This large, smoothly spinning finger top is decorated to resemble the Andromeda galaxy. (To get the full effect, watch the video full screen.) Strong twirls yield smooth sleepers with speeds and spin times of over 400 RPM and 2 minutes!
About this creation
Please feel free to look over the images and skip the verbiage.
I decorated this large, heavy disk-based finger top to portray (very loosely) the Milky Way's big sister, the Andromeda galaxy (aka Andromeda nebula, Messier 31, M31, NGC224).
Hereafter, I'll refer to Andromeda the galaxy as "M31" to distinguish it from Andromeda the top.
∨ NB: The top's greatest likeness to M31 occurs while spinning in the dark. To get the full effect and make the captions visible, please watch the video below full-screen.
With practice, vigorous twirls can produce very smooth sleepers with release speeds of over 400 RPM and spin times of over 2 minutes. Not bad at all considering the lousy aerodynamics!
BTW, Andromeda here and Asteroid (1st photo below) aren't my only tops with astronomical themes...
∧ The only intact one-armed spiral galaxy yet discovered.
A look at tops through history reveals a long and deep but hardly surprising connection between tops and the workings of the heavens.
Spiral attitude adjuster
Andromeda the top (early version below) sits on my desk as a reminder that things could always be worse.
M31 appears to be on a collision course with our own Milky Way. The fireworks should begin in about 4 billion years -- just about when our beloved Sun is due to go red giant and vaporize us all, bless its heart. 1
Warning: Unimaginably large and small numbers ahead. E-notation (AeB ≡ A x 10 B) doesn't make them any easier to comprehend, but it does make them a little easier to read and compare.
The top's scale is ~1:1.3e22 in diameter and ~1:2.1e43 in mass -- i.e., it's too heavy for its size by a factor of ~1e21. No surprise there, though: M31 is mostly empty space, whereas the top is mostly ABS plastic.
∧ Public domain image of M31 in UV light captured by NASA's Galaxy Evolution Explorer satellite. The hot, young stars highlighted by the chosen UV band mark the ring system as a hotbed of star formation.
Being the closest large galaxy beyond our own (a mere 2.4e22 m = 2.5e6 light-years away) makes M31 one of the very few galaxies visible to the naked eye. Its atypical morphology is perhaps closest to a somewhat open barred spiral.
M31 contains roughly a trillion (1.0e12) individual stars and 460 globular clusters (GCs). It has a mass of 3.0e42 kg = 1.5e12 solar masses, a disk diameter of 2.1e21 m = 2.2e5 light-years, and a GC/star ratio of ~4.2e-10.
The top's "stars" also form a barred spiral pattern, but the top is never more than 1 flight of stairs = 4.3e1 m = ~4.2e-16 light-years from Earth.
The top contains 6 = 6e0 token "GCs" and roughly 200 = 2e2 token "stars". It has a mass of 1.41e-1 kg = 7.1e-32 solar masses, a disk diameter of 1.60e-1 m = 1.7E-17 light-years, and a "GC" / "star" ratio of ~3e-2.
That last figure is only off by 8 orders of magnitude.
A straight-across comparison of rotational speeds isn't possible due to the vastly different styles of rotation involved, but perhaps this will give you an idea...
Our Sun's orbital period about the Milky Way's galactic center is ~7.9e15 sec = 2.5e8 yr, whereas every "star" on the top orbits the spin axis once every 2.5e-3 sec = 7.9e-11 yr after a typical hard twirl. These periods differ by a factor of ~1e19.
What's shown and what's not
The top portrays some of M31's more conspicuous structural features at IR, visible, and UV wavelengths. These include...
The main disk, where most of its stars and gas and dust clouds (hereafter, simply "clouds") reside
The GCs arrayed mainly above and below the disk near the galactic center
Two spiral arms and the small bar linking them across the galactic center
The large ~spherical dark matter halo thought to extend well beyond the visible parts of the galaxy.
Since the dark matter halo is inferred to contain >90% of M31's mass, the part of M31 you can actually see -- even with something like the Hubble or Spitzer Space Telescope and sensors spanning IR through UV wavelengths -- may well be just the tip of the iceberg.
With the top, on the other hand, what you see is what you get.
Spiral arms and rings
The top grossly oversimplifies the complex spiral arm and ring structure of M31's main disk. M31's high inclination to our line of sight makes its arms hard to count, but it clearly doesn't have the 2 broad, distinct, symmetrical spiral arms shown on the top.
