Monday, August 10, 2020

Sunsets and mountains

Suddenly, I'm hiking again. The bug has bitten one of my housemates. We have been to the Lair O'the Bear, between Morrison and Kitteridge, Colorado the last two weekends. At the western end of Bear Creek Canyon, it's a short drive from home and it's near a new favorite restaurant, the Switchback Smokehouse, in Kitteridge (they have an ice cream shop next door!), so it's a great destination for me.

I didn't get many photo-ops the first time. Everything's so big it's hard to get a good picture, but Panorama Point provides some workable views. Here are some of the pictures.


Maidenhair ferns

Penstemon. The main wildflower season is done, but there are still some nice surprises out there. We also saw a lot of anemones but they looked pretty tired.


I don't know why there are things in this tree but it makes an interesting subject. There may have been people rappelling off the Point.


View to the southwest

Kitteridge and, in the distance, Mount Evans


I've also picked up some nice shots from home.

An airplane. We're near Centennial Airport and get a lot of air traffic over our house.

The sunsets have been nice recently.

I'm still working on physics and astronomy excursions and should have something to show for it soon. In the meantime, keep exercising that camera.

Saturday, July 25, 2020

Clouds

"I've looked at clouds from both sides now"
Joni Mitchell


Lenticular clouds in Centennial, Colorado.

People have looked for images in clouds for at least as long as humanity has been recording it's activities.

I lived most of my life in the Southeast United States leaving only for a construction job in Montana, four trips to or through Denver (and the states I passed through on the way), and two seasons on a laybarge in the Gulf of Mexico. But I've seen some weather.

Every area has its distinctive weather. The reason we could predict our weather with any certainty in Alabama was that it was coming from where I live now, Colorado, and we had plenty of time to see it coming.

As each area has its characteristic weather, each has its characteristic clouds.

The massive high-topped thunderheads with anvil shaped tops are rare here. We get a lot more hail; they get a lot more tornadoes. They also get hurricanes.

We get these weird lenticular clouds like the ones in the picture above.

As air flows across the Rockies and out over the plains, it can set off standing waves, like those that form when a person blows across the top of a soda bottle. At the bottom of the waves, the air is warm and can hold moisture as invisible vapor, but when the air is carried to the top of the waves, it cools off and releases the water as cloud droplets. A person from the east might think "rain coming," but these are actually stable weather clouds, like the big fluffy cumulus clouds of the Southern summer.

Those Southern cumulus clouds could build up into far from stable cumulonimbus clouds. I had one drop a tornado into a farmer's field next to where I was driving once. I didn't usually speed. I did that time. Clouds can cause you to get excited.

I was driving near Tuskegee, Alabama on I 75 and there was this huge thunderhead over me. The bottom was flat and it looked like I could reach up and touch it. It was electric blue. There was so much water in the cloud that it piped the color of the sky above it right down to the bottom. That's the kind of cloud that can drop a tornado down right on top of you without any warning.

The funny thing is that I saw so much storm activity before I became a storm watcher about five years before my retirement and never saw sign of another tornado, not even during the disastrous outbreak of 2011.

One of the weirdest cloud formations I have ever seen were the hole-punch clouds one summer in Selma. An even sheet of clouds had big circular holes in it, all the way up to clear blue. We didn't know what caused them back then. It turns out that planes flying through clouds can cause droplets to coalesce, like when you put a drop of detergent in a bowl of greasy water.

The most beautiful display of weather I have seen was a very darkly overcast afternoon on a laybarge. There was a clear band on the horizon where the sun was setting blood red. It cast a red glow over the bottom of the clouds and there was a brilliant triple rainbow.

I've been chased up Mount Carbon three times by thunderstorms. Walking east from Morrison on the Bear Creek Trail carries you through a broad, treeless area of Bear Creek Lakes Park. With no cover behind me and no cover and a lung busting switchback before me, I heard a rumble at my back and turned to see massive black clouds boiling up over Mount Falcon. There was green-ness in them, indicating hail, which I didn't want on me, so I walked fast.

All three times I reached the shelter at Mountain View before the storm hit.

What causes cloud colors. Well, I talked about sunrise and sunset clouds in the last blog. Why are clouds white and, of all colors, dark gray? Is water gray?

