physics, short, silly, thought experiment

Late for Work

I work a pretty standard 9-to-5 job. Now I know 9 to 5 is actually pretty cushy hours. I’ve got friends whose hours are more like 6 AM to whenever-it’s-done. But my lizard brain won’t get the message that 9 AM isn’t that early a start. Apparently, my brain thinks that getting up at 8 AM is the same as getting up at 3:30 and having to walk ten miles to work (in the snow, uphill both ways).

Luckily, I really don’t like being late, so I manage to be on time by pure stubbornness. But sometimes, it’s a pretty close shave. And while I was driving to work the other day, I got to wondering just how late I could leave the house and have any chance of getting to work on time.

My commute to work is 23.1 miles (37.2 kilometers). According to Google Maps, it should take about 39 minutes, which seems about right. That means an average speed of 35.5 miles per hour (57.2 kilometers per hour). Considering at least half that distance is on the highway at 70 miles per hour (113 km/h), that seems a little slow, but to be honest, there are a lot of traffic lights and weird intersections in the non-highway section, so it probably works out.

But the question remains: how quickly could I possibly get to work? And, therefore, how late could I leave the house and still get to work on time?

The most obvious solution is to convert myself into a beam of light (for certain definitions of “most obvious”). Since there are no vacuum tunnels between here and work, I can’t travel at the full 299,793 kilometers per second that light travels in vacuum. I can only go 299,705. Tragic. Either way, by turning myself into a beam of light, I can get to work in 0.124 milliseconds. So as long as I’m dressed and ready by 8:59:59.999876 AM, I’ll be fine.

Of course, there’d be machinery involved in converting me to light and then back into matter again, and considering what a decent internet connection costs around here, it ain’t gonna be cheap to send that much data. So I should probably travel there as matter.

It’d make sense to fire myself out of some sort of cannon, or maybe catch a ride on an ICBM. The trouble is that I am more or less human, and even most trained humans can’t accelerate faster than 98.1 m/s^2 (10 g) for very long without becoming dead humans. I am not what you’d call a well-trained human. Sadly, I don’t have easy access to a centrifuge, so I don’t know my actual acceleration tolerance, but I’d put it in the region of 3 to 5 g: 29.43 to 49.05 m/s^2.

Figuring out how long it’ll take me to get to work with a constant acceleration is pretty simple. We’ll assume I hop in my ridiculous rocket, accelerate at 3 to 5 g until I reach the halfway point, then flip the rocket around and decelerate at the same pace until I arrive. And since the math for constant acceleration is fairly simple, we know that

distance traveled = (1/2) * acceleration * [duration of acceleration]^2

A little calculus tells us that

duration of acceleration = square root[(2 * distance traveled) / (acceleration)]

Of course, I have to divide distance traveled by two, since I’m only accelerating to the halfway point. And then double the result, because decelerating takes the same amount of time, at constant acceleration. So, at 3 g, I can get to work in 71.2 seconds (reaching a maximum speed of 1,048 meters per second, which is about the speed of a high-powered rifle bullet). So, as long as I’m inside my rocket and have the engines running by 8:58:48.8 AM, I’ll be at work exactly on time. Though after struggling with triple my usual body weight for a minute and twelve seconds, I’ll probably be even groggier than I usually am.

I have no idea if I can even physically tolerate 5 g of acceleration. I mean, I’m hardly in prime physical condition, but I’m not knocking on death’s door either. But I’m gonna venture to guess that anything above 5 g would probably kill me, or at least leave me needing a sick day by the time I actually got to work, which would defeat the whole point. At 5 g, I only need 55.06 seconds to get to work, reaching a maximum 1,350 m/s. So, if I’m in my rocket by 8:59:04.94, I’m golden!

Of course, that was assuming that, for some reason, I do all my accelerating along my usual route. And frankly, if you’ve got a rocket that can do 5 g for over a minute, and you’re not flying, you’re doing it wrong. According to an online calculator, the straight-line distance between home and work is 13.33 miles (21.46 km). Re-doing the math, at 3 g, I can make it to work in 38.18 seconds (meaning I can leave at 8:59:21.82 AM, and will reach 568.1 m/s). At 5 g, I’ll be there in 29.58 seconds (leaving at 8:59:30.42, reaching 936.4 meters per second).

And yet, no matter how quickly I can get to work, I’m still gonna wish I could’ve slept in.

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engineering, physical experiment, physics, short, silly

Crappy Plastic Bags

Plastic grocery bags suck, and for many reasons. They’re light enough to be carried away by a particularly motivated fruit fly, which means they turn into litter very easily. And since they shred easily into tiny, tiny pieces, they’re probably an excellent source of plastic pollution, which is looking more and more like a major problem every day.

