# Galaxy of snowflake stars

It's snowing outside my window today. Swirling galaxies of snowflakes. So...

Say snowflakes are separated by a few inches, or a couple of feet. Order of magnitude wise, those are factors of 0.1 meter (tens of centimeters). When the snow started it was large and fluffy with lots of space between. It later got smaller, wetter, closer. Is 0.1 meter a good beginning? Well, a larger separation, of meters, would be a very light snow. And a smaller separation, of centimeters (0.01 meter), would be a white-out. So lets go with 0.1 meter. And as our scale is about to change radically, lets write the 0.1 as 10^-1 (1 is 10^0, 10 is 10^1, 100 is 10^2, 0.01 is 10^-2, a million is 10^6, a trillion is 10^12, etc).

Stars are separated by light years. The three Alpha Centauri stars being the closest to us at 4 light years distance. Sirus, one of the more easily visible stars, is 9 ly away. Within 10 ly there are eight stars (counting our own Sun). Stars deep in the galactic center are a bit more scrunched together (distances like 0.1 light year), and in the voids between galactic arms, get really sparse, but not around here, so lets go with light years.

A quick check of a conversion table shows 1 light year is 10^16 meters (9.46 x 10^15).

So snowflakes are separated by some 10^-1 meters, and stars by some 10^16. A scale difference of 10^17. (100,000,000,000,000,000)

Ok, so now what?

Hmm. How big is the snowflake galaxy?
Well, the stars of the galaxy are in a frisbee, with ball for the galactic center in, well, its center. The frisbee is 25 thousand parsecs in across, and about 2 thick around us, here in the disk. Another check of the conversion table gives 1 kpc as 3 x 10^19 meters. So lets call the galaxy 10^19 meters thick and 10^20 meters across.
Our snowflakes are at 10^17 scale. So the snowflake galaxy is 10^2 meters think and 10^3 meters in diameter. 100 and 1000 meters. 300 and 3000 feet. 1/5 and 1/2 miles. So about 30 stories thick, and 1/2 mile (or 1 km) in diameter. Sort of like downtown Boston. Made of snowflakes. Which are stars.
Hmm. I get "big", but I can't picture it very well. Lets see... I can see something like 1/10 mile out my window. So I guess thats a good hunk of a galactic arm, with the disk thickness stretching from parking lot to cloud base.

Ok, so what else?
When I walk along, snowflakes zooming by my face, how fast am I going?
Say I am walking around 1 meter per second (2 steps, 1 pace, or 1 yard per second). In snowflake land, thats 10^17 meters / second. The speed of light is 3 x 10^8 m/s, so thats 10^9 difference. I am going a billion times light speed (US billion; a thousand million British). Hmm, too big to grok. Well lets see...
Snowflakes zipping by like stars on a StarTrek viewscreen... StarTrek's warp 9 is 1000 times light speed. So that gets us down to 10^6. A day is about 10^5 seconds (24*60*60=86400). So walking along one's seeing starflakes zip by at 10 days worth of warp 9 every second. Say each step is a week's worth of warp 9. Yipes. With a 1/2 mile galaxy, StarTrek Voyager's crew have a long walk home.

Hmm. Anything else easy before wrapping up this exercise?
The snowflakes are way way WAY too big to be stars. A snowflake a few millimeters (10^-3) across at 10^17 scale is 10^14 meters. The sun is only 10^9 meters. Off by 100,000. Ah, Neptune is 10^13 meters across. So a tiny snowflake is 10 times as big as our solar system. A big flake is 100 times as big. The 10^9 meter sun is a 10^-6 meter snowsun. Hmm, 10^-6 m, a micro-meter, say a blood cell or a bacteria. The the snow "stars" we have been zipping by are really big stellar envelopes, bigger than solar systems, each with a little bacteria star or three nestled within.

Say the snow swirling is their natural movement. Its going way too fast to be real time. What's the time compression? Well, a 1 meter / sec swirl is 10^17 m/s. Actual stellar velocity is about 10^4 m/s. At snow scale, thats slower than continental drift. Each second we're seeing 10^13 seconds of movement. A day again is 10^5 sec, so 10^8 days. 10^6 years. So million years of movement per second. Hmm, and stars live for something like 10 Gyr (10^10, or 10 billion (us) years). So snowstars like our sun should last around 10^4 seconds. An hour or so. More massive stars, with a tenth of the life, would be five minutes. Hey, atleast something matches. I wonder how long snowflakes spend bouncing up and down inside of clouds before beginning their plunge?

I am out of time. If you come up with a neat one and let me know, I can add it.
And a warning: I have not checked this. I have not reread the argument, nor done end checks (such as comparing the calculated stellar distances with a known local value of 0.1 stars per cubic parsec). This is, of course, a serious lack. I suggest taking the comparisons with a grain of salt until you've checked them for yourself.

The snowfall is tapering off...
Mitchell
09 December 1996, Boston MA

Comments encouraged. - mcharity@lcs.mit.edu.
[Musings][Top]
```History:
1996.Dec.11  Brushed up warning at end.
1996.Dec.06  Created.
```