The colored "stars" outlining the top's otherwise white spiral arms are meant to evoke the more gradual color gradient consistently observed across the arms of spiral galaxies.
∨ My attempt to suggest this color gradient across the spiral arms shows up best in low light, as I used greenish glow-in-the-dark white "stars" to mark the leading edges of the spiral arms and yellow and orange "stars" to mark the "trailing edges".
∧ As a faint nod to M31's conspicuous but poorly understood outermost ring, I had the top's spiral arms almost touch at the edge of the disk.
No comprehensive theory of galactic spiral arms exists. The reigning density wave theory recounted below accounts for some of the observations, including the color gradients within the arms. It can't be the whole story, but it might be a good start.
The theory holds that spiral arms aren't material things but rather dynamical patterns of star formation, aging, and death produced by density waves (DWs) that circulate through the disks of spiral galaxies.
The contractional phases of DWs are made visible by the enhanced star formation triggered by their passage. The dark lanes between arms correspond roughly to the expansional phases.
The DWs are thought to arise from orbital instabilities ultimately rooted in chance close encounters between stars with adjoining elliptical orbits about the galactic center. At any given radius, however, the waves move around the disk more slowly than the orbiting stars and clouds do.
When a particular stellar neighborhood first overtakes a contractional DW phase in the course of orbiting the galactic center, the neighbors (stars and clouds) therein end up a little closer together than usual. This causes their mutual gravitational interactions to intensify, and the added commotion triggers gravitational collapse in some of the denser clouds.
The ensuing bout of rapid star formation in the collapsing clouds results in a local excess of very bright massive young stars so hot that their visible light is much bluer than usual. From our distant vantage, the entire neighborhood gets brighter and bluer.
The overly blue stellar population along the contractional DW front is referred to as the spiral arm's leading edge.
The biggest and brightest of the blue stars formed at the front die out quickly just behind the leading edge. At some point even farther behind the leading edge, blue stars are no longer over-represented. Instead, the stellar population comes to be dominated by smaller, longer-lived white and yellow stars (like our Sun) left over from previous frontal passages.
Greater distances behind the leading edge correspond to longer times since the most recent frontal passage. More of the larger and hotter stars will have died out while the smaller and cooler stars continue to hang on, becoming an ever-increasing percentage of the brighter stars remaining.
The aging stellar population along the trailing edge of the arm takes on the red color of the old, cool stars that have come to dominate it. The dark lanes behind the trailing edges are largely filled with old, dim stars and stellar remains of various kinds.
Central bulge and bar
M31, the Milky Way, and many other disk galaxies are found to have prominent central bulges of densely packed stars.
These bulges rise a disk-thickness or so above and below the main disk and typically outshine the rest of the galaxy. Since M31's bulge is no exception, it had to be portrayed somehow.
∧ The top's "bulge" doesn't photograph well. These shots of an early version of the top show it best, especially with the the stem removed.
Galactic bulges stand at the geometric centers of their host galaxies. Some are elliptical and rather featureless, while others have their own spiral arms.
The Milky Way's bulge is probably its oldest part, and the same may be true of M31's. Compared to most main disk stellar populations, bulges seem to be exceptionally rich in very old stars (1.2e10 years or older).
The central bars of barred spiral galaxies like the Milky Way and now M31 generally overlap their bulges. M31's recently discovered small bar is largely buried within its bulge. Like spiral arms, the bars are thought to be non-material dynamical patterns.
How central bulges and bars form remains far from clear and may well vary from galaxy to galaxy. Many astronomers believe that a supermassive black hole lurks at the center of M31's bulge, but others question that conclusion.
Scattered above, below, and probably within M31's central bulge and the inner portion of its main disk are hundreds of more or less spherical globular clusters (GCs) of very tightly packed old, dim stars. GCs are a common feature in spiral galaxies.
Available LEGOŽ parts and scaling issues being what they are, I had little choice but to suggest the "GCs" on the top with stacks of white 1x1 round plates rising above the disk on stacks of black ones.
The GC representation is lame at best. For starters, the top's "GCs" are way too small and way too numerous for its individual "stars".
Each GC contains on the order of 1e5 stars but no clouds, as all that material went into star-making long ago.
The CGs are themselves distributed more or less spherically around the galactic center far from the edge of the main disk. Though deeply embedded in the dense halo of dark matter thought to surround M31, they show no evidence of having been shaped by something flowing around them.
