Symbolic Forest

Back in the mists of time on Boxing Day, I posted a clue as to what one of my Christmas presents was. A model tram from UGears, which I have been slowly assembling since.

It’s been a fun project, but I’m not completely sure it lives up to the promise on their website that “no glue, special expertise, tools or equipment are required”. With a fair wind and if everything goes well, then maybe. When I opened the box, the kit consisted of:

• Various laser-cut plywood sheets.
• Two rubber bands.
• A small square of fine sandpaper.
• A number of cocktail sticks, individually wrapped.
• A glossy and comprehensive instruction book.

The instruction book is very good and very clear, with each step being shown as a 3D-rendered diagram. However, it starts off listing the extra pieces of equipment you need which aren’t supplied:

• Candle wax, to lubricate the moving parts.
• A knife, to cut some of the cocktail sticks to length.

With those to hand, you start off by assembling various gear shafts. Each of these assemblies consists of the gears themselves, four wooden wedges that are inserted through the gear centres, and a cocktail stick that has to be squeezed through a small hole left right in the middle where the four wedges meet.

These are the first ones in the instructions; gears, but also the main “wheels” that the tram sits on. The instructions say the cocktail stick should be inserted symmetrically, with the same length protruding from each end, so it’s very helpful to have a small steel rule to assist with doing it by eye. If the “axle” isn’t symmetrical, a measuring tool is included in the kit to indicate how much the stick should project from one end.

Inserting the cocktail sticks was the first big hurdle. Making the kit in the advised way—assemble the wedges into the gears then slide the cocktail stick down the middle—is very hard to do without accidentally blunting the sharp points at the ends. Unless you’re dealing with one of the gear shafts which needs one or both ends trimming short, this is a problem, because it’s very easy to blunt the sticks to the extent they won’t work any more. I found for most it was easier to assemble the shafts in a slightly different order: take one gear, insert the wedge pieces and the cocktail stick into that gear alone, then squeeze the wedges together at the other end and slide the other gear over the wedges’ clip-shaped ends.

The tolerances of the cocktail sticks don’t help, either. Some parts require sticks to be inserted into holes in the plywood parts, and these are all supposedly a push fit. What quickly became clear is that the cocktail sticks are made to rather looser tolerances than the laser-cut parts: some sticks will be a reasonable push-fit in the holes, and some will have no chance of going in. With these parts, I ended up picking which stick I was going to use, then opening out the hole with a broach to fit. If I went a bit too far and made it a sliding fit, I used a little dab of Resin W to glue the stick in place.

You can see this under way with these parts for the pawl which holds the “rubber band shaft” tight after it’s been wound. You can also see that here I’m reusing a cocktail stick whose end I have already wrecked, in a position where it will be trimmed off short. As the lowest of the three holes in each pawl piece is rather close to the edge, I found one of the narrower sticks in the kit for that position, so it wouldn’t need opening out at all. You can clearly see the different widths of the supplied cocktail sticks, and on the right-hand pawl piece you can see how much I’ve had to open out the uppermost hole, compared to the unmodified bottom hole, in order for the fat stick at the top to be a push fit into it. Using a broach for this, it’s easy to roughly remember how much of the broach’s cutting length is needed to get the hole to around the right width before you start testing for fit.

Once the parts were pushed onto the sticks, the ends of two could be trimmed off, leaving a single shaft for it to pivot on.

Building all the various gears and related parts took quite a few hours, so it was rather pleasing how easily the main framework of the tram fitted together, and how straightforward it was to slip the ends of each shaft into their appropriate hole in the frames. It was rather pleasing, too, to find how well the initial gear chain rotated. It links the wheels together, and also includes a shaft which seems to be in there purely to make a clicking noise.

You might notice that the pawl from the previous photos hasn’t been fitted to the main assembly yet. That comes later, and was a little bit more fiddly. We’ll come on to that another time.

To be continued.

Keyword noise: trams, railway, tramway, model, model trains, UGears, crafting.

“Is it cloudy or clear?” said The Child Who Likes Animals yesterday evening after finishing his tea.

“I don’t know,” I said, knowing the weather forecast was showing a solid grey sky for the whole of the evening. “Let’s have a look,” knowing there was little risk of us being able to look at the stars.