Luckily, the flimsy grocery bags I’m talking about are made of LDPE: low-density polyethylene. And while LDPE isn’t exactly the kind of thing you wanna put on a sandwich, as far as plastics go, it’s relatively mild. Chemically, it’s very similar to wax. Unlike, say PVC and polystyrene, LDPE is a lot less prone to breaking down into scary aromatic and chlorinated hydrocarbons. Plus, it’s not full of the slightly scary plasticizers found in many other plastics.

But my real issue with grocery bags is that they suck. They’re pretty shitty at the one thing they’re made for, which is holding groceries. This morning, on my way to work, I stopped to get some milk. The jug couldn’t’ve weighed more than three or four pounds, but that didn’t stop it from bursting right through the bottom and falling on the floor. I realize I’m making myself sound like a cranky old man when I say this, but I don’t remember plastic bags being quite that fragile when I was younger. And I would’ve noticed if they were, on account of the number of times I tied a grocery bag to a string and tried to fly it like a kite. They didn’t last a long time doing that, but I’d be willing to wager the modern ones would rip before you could get the kite string tied on.

But I’m going to do what crotchety old men never seem to: I’m going to back up my whining with evidence. Here is my evidence.

Crappy Plastic Bag

I’m sorry for the godawful picture, but it gets the point across. What you’re looking at is a pair of lower-mid-range digital calipers, which are pretty handy for measuring things to decent accuracy and precision. The calipers are clamped down around a flat strip of grocery-bag material which has been folded three times, giving eight layers. In the name of fairness, let’s assume that the actual thickness is 0.095 millimeters: just barely thin enough that the calipers didn’t round it up to 0.1. Divide 0.095 by eight, and you get 0.011875 millimeters, or 11.875 microns. For comparison, a human hair is usually quoted in the neighborhood of between 80 and 120 microns. The one I just pulled out of my own scalp (you’re welcome) measured 50 microns. Measuring ten sheets of printer paper and dividing by ten gave me 102 microns. A dust mite turd is apparently between 5 and 20 microns. (Wikipedia says that this book says so, and while I’ll do a lot of things for my readers, I’m not reading a thousand pages to find a passage on dust mite poop.) Human cells usually range between 10 microns and 50 microns (though some get a lot larger).

To get some more perspective, an American football field is 150 yards long and 55 1/3 yards wide. If we were to cover an entire football field with a single layer of grocery bag material, the whole damn thing would only weigh 162.9 pounds (73.9 kilograms). That’s less than me. Less than the average American football player. Hell, that’s less than my dad, and he’s built like a lean twig. Imagining the horrendous suffocation hazard that sheet will pose when it inevitably blows into the stands is making me nervous.

Now, this is only one data point, admittedly. I didn’t measure the thickness of plastic bags when I was a kid (I was too busy making kites out of them, or walking around the house with a mirror pretending I was walking on the ceiling). But that seems excruciatingly thin to me. In order for a soap bubble to be iridescent, it must undergo thin-film interference. This means that, in order to reflect violet light (the shortest wavelength visible to the eye: around 380 nanometers), the bubble can be no thicker than 71 nanometers. My grocery bag is only 167 times thicker than a damned soap bubble. No wonder my groceries fell out this morning, and no wonder every time I go to the hardware store, something pokes a hole in the bag and makes my tools fall out.

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astronomy, physics, short

Weight of the World

According to this report, the Earth’s mass (M⊕) is

5,972,190,000,000,000,000,000,000 kilograms

You might notice that there are an awful lot of zeros in that number. That’s because the report doesn’t actually directly specify the Earth’s mass. Like a lot of astronomical papers, it instead uses the Earth’s gravitational parameter, which is the Earth’s mass multiplied by the Newtonian gravitational constant. You see, when it comes to gravity, the force is ultimately determined by the gravitational parameter, rather than directly by the mass. As a result, the gravitational parameter is, as a rule, known to much higher accuracy than the mass. Newton’s gravitational constant is hard to measure, since it’s so tiny, so the report only gives it to six significant digits. So six significant digits is what I gave for the Earth’s mass.

I imagine you’re wondering why the hell I’m talking about all this. Well, I was thinking about planets, whose masses are very often measured in Earth masses. That made me wonder what the mass of say, a person, is, compared to the mass of the Earth. So, without further nonsense, here’s my big list of random objects measured in Earth masses. (I probably need to come up with a better name.)

2.78045 × 10-51 M⊕ : Hydrogen atom.

1.13926 × 10-24 M⊕ : a dumbbell

2.279 × 10-23 M⊕ : me

1.674 × 10-22 M⊕ : my car

7.023 × 10-20 M: the International Space Station

9.878 × 10-16 M⊕ : the Great Pyramid of Giza

1.671 × 10-12 M : Comet 67P/Churyumov-Gerasimenko

8.620 × 10-7 M⊕ (not quite a millionth): The Earth’s atmosphere

4.470 × 10-5 M : asteroid 4 Vesta.