One theory of GC formation in M31 holds that they represent chunks of a much younger M31 that were ripped out in a collision (read "strong gravitational interaction") with another galaxy perhaps 10 billion (1e10) years ago. The chunks that failed to escape M31's gravitational field self-organized over time into the dense star-balls we call GCs today.
The differential rotation of a galaxy bears little resemblance to the rigid-body rotation of a top.
∧ When I spin the top, every part of it executes a circular orbit about the spin axis with the same orbital period (time required to complete 1 revolution) as every other part.
Hence, every "star" and stud at the same radius from the spin axis has exactly the same orbital speed, and that speed increases linearly with radius by exactly the same proportionality constant. Very tidy.
When orbital speeds on the top's disk are plotted against radius, the resulting rotation curve is a straight line with a positive slope equal to the top's angular velocity 2 and inversely proportional to the common orbital period.
A rising straight-line RC is the hallmark of a spinning rigid body, in which every part stands at a fixed position relative every other part.
Galaxies, however, don't rotate like tops. They aren't rigid bodies, and their RCs aren't straight lines.
Instead, galaxies exhibit differential rotation. Every star and cloud orbits the galactic center at a speed dictated (i) by the gravitational fields of all the masses in the galaxy combined and (ii) by recent close encounters with other objects.
Hence, there's a good bit of spread around the average orbital speed found at every radius. When one constructs an RC using these average speeds, the graph looks a hockey stick with a blade rising sharply from the origin (galactic center) and a nearly horizontal wavy handle.
The crook between blade and handle lies much closer to the galactic center than the edge of the disk. Beyond the crook, the general trend is a very slow rise in average orbital speed with distance with minor reversals here and there in some cases. M31 is the poster child for this kind of RC.
The realization that M31's RC can't be due to gravitational interactions limited solely to its observable stars, clouds, and CGs led to the discovery of dark matter. It's no exaggeration to say that M31 forever changed our view of the entire universe, which is now thought to be mostly dark matter. 3
Though the existence of dark matter is no longer disputed, we still know almost nothing about it. One thing's for sure, though: It's nothing like the ordinary (aka "baryonic") matter making up you and I and LEGOŽ plastic and the stars and clouds of M31's main disk, bulge, and GCs.
Wrong on so many levels
Here's a list of the top features most misrepresentative of M31 and, for that matter, all other spiral galaxies.
Scaling:The top is too dense by a factor of ~1e21, the "stars" and "GCs" are way too big for the disk, and the "GCs" are way too small for the "stars".
Spiral arms: The top's arms are too few, too distinct, and too symmetrical. Their color gradients should be more gradual, with bluer leading and redder trailing edges.
"GC" number and distribution: There are too many "GCs" for the number of main disk "stars" shown by a factor of ~1e8.
Central bulge: The "bulge" is obscured by the "GCs" (if anything, it should be the other way around) and doesn't "outshine" the disk.
Rotation curve: The top's rigid body rotation is nothing like M31's differential rotation and too fast by a factor of ~1e19.
Nonetheless, I like having a spiral galaxy on my desk, however imperfect, and especially like giving it a spin now and then.
∨ This top's rotor and those of the smaller tops in the group shot below all have one thing in common: No center hole for a through-going axle.
Attaching a proper stem and tip to such a top can be a challenge, as any misalignment or wiggle in either one could easily turn an otherwise smoothly spinning top into a jerky one -- especially in a top as heavy as Andromeda.
∨ The solutions shown in the next 5 photos have worked well in such situations.
∧ I reamed out the open stud of the 2x2 white cone holding the stem to Andromeda's "disk" to allow a cross-axle to pass all the way through it. Other stem holders I tried (e.g., here) obscured the "bulge" and "GCs" too much.
∧ Coming up with a tip holder (white) rigid enough for this heavy top involved a good bit of trial and error. The tip itself (black) is my standard -- the severed end of a round-tipped 4L antenna.
∧ A similar tip holder on an 8x8 round tile top.
When smoothly spinning LEGOŽ tops with little tendency to walk are the goal, the use of these tips constitutes an unavoidable act of selective impurism. The reamed-out cone was a little more gratitous.
∨ Star colors were a challenge for 3 main reasons: (i) Real star colors are a lot closer to white than they are to most LEGOŽ colors. (ii) The 1x1 round plates used as "stars" don't come in some of the paler LEGOŽ colors. (iii) I don't do pink.