I opened the back door, and was rather surprised to see clear skies and good visibility. “LET’S GET THE TELESCOPE OUT!” screamed The Child Who Likes Animals Space. I had been planning to head straight to the sofa and the book I’m in the middle of reading,^* but agreed that, if we could come up with a sensible plan for what we were actually going to look at, I would set it all up for him.

We fired up Stellarium and I tried to find things that would be interesting to see and straightforward to find. Outside, I had already seen the cross of Cygnus was fairly high in the sky, with Cassiopeia above it, so I make a risky suggestion. “Why don’t we try to see the Elephant’s Trunk Nebula?” I said, knowing that with our inner-city skies nebulas and other deep-sky objects do not put on a very good show. It does, though, have a very child-friendly name.

I set the telescope up on the table outside, and tried to get my eye in. It was immediately obvious that viewing conditions were on average far, far better than they had been on New Years Eve. The Elephant’s Trunk Nebula has the benefit that it’s close to an easy-to-find star, Alderamin (α Cephei). I quickly navigated ten degrees south to the location of the nebula, was confident I was there from the pattern of the stars. And was there anything? Well … maybe. Charitably, I could convince myself that the sky did indeed look slightly brighter than elsewhere in the sky; that I could see hints of structure that were not just inside my own eyeballs and brain. The Children, though, would have none of it.

Luckily, I’d noticed there was something interesting just by the nebula, and confirmed with the computer that I was looking at Herschel’s Garnet (μ Cephei). It’s a red supergiant star, a thousand times broader than our sun, and a distinctive pale peach colour to the eye—the astronomer William Herschel described it as “deep garnet”, hence the name. As its colour is so clear to see, The Children were reasonably impressed.

As it was so clear, we also pointed the telescope at the Pleiades, the view of which wowed The Child Who Likes Fairies (“There’s literally trillions of stars!”) then, the cluster NGC 7686 and the Andromeda Galaxy. The latter was, to my eyes, a slightly clearer fuzzy blob than it has been in the past, but still just a fuzzy blob. The Child Who Likes Animals said he could see it clearly; The Child Who Likes Fairies could not.

Thinking about what we should be able to see in the sky, I did a bit of maths. Say the pupil of one eye when it’s dilated is about 8mm wide—I’m just guessing this part really. We’re using a 150mm telescope: that’s 350 times as large as a pupil, so it gathers 350 times as much light. That’s a difference in astronomical magnitude of just under 6.4. Now, when I was aiming the telescope last night, once my eyes were adapted I could just about make out stars of magnitude 3.8 to 4.2; such as the stars λ Andromedae, κ Andromedae and ι Andromedae, which I used to find NGC 7686 and which I’ll have to write about again some other time.^** I suspect that that’s as good as things are ever going to get in our hazy and light-polluted urban sky. But taking the telescope’s light-gathering power into account, if I’ve got the theory correct, I should be able to see things of magnitude 10 to 10.5 or so through it. Next time we have good seeing, I should test this out: look up at a few things and find out what the official magnitude of the stars I can just barely see is.

When I’ve done that, of course, I should probably think about getting some way to record what I can see, rather than just trying to describe it to you. The Child Who Likes Animals’s telescope is a Dobsonian with an altitude-azimuth mount, which means long-exposure photos are probably out, but I’d like to look at our options and see exactly what we could try to do instead.

* The Northmen’s Fury: A History of the Viking World by Philip Parker.

** Because in looking up their names for this post, I’ve discovered they form part of the former constellation named after Friedrich the Great of Prussia, Honores Friderici.

Keyword noise: astronomy, The Children, Elephant's Trunk Nebula, Herschel's Garnet Star, Alderamin, Pleiades, NGC 7686, Andromeda Galaxy, Messier objects, magnitude, Honores Friderici.

Another small astronomy note: the first of the year’s big meteor showers occurs over the next couple of days. I know it’s less than a month since the last big meteor shower of 2020, the Geminids, but tomorrow we have the peak of the Quadrantid shower. They’re a bit harder to see than the Geminids, partly because they’re usually fainter and partly because they’re concentrated into a narrower stream, so they’re seen over a much shorter time-range. Moreover, looking at the weather forecast, I doubt we’re going to have clear enough skies to have any chance of seeing them.

