Time"

Dan Fogelberg, "The First Christmas Morning"

I was struck by the very clear Christian message in these two songs. I never knew Fogelberg identified himself as a Christian, but he did things in those songs (especially the second one) that I don't think a non-Christian could or would have done.

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An astrophotography test session

The strange thing about astrophotography in 2022 is that new versions of software, firmware, etc., come more frequently than clear nights! So I am often preoccupied with verifying that new setups work.

So it was on the evening of the 3rd. I set up my GEM45 mount, Askar 200-mm f/4 lens, Nikon D5500(a), etc., in the driveway. The guidescope was an SVBony mini-guidescope (30×120 mm) that I had used only once before; the guide camera, my ASI120MM-S, but connected through USB-2 cables running through the mount rather than the usual USB-3; the guiding software, a new version of PHD2; and the computer, my Thinkpad T490s, since I'm finally retiring the almost 9-year-old Asus UX32A.

Inside the Askar lens I mounted my Orion SkyGlow broadband light pollution filter (same as what I used on the California Nebula last time), and my main question was whether it was good for photographing reflection nebulae, which are white and do not have a line spectrum.

Success! This is a stack of ten 2-minute exposures, and the reflection nebulosity around the Pleiades is quite visible; you can even see that the thickest part is less bluish.

Since we don't have sodium streetlights any more, I don't know how much good this filter actually does in such a situation, but it does no harm, and it should have some effect suppressing the 450-nm deep violet peak of the LED streetlights.

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And a monkey head

The same setup works well with red nebulae, of course. The bright round nebula here is NGC 2174, the Monkey Head Nebula, in northern Orion. (Up at the top you see IC 443 in Gemini.) The monkey's head is upside down, and he's facing to your right. Stack of twelve 2-minute exposures.

A dramatic cloud over East Athens

Taking advantage of the warm weather (76 F) and the fast-changing lighting due to fast-moving clouds, Melody and I decided to go on a photography expedition and ended up on the top level of the Jackson Street parking deck, more or less directly above the site of the old Graphic Design Annex in which she did much of her studio work as a student. This cloud caught our eye. Nikon D5300, 18-55mm zoom lens.

In the second picture, you see, in the foreground, a building on Thomas Street that belongs to the School of Art; that's where Melody studied sculpture. Beyond it is a big, luxurious apartment building recently built on the site of the old Armstrong and Dobbs lumberyard.

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