1.590 × 10-4 M : asteroid 1 Ceres (the largest in the solar system)

2.344 × 10-4 M (two ten thousandths and change): the Earth’s oceans

 0.00219 M⊕ : Pluto

0.0123 M⊕ : the Moon

0.0552 M: Mercury

0.107 M: Mars (I always forget how small Mars actually is…)

0.815 M⊕ : Venus (Venus was my second-favorite planet as a kid, after Pluto, which was still a planet back then)

1.000 M⊕ : Earth (Might as well stick it in the list…)

10 M: Planet Nine (Lower bound. If it exists.)

14.536 M⊕ : the mass of Uranus (I still think it’s funny…)

17.148 M⊕ : Neptune

95.161 M⊕ : Saturn

317.828 M⊕ :  Jupiter

332,949 M⊕ : the Sun (1 solar mass, 1 M. Guess who finally learned how to do subscripts!)

26,600 M⊕ : the mass of TRAPPIST-1, which is significant for being one of the smallest stars ever observed, for having seven rocky planets, and for having three planets in its habitable zone. If there’s radio-communicating life on one of them, and we send a message right now, some of you might still be alive if we get the response. Not me. I’d be 98, and I suspect I’m gonna fall into a vat of curry or something stupid like that before then.

672,600 M⊕ : Sirius A, the brightest star in the sky (besides the Sun, obviously)

710,850 M⊕ : Vega, a fairly bright nearby star distorted into a lozenge shape by its rapid rotation.

1,270,000 M⊕ : Alcyone, the brightest star in the Pleiades

2,830,000 M⊕ : UY Scuti, a likely candidate for the largest known star as of March 2017. It’s around 1,700 times the diameter of the Sun, and if you placed it where the Sun is, it’d engulf Jupiter and come close to engulfing Saturn.

3,862,000 M⊕ : Betelgeuse, the bright reddish star on the shoulder of Orion (cue Rutger Hauer.) It’s also an enormous, lumpy star. If you put it where the Sun is, it’d reach at least as far as the orbit of Mars.

33,295,000 M⊕ : the larger component of Eta Carinae, an enormous, extremely bright, angry multiple star that’s so massive and so hot that it’s vomiting its own guts into space and making a pretty nebula in the process.

38,622,000 M: the poetically-named NGC 3603-A1. With 116 times the Sun’s mass, this is the largest star (as of March 2017, blah blah blah) whose mass is known with any certainty. There are other stars predicted to be more massive, but while their masses are estimated from models of stellar evolution, NGC 3603-A1’s mass is inferred from the orbital period of it and its binary companion, which is much more precise and less guess-y.

2.331 × 1015 M: the mass of the Small Magellanic Cloud, one of the Milky Way’s small galactic neighbors.

2.830 × 1017 M: the mass of our Milky Way galaxy (roughly).

4.994 × 1017 M: the mass of the Andromeda galaxy (roughly).

1.647 × 1028 M: mass of ordinary matter in the observable universe (atoms and other familiar stuff) (very roughly)

3.349 × 1029 M: mass of the observable universe, including weird stuff like dark matter and dark energy (very roughly)

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astronomy, image, pixel art, science, short, Space, Uncategorized

Pixel Solar System

pixel-solar-system-grid

(Click for full view.)

(Don’t worry. I’ve got one more bit of pixel art on the back burner, and after that, I’ll give it a break for a while.)

This is our solar system. Each pixel represents one astronomical unit, which is the average distance between Earth and Sun: 1 AU, 150 million kilometers, 93.0 million miles, 8 light-minutes and 19 light-seconds, 35,661 United States diameters, 389 times the Earth-Moon distance, or a 326-year road trip, if you drive 12 hours a day every day at roughly highway speed. Each row is 1000 pixels (1000 AU) across, and the slices are stacked so they fit in a reasonably-shaped image.

At the top-left of the image is a yellow dot representing the Sun. Mercury and Venus aren’t visible in this image. The next major body is the blue dot representing the Earth. Next comes a red dot representing Mars. Then Jupiter (peachy orange), Saturn (a salmon-pink color, which is two pixels wide because the difference between Saturn’s closest and furthest distance from the Sun is just about 1 AU), Uranus (cyan, elongated for the same reason), Neptune (deep-blue), Pluto (brick-red, extending slightly within the orbit of Neptune and extending significantly farther out), Sedna (a slightly unpleasant brownish), the Voyager 2 probe (yellow, inside the stripe for Sedna), Planet Nine (purple, if it exists; the orbits are quite approximate and overlap a fair bit with Sedna’s orbit). Then comes the Oort Cloud (light-blue), which extends ridiculously far and may be where some of our comets come from. After a large gap comes Proxima Centauri, the nearest (known) star, in orange. Alpha Centauri (the nearest star system known to host a planet) comes surprisingly far down, in yellow. All told, the image covers just over 5 light-years.