Interestingly, the Quadrantids are named after a constellation that doesn’t officially exist any more. Their name comes from Quadrans Muralis, “the wall-mounted quadrant”, a constellation named in the late 18th century by Jerome Lalande—he named it after an astronomical instrument he’d used to help him map the sky. Naming constellations after scientific machinery was quite fashionable in the 18th century; we still have Antlia, Horologium, Microscopium, Octans and Reticulum in the sky, to name just a few. Nevertheless, when the boundaries of the constellations were officially defined by the IAU back in the 1920s, Quadrans Muralis was left out of the list. Its part of the sky is now mostly split between Draco and Boötes, with a small piece in Hercules. You could argue the Quadrantids should really have been renamed the Boötids, but the old name has stuck.

Keyword noise: astronomy, meteors, meteor shower, Quadrantids.

Happy New Year!

Last night was the first clear night for a few weeks; and the only clear night at any point in the forthcoming weather forecast. Naturally, as soon as I mentioned the clear skies to The Children, they immediately jumped up and down and shouted “LET’S GET THE TELESCOPE OUT!”

The decking was already slippery with frost, and there was a lot of light and noise from the surrounding houses, but we started out by pointing the telescope to Enif (ε Pegasi), a red supergiant with a very distinctive orange colour. From there we navigated to the nearby globular cluster Messier 15, which I could see in the telescope as a somewhat hazy blob, but which The Children weren’t sure they could actually see.

After they were in bed, I went outside again and looked up at the sky, but it was already filling up with haze and smoke from the fireworks sporadically going off all around the neighbourhood. I tried to find Messier 36, an open cluster in Auriga apparently also called the Pinwheel Cluster, but could not actually make out any of the stars in it. I looked at the Pleiades to calibrate myself, and realised there seemed to be far fewer of its stars visible than normal. As Orion was rising higher in the sky I pointed the telescope at the Orion Nebula, just about visible as a couple of fuzzy points; and the nearby Coal Car Cluster (NGC 1981). The latter’s stars are around magnitude 6.4 to 7.4, which normally would be clearly visible in the telescope even in our inner-city skies, but with last night’s firework haze I could just about make them out.

Ah well, there will be clear nights later in the winter I’m sure. I got up again about 3am to get myself a drink, and the garden was covered in a thick fog of smoke still from all the fireworks of midnight. Fireworks and astronomy do not mix. Hopefully later in the year, too, we’ll be able to take the telescope to somewhere with properly dark skies one night.

Keyword noise: astronomy, New Years Eve, Hogmanay, fireworks, The Children, Messier objects, Enif, Pinwheel Cluster, Orion Nebula, Coal Car Cluster.

Sadly, I didn’t get to see the Great Conjunction of Jupiter and Saturn, at least not at the closest approach that would have been visible. We had heavy rain here this afternoon; and after sunset the sky was a uniform, undifferentiated cloudy mass with not even the moon visible.

Oh well: we had clear skies last night, at least, and I did see them both, maybe only about 10 minutes or so apart in the sky, just over the horizon after sunset. I tried to take a photo on my phone, but although Jupiter was clearly visible on it, Saturn was only really spottable if you already knew it was there. Maybe it’ll be clear skies tomorrow, when they are parting again.

The solstice has passed too, of course. Politically this country might seem be descending into some sort of nightmarish *fimbulvetr* right now, but at least the heavens don’t know that.

Keyword noise: astronomy, Jupiter, Saturn, conjunction, Great Conjunction, winter, solstice, winter solstice.

This is an astronomy post, but it’s also not really an astronomy post; it’s more a post about me and the way I think.

When I was small, I was terrified by the size of the universe. I can remember, about seven or eight or so, really struggling with the concept that the universe might be infinite and might not be, and I can still remember the mental picture I tried to come up with of a universe where the stars just, at some point, stopped; and beyond there was just blackness.

It probably doesn’t work like that, but still in my head somewhere is the concept that it might do. Moreover, I have trouble with another, broader concept, which is that—assuming you can travel between both hemispheres—we can “see” all of the observable universe.

“See” is in quotes there because, well, you can’t see everything for practical reasons. Most things are too faint, firstly. At any given time half the sky is too close to the Sun, too: you can’t see Mercury right now for example. But in theory, barring things being too faint, barring you having to wait for the Earth to move a bit or having to travel from one side of the Equator to the other, the whole universe is up above some point on the planet’s surface at any given time.