We talked about Rayleigh and Mei scattering last time. Mei scattering is caused by aerosols, particles that aren't molecules but they're still small enough to stay suspended in air. And remember that Mei scattering doesn't pick and choose specific wavelengths of light like Rayleigh scattering does, so it's not surprising when clouds are white, but gray?

A few years ago, I built a Joly Photometer. It's basically two chunks of paraffin separated by aluminum foil. Here it is.


If you put a standard light source on one side and a light source of unknown brightness on the other, then move the unknown source nearer or further away until both sides of the Photometer look the same, you can calculate from the difference in distances of the light sources from the photometer how bright the unknown source is.

But notice that the two halves, which are from the same slab of wax and, therefore, the same color, look different. The apparent color is from the white light illuminating the wax. The top slab is lit by more white light ..therefore, whiter.

Clouds are the same way. Less light makes its way down through the cloud so places with less light look less white and our eyes are rigged to emphasize contrasts so, next to the bright white of the tops of the cloud, the bottom sometimes looks positively black.

Notice that the gray parts of clouds are usually a cool gray until sunset. The blue of the sky also comes through misty clouds.

If you ever visit the Great Smoky Mountains, you will see that they, indeed, do look smokey. That area has always funneled aerosols in, hardwood tree pollen, smoke, and more recently, abundant industrial pollutants and they disperse white light efficiently. Add in the sky blue and there's smoky mountains.

Green clouds are a place where light has to pass through so much dispersion that all the blue is gone. Notice that it's a sorta dirty brown, meaning that light at the red end of the spectrum is there, too . Clouds with that much water and ice in them will often mean hail. I run from those! Mother Nature doesn't want me there.

Hail forms in clouds with strong updrafts. High up in cumulonimbus clouds, water freezes into tiny ice crystals until they are too heavy to remain suspended in the air and then they start to fall, but they get caught in the updraft and are blown back up. They pick up more moisture and freeze another layer. These little balls of ice will ride winds up and down until they're no longer little balls of ice. When they finally fall to the ground, they can be destructively big balls of ice!

Cloud watching is a great pastime. You can get a good idea of what to expect of the weather in your area and, occasionally, you'll see something rare and spectacular!


Thursday, July 23, 2020

What about that sky color?

There are a couple of hints as to why the sky is blue that are easy to obtain.

First, look straight up through a polarized sunglasses lens. Rotate the lens and see what happens. You'll see it lighten and darken. Second, note that the sky is not always blue. There's a definite sequence of colors as the day progresses: reds and oranges, yellows, blues, then the reverse.

What polarizes light? Reflection! When light bounces off something, it comes off organized. That's what causes glare and glare is why there are polarized sunglasses to start with.

Light is sorta complicated and maybe you don't want the excruciating details, but, at base, it's a wave (like ocean waves) made up of electric and magnetic fields. The fields move at right angles to each other. The waves can be oriented in any direction and they are when they leave the sun.

But when light hits a surface, whether it's a molecule or a lake, it's absorbed by the atoms in the surface. Some of the atoms send out light when they calm down, sometimes in a different color but often unchanged. Different materials are better at this than others. That's why metals reflect better than glass.

But the gas molecules in the atmosphere absorb and re-emit sunlight and the light they re-emit is polarized. Although molecules tend to be neutrally charged overall, most of them have different charges in different places. Remember that like charges repel so molecules next to each other tend to drive each other's electrons away from each other. So molecules tend to organize themselves. I say "tend to" because it's not a strong phenomenon and not all the molecules in air are lined up like a high school marching band. But light coming off these molecules also tends to be lined up. It's called Rayleigh scattering.

Here's a shot of the sky through a polarizing filter.


After turning the filter ninety degrees, it looks like this.


Notice the gradation of light toward the sun. There is another kind of scattering in the atmosphere. Mie scattering is from larger particles: dust and other aerosols like water droplets. A big difference between Mie and Rayleigh scattering is that Rayleigh scattering is affected by light wavelengths. The shorter wavelengths (violet, indigo, blue) are scattered more than the longer wavelengths (red, orange, yellow). Mie scattering disperses all the colors about the same. 