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geology, image, physics, science, short

Pixel Earth 1

I present you: a scale model of the Earth’s surface, from an altitude of 400 kilometers down to a depth of 300 kilometers. At this scale, every pixel is 1 km by 1 km.crust-1-px-eq-1-km-numbered-large

 

Legend:

  1. The International Space Station at perigee.
  2. The aurora borealis.
  3. The greatest altitude at which human beings have died: cosmonoauts Georgy Dobrovolsky, Vladislav Volkov, and Viktor Patsayev died just before the reentry of Soyuz 11, when the explosive decoupling of the descent module opened an oxygen seal in the cockpit.
  4. The highest altitude reached by the Air Force’s X-15, which still holds the speed record for a crewed aircraft, and which was among the first crewed vehicles to cross into space.
  5. The official edge of space: the Kármán line, at around 100 kilometers’ altitude. Above this line, you have to move faster than orbital velocity for wings to provide usable lift, so you might as well just orbit.
  6. The streak denotes the range of altitudes at which meteors glow.
  7. The streak denotes the altitudes at which the 2013 Chelyabinsk meteorite glowed. The starburst denotes the approximate altitude at which it exploded.
  8. The altitude at which the Space Shuttle Columbia stopped sending telemetry and began its final breakup.
  9. On a less sad note: the altitude from which Felix Baumgartner began his famous skydive.
  10. The top of the troposphere (where weather happens); the beginning of the stratosphere; the top of thunderstorms in middle and tropical1 latitudes.
  11. 10,000 meters: the altitude at which passenger airplanes cruise.
  12. The summit of Mt. Everest.
  13. The Challenger Deep (over 10,000 meters deep).
  14. The deepest active mining operation: 4,000 meters, at the Mpomeng gold mine in South Africa.
  15. The deepest human beings have ever drilled: 12 kilometers at the Kola Superdeep Borehole, in Russia.
  16. The deepest confirmed location in a natural cave: 2 km, in Krubera Cave, in Abkhazia, Georgia (the Eastern European Georgia, not the American one.) The cave very likely goes deeper.
  17. Volcanic magma chambers. Contrary to popular belief, most of the mantle is a plastic solid (like very, very stiff Silly Putty), rather than molten. Magma is the exception. The magma chamber that feeds Hawai’i’s volcanoes is on the shallow end of the spectrum. The magma chamber underneath the Yellowstone Caldera (which provides heat for Yellowstone’s famous geysers) sits at around 25 to 35 kilometers deep. We have actual rough maps of it. It’s awesome.
  18. The Mohorovičić discontinuity (or Moho; no, not the KSP one): the official boundary between crust and mantle. It can be as shallow as 5 kilometers deep (beneath the seafloor) and 90 kilometers deep (under mountains); it averages 35 kilometers deep.
  19. Very deep magma chambers.
  20. The end of the asthenosphere, a region of rock made weak and squishy (relatively speaking) by the enormous temperature and pressure. This starts beneath the solid crust (the lithosphere). Its boundary isn’t well-defined.
  21. A hot plume in the upper mantle. Droplets (well, droplet-sized compared to the whole Earth) of lower-melting-point material rise through the mantle to fill magma chambers.

(I should point out that I’m not a geologist. If I’ve made a mistake, please let me know. You won’t hurt my feelings. I’d rather admit I’m wrong than put out a misleading graphic.)

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image, short, Space

Earth versus Sun

Earth vs Sun at 1 AU.png

Nothing too special here: just a size comparison between the Earth and the Sun. The only difference from the usual ones, is that I’ve based their relative sizes on their angular diameters. For the Sun, I computed the angular diameter at a distance of 1 AU (which is how we see it here on Earth). For the Earth, I computed the angular diameter at a distance of 1 AU minus the diameter of the Sun. In other words, the Earth appears as large as it would if it were sitting at the point on the Solar surface nearest us. This is how the Earth would look as a very unfortunate close-transiting planet.

To paraphrase Carl Sagan: that little blue blob is home. That’s us. Everything that’s ever happened to you happened there.

Now consider that compared to the Sun…

Earth vs Sun Closeup.png

Here’s a closeup of the same image, showing the Earth compared to the weird convection granules on the Sun’s surface.

Both images are from NASA. The Solar image is from the Solar Dynamics Observatory (HMI intensitygram, February 7th, 2016), and the Earth-disk image is from the GOES earth-observing satellite.

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