This probably seems tediously self-evident if you think of the planet as a ball spinning through space. For some reason, though, the whole concept still catches me by surprise occasionally. I still think that things must be able to, I don’t know, hide around a corner or something like that. I think I must have picked up the idea from a book I had as a child about Halley’s Comet, which included diagrams of where you would be able to see the comet in the sky in 1986, and talked about how comets appeared and disappeared in the sky. That’s the general tone when talking about comets and asteroids and so on: they appear in the sky and they disappear again. So it took me a long time to realise that all of the comets and all of the asteroids are up there, in front of us, all along; we just can’t see them right now. Halley’s comet doesn’t just pop out from behind a tree every seventy-five years: it’s up there in the sky the whole time, just not visible.

Halley’s comet is maybe a bad example for this. Because it’s so famous, and because of the light-gathering power of modern telescopes, we can now track it through its entire orbit. According to Stellarium it’s currently at coordinates 8h26m/+1°46’, but as it’s only a few years from perigee it’s an incredibly-faint magnitude 25.5 so will appear as a just a fuzzy handful of pixels on any photo. Nevertheless, if you go outside tonight and look up at the constellation Hydra close to its tripoint with Monoceros and Canis Minor, up there it is. As are all the others. Everything in the sky that you’re likely to see in your lifetime is already up there in the sky, just invisible and unrecognised. And despite the fact that I know this, that I know on a rough, superficial level how the mechanics of cosmology work, it still feels a little strange to me. It still feels in my mind as if there should be some patch of the sky that we can’t see, that is hiding around some sort of galactic corner.

Whenever I see diagrams of the whole sky that say “this is the whole universe”—cosmic background radiation maps, for example—I’m slightly disturbed that in some sense the whole universe fits into one small image. “Surely it must be bigger?” my mind ends up thinking. The edges trick me: that’s not the edge of the universe, it’s just an artifact of plotting a spherical sky onto a flat piece of paper, just like any sort of atlas. The mental disconnect, though, leaves me feeling deeply uncomfortable.

Really, what I feel I should inspire me here is to take away that the night sky is far more mysterious and secretive than we know. It’s not just laid out flat in front of us as it appears to be: it’s full of unknown things and unanswered questions, even though all of them are genuinely sitting right there up above us somewhere. I don’t know if I’ll ever manage to change the way my head thinks about the night sky, but if I can, there is a whole universe of wonder concealed but fully within sight.

Keyword noise: astronomy, cosmology, comets, asteroids, Halley's Comet.

A few weeks ago, I read on Twitter—sadly I seem to have lost the reference—that the Welsh Hydref, used for either the month of October or autumn as a whole, originally had the literal meaning of “stag-cry”. From that, it turned into “stag-rutting season” and hence autumn. Geiriadur Prifysgol Cymru lists “stag-rutting”, but not “stag-cry”.

Moreover, November, mis Tachwedd, literally means “the month of slaughter”. Together, I think they make a beautifully evocative phrase. The stag-cry and the slaughter. Winter is setting in.

I spent a while sitting outside on clear nights over the past week, hoping to see the Geminid meteor shower. Nothing much, sadly, came of it. On Saturday, though, I did see a handful of meteors in the night sky. I’ve always looked for summer meteors before, flashing across the sky in a razor-thin line; but these were relatively slow-moving, fat things. I say “slow-moving”: they still crossed my field of view in little more than an instant. Their light was a much broader line, though, tapering at start and finish. If nothing else, it gave me good inspiration for the story I posted yesterday. Hopefully I’ll have better luck when the Geminids come around again next year. This year, though, is now nearly at an end. The stag-cry and the slaughter, and winter is upon us again.

Keyword noise: Cymraeg, seasons, autumn, yr Hydref, meteor shower, meteors, Geminids, astronomy.

This is not going to turn into an astronomy blog, I promise, and I know I already mentioned some exciting upcoming astronomy news just over a week ago. There is something else interesting and astronomical happening in December, though.

In the meantime, the clouds did briefly break on Saturday evening to give us our first chance of using The Child Who Likes Space’s telescope without the moon shining bright in the south. We had a look at Mars, and then I successfully found Uranus, navigating downwards from Sheratan, the nearest naked-eye star I could easily pick out; it’s currently near to the boundary between Aries and Cetus. Looking just like another blue star, I would have had no idea, without guiding myself with a map on the computer, that we were looking at a planet instead.