In the end, I rendered the bluish leading edges of M31's spiral arms with slightly greenish glow-in-the-dark white "stars" and the reddish trailing edges with yellow and orange, as available bluish "stars" were either too dark, too hard to find, or too expensive, and available reddish "stars" were either too dark or (gasp) pink.
160x76 mm (DxH) including stem
Token globular clusters:
Maximum spin time by hand:
Maximum speed by hand:
Modified LEGOŽ parts:
(i) Tip cut from the end of a round-tipped 4L antenna; (ii) Open stud of white 2x2 cone serving as stem attachment reamed out to accommodate a cross-axle
1 Unfortunately, if you live in Southern California west of the San Andreas Fault System, your number will be up a lot sooner, as you'll be flushed down the Aleutian trench in a mere 10 million (1e7) years -- much to the relief of Northern Californians east of the fault.
2 Angular velocity (Ω), expressed in radians/sec, is given by
Ω = n π / 30 ≈ n / 10,
where n is rotational frequency in RPM. Orbital period in sec is then
T = 2 π / Ω
3 M31's troubling rotation curve (RC) first drew attention to the so-called "missing mass problem" enountered in gravitationally bound systems of masses at galactic and larger scales. The many RCs determined since then have only pounded the problem home.
These RCs summarize the relative motions of stars and other masses gravitationally bound within galaxies. They can be explained without appeal to invisible but gravitationally active dark matter if one's willing to diddle with Newton's Universal Law of Gravitation (ULG), which holds that the gravitational attraction between two masses is proportional to the inverse square of the distance between them.
However, diddling with the ULG is a good way to pick a fight with many physicists and only fixes the problem at galactic scale. Some form of dark matter is still needed to explain the observed motions of gravitationally bound clusters of galaxies.
Modified gravity approaches drastically reduce the amount of dark matter needed to reproduce these larger-scale observations, but they don't eliminate the need for it entirely -- at least not yet.
It will be interesting to see how these very different but equally outlandish and disconcerting approaches to a very thorny astronomical problem will fare as evidence continues to accumulate and improve over the coming years.
Quoting J Raab
I got a bit lost in the numbers, not going to lie. But the top is really cool. I wasn't expecting the glow in the dark pattern, neat idea.
Getting carried away with the numbers is one of my centers of excellence, along with losing hats. I'd use more phosphorescent (glow-in-the-dark) parts if they were more plentiful and less expensive. But I've had a lot of fun with fluorescent parts on various spinning gizmos.
Quoting David Roberts
That's so simple but very clever at the same time. I love that it's a hand spun top. At first I assumed that it was one of those things that you put on a record turntable. I love the dark videos too.
Thanks, David. Geez, you must be almost as ancient as I am to remember record turntables! (I go back to the Late Bronze Age.) Really glad you like the way it looks in the dark. That started out as just a little gimmick but turned out to be my favorite part.
Quoting Sam the First
Mildly hypnotic. :D Nice work, it looks really nice! Arty, with all the dots, and love that playability your models always have. Awesome stuff!
Many thanks, Sam. One of the fun things about tops is the challenge to get them to spin as smoothly and as long as possible, as both of those things have a huge influence on play value. The lousy aerodynamics shortened this top's spin times a good bit at first, but the peripheral mass added later nicely offset that.
That is a really cool series of tops!
Yeah, I was big into astronomy back in the mid eighties. Had a Meade 8" reflector with which most of the deep sky and planetary observing was done. At one point was a member of the Association of Lunar & Planetary Observers and the British Astronomical Association for a couple of years. Did a lot of observation drawings of Saturn and Jupiter at the eyepiece which I would submit to these entities. Eyesight is no longer keen enough for this kind of detailed work. Still have a small 60mm refractor that I take out stargazing once in awhile with the grand kids. Amazingly, after 30 years, I still know my way around most of the constellations and where the better deep sky objects are. Forgotten a lot, though.
Quoting Ed Mitton
I got a little chuckle out of this line in the text:
" M31 is mostly empty space, whereas the top is mostly ABS plastic."
Many thanks for the comments and like, Ed. Glad you liked that line. Scientific humor (which many doubt even exists) is definitely an acquired taste. Dabbled in amateur astronomy many years ago but the nearest good seeing was too far away to sustain the hobby. Sounds like you might have a telescope or 2. I've just been a science and engineering nut since grade school, and astronomy's always been a favorite among way too many interests.
You wouldn't by any chance happen to be an amateur astronomer, would you? Hard to tell from your post ;)
What kind of scopes do you have?
Nice build and excellent accompanying text and photos.