And then, naturally, I started sending messages to people saying “Guess what? I’ve been spying on Uranus”, because I still have the sophisticated sense of humour of a ten-year-old.

The exciting event that’s coming up in a week or so’s time is: the Geminid meteor shower. I say “coming up”: it’s expected to be at its strongest at around 2 in the morning next Monday (the 14th), but if it is a strong shower this year, there should be activity visible for a few hours either side of that time, and even for a few days. Incidentally, because of the geometry of how meteor showers work—they happen when the Earth passes through the trail of dust left behind a comet or asteroid—the peak time is the same wherever you are, with the location of the peak moving around the planet as it spins. The Geminids were first noticed in the 1860s, but their “parent”, the asteroid 3200 Phaethon, was not discovered until 120 years or so later.

I’m not sure I’m going to risk keeping The Child Who Likes Space up until midnight to watch for meteors, much as I’m sure he would like to. If the skies are clear late one night this week, though, I might try wrapping up warmly and setting up my deckchair in the garden. There’s no point trying to use a telescope or binoculars to spot meteors; all you need is a comfy chair you can lie back in and look up at the sky. Give your eyes half an hour to adapt to the dark, then look up, look around, and wait for them to streak across the sky.

Keyword noise: astronomy, meteors, meteor shower, Geminids, Uranus.

One last astronomy post for a while, and then I’ll talk about something different, I promise: in a few weeks time, on December 21^st Saturn and Jupiter will be at their closest conjunction for several hundred years.

The Plain People Of The Internet: Conwhatnow?

They’ll come close together in the sky. The closest they’ll be for a few hundred years, in fact. They’re already fairly close in the sky right now, but on December 21^st they’ll be so close that to some people they’ll look like a single spot of light, although people with 20/20 vision should still be able to see they are two separate dots.

Unfortunately … I’m not sure I’ll be able to see it. They’re both on the far side of the sun from us right now, and we’re basically watching Jupiter passing in front of Saturn from our perspective on the other side of the solar system. Because of this, they’re also fairly close to the sun in the sky, which means you don’t get a very long window of opportunity to see them. They will set together in the south-west sky only about 90 minutes after the sun does, so you have a brief window of time to see them together at dusk. If you’re on a south coast then things are grand; if you’re in a town, they may well be already below your neighbour’s roofline before the sky gets dark enough to see them. Personally, our only chance will be from an upstairs window. Fingers crossed, though, the sky will be clear enough to see something of them both together.

Keyword noise: astronomy, Jupiter, Saturn, conjunction, Great Conjunction, The Plain People Of The Internet.

Yesterday afternoon, sitting at my desk as dusk was falling, the skies were clear and I could clearly see the moon and Mars rising in the sky. As soon as I logged off from work, I scampered downstairs and went outside, and saw Jupiter and Saturn just visible above the rooftops at the back of the house. “Let’s get the telescope!” I said to The Child Who Likes Animals Space. “Before they set!”

“Before what set?” said The Child, but I was already rushing off to get his telescope and set it up in the back garden.

By the time I’d hoicked it out of its box, Jupiter had already gone down below the roofline, but Saturn was still there. Sadly, I could only see it when I was stood up. The telescope, sitting on a camping table, was too low down to spot it. I briefly considered setting the smaller camping table on top of the larger camping table and making some sort of rickety makeshift telescope-tower, but it would probably have ended in some sort of injury to one or both of us. So, like we’d done before, we looked at the moon, we looked at Mars, and we looked at random bright stars. “Point it at that blue thing!” he shouted. “That’s a very hot star!” This time, at least, he was a lot calmer and could stand still looking through the eyepiece without having to break off every couple of seconds to run back and forth with excitement. I experimented with holding my phone camera in front of the eyepiece. Worst. Astrophotography. Ever.

After The Children decided they’d rather go inside and watch TV I left the telescope set up; and after they’d gone to bed, the skies were still clear. Time for some telescope practice for me, I decided. Using an app on my phone to show me roughly where things were, I tried focusing on key visible stars then swinging the telescope sideways to find a nearby Messier object. The results? Not very successful, other than a possible sighting of M29, the Cooling Tower Cluster.

Getting a rough fix and vaguely hoping to spot the thing clearly wasn’t working. So, I fetched my laptop, and fired up Stellarium in Night Mode. I picked a target—the Triangulum Galaxy—and went looking for it.

Although the skies were clear, the seeing wasn’t great. Even a newbie like me could tell that the seeing wasn’t good. Vega normally stands out to me like a sore thumb, but last night it didn’t really appear any brighter or more significant than the stars of the Northern Cross to its south, which normally are noticably fainter. Nevertheless, I could see Hamal and Sheratan, the brightest stars in Aries, and could spot the telescope nicely onto Hamal and swing it between the two. Zooming in on Hamal in Stellarium, and flicking my head back and forth from the telescope eyepiece to the dim red screen of the computer, I could slowly navigate my way upwards from star to star until I reached Mothallah, which I hadn’t managed to see with the naked eye.

From there, I could similarly hop south towards the spot where the Triangulum Galaxy should be, navigating from star to star and matching the scene in the sky to the screen of the computer. But when I reached it: nothing. Just a blank patch of sky. I found Mothallah again, then worked my way across by a different route. Still nothing. The Triangulum Galaxy has been stolen!

Let’s try the Andromeda Galaxy instead, I thought, given that it’s one of the brightest galaxies in the sky. I found Mirach by eye, spotted the telescope on to it, and walked over to where the galaxy should be. Another blank patch of sky, with a faint hazy blob in the middle of it. Hurrah! A faint hazy blob!

I’m almost glad I hadn’t found it the other day when The Child Who Likes Animals had asked me to find it, because I suspect if I had he’d have been awfully disappointed. I was a bit puzzled, though, because in theory the Andromeda Galaxy is of naked-eye magnitude. I should have seen much more than a fuzzy blob, surely?

A quick note about how astronomical “apparent magnitude”, or brightness to you and me, works. It’s a relative scale based loosely on the subjective scales used by ancient astronomers, and as it’s relative it’s written down as a number without units. The higher the number, the fainter the thing is; and a difference of five in the apparent magnitude number means “a hundred times brighter”. If you have a calculator to hand you can work out that a drop in magnitude of 1 therefore means “2.5119 times brighter”.^* The star Vega, mentioned earlier, has magnitude 0, so a few things in the sky have negative magnitudes: Sirius is -1.47, Jupiter varies from -1.66 to -2.94, and Venus from -2.98 to -4.92, almost 100 times as bright as Vega.

On a good night, with a clear dark sky, the human eye should in theory be able to see things as faint as magnitude 6 or so. Last night was clearly nowhere near that: I could see Sheratan at 2.655 and Albeiro (in the Northern Cross of Cygnus) at 3, but couldn’t see Mothallah at 3.42. Through the telescope, though, I was happily stepping my way across the sky using stars of 8 to 8.4, roughly speaking, stars around 140 times less bright than the faintest I could see without it.

The Triangulum galaxy, though, is officially^** of magnitude 5.72. Andromeda is considerably brighter still, around the same magnitude as Mothallah. So what was going on?

A galaxy isn’t a point of light, like nearly all stars are. Nearly every star in the sky, other than a handful of stars like Betelgeuse when seen through very high magnifications, appears to be just a single point of light to the viewer here on Earth. A galaxy, by comparison, covers a broad chunk of the sky. That small fuzzy blob I could make out in Andromeda was really just the very brightest core of the galaxy; and the rest of that 3.4 magnitude of light is spread out over an area wide enough to fill my entire eyepiece. Through the telescope, it just becomes a vaguely paler area of sky.

Hopefully at some point we will get the telescope out on a night with rather better viewing conditions, and be able to see all of these things properly. Until then, it seems strangely unintuitive to be able to see hundreds of dimmer stars but not a theoretically many-times-brighter galaxy. That, though, is just how the physics works.

* Apparently, the formal definition “five means a factor of 100” was set down by a Victorian astronomer with what I think is a great name, N R Pogson. The relationship 1:2.5119 is therefore known as Pogson’s Ratio.

** I say “officially”. I mean “according to what I’ve just read on Wikipedia”, of course.

Keyword noise: astronomy, The Children, Saturn, Triangulum Galaxy, Andromeda Galaxy, Messier objects, magnitude, The Moon.