Space is black and the sun is almost white. As sunlight comes into our atmosphere, ultraviolet (eaten up largely by ozone in the upper atmosphere), violet, and indigo goes first. What reaches us is blue. As a spot on the Earth rotates away from the sun, light has to travel through more atmosphere to reach it. Green drops out, but you can't see much green since it's still mixed with a lot of blue. Yellow drops out, and then you get the oranges and reds of the sunset.

Keep in mind that the same sun creating beautiful sunsets over the Rockies is creating a blue California sky at the same time.
The sky closer to the sun looks whiter due to Mie scattering. So that's why the sky looks blue...and white and orange and red…

So, using color filters.

Filters have a coding system that looks rather arcane. I mentioned it in the last blog. The filter I used was a CTO ¼ 6500 to 4500 K ½ f/stop gel correction filter.

CTO stands for "color temperature orange". There are also CTB (color temperature blue) and "plus green" or "minus green" filters. CTB filters are specifically there to make tungsten light look like sunlight. They "cool down" yellowish light. CTB does the opposite. I wanted to take blue out of my picture so I needed a warmer filter. ¼ is just the strength of the color change. ¼ is a light colored filter.

The K number is color temperature. All bodies above absolute zero have molecules that vibrate - that's what heat is - vibrating molecules. And if molecules are vibrating, so are the charges within them. Moving charges are what causes magnetic fields. Moving magnetic fields create electric fields and when magnetic and electric fields start moving together, you get electromagnetic fields - light.

Relatively cool bodies like a summer sidewalk (see my blog for Friday, August 30, 2019, "Trail temperature vs. air temperature") might seem hot, but they're not hot enough to glow. But they are giving off light in the invisible, infrared range.  Infrared light is how heat is radiated because when infrared light hits matter, the matter heats up. 

As objects get hotter, they begin to glow a dull red, then orange, then yellow, then blue, and then they go white. The K number in filters stands for "Kelvin" as in "Lord Kelvin" after whom the Kelvin temperature scale, preferred by scientists, is named. The K number is the color that most closely resembles the color given off by a hot body around that temperature. A hot body from 6500 K to 4500 K will give off a yellow color. Larger numbers denote bluer colors, smaller numbers mean redder colors.

The f/stop is how much light the filter lets through. On a camera, the f-stop is the ratio of the lens' focal length to the diameter of the aperture. That might sound complicated but remember that the camera's focal length is related to its light gathering power and the larger the aperture, the more light can get in, so the smaller the f/stop number, the larger the aperture, and the more light is passed through.

An f/stop of ½ does not mean that half the light gets through. It's actually a very light filter that lets a lot of light through. An f/stop of, say, 8 would be much darker.

Correction or compensation filters tend to be pretty light. There are also color filters that are intended to really alter the color of photographs for special effects. They cut out a lot more light in specific colors. There are also neutral filters that just cut light in all wavelengths, polarizing filters, and special effects filters like diffraction gratings that give you rainbows.

Some photographic filters are made of glass or thick plastic. Gels are thin plastic films. I like them because they're inexpensive but they do the job and the thicker filters are harder to mount on my cell phone. I just slip the gel between my camera lens and the phone case and I'm ready to go.

The sky is what you have to look through to do astronomy so, if you're interested in sky watching, it behooves you to understand the weather.

Wednesday, July 22, 2020

Can I trust my phone? Part 2

A while back, I downloaded an app that would do spectrometry. It would split light coming into the camera into its constituent "rainbow", which is cool since that is a way to analyze a substance. Each element has a rainbow fingerprint.

I was excited! I wondered if the representations of incandescent elements on the Internet would be true enough to create a faithful spectrum, so Zi pulled up a picture of a hydrogen lamp and looked at it with the spectrometer. Hydrogen has a very well known spectrum so I knew what it was supposed to look like. 

Wow! It looked great!...except…why was all that blue there? Hydrogen isn't supposed to have that big blue spike at the left end of it's rainbow.

I took my phone outside and looked at the sky through it's camera  Wow! Blue skies smilin' at me...way too blue skies, did I see. I was blue. I dumped the app.

It wasn't the app's fault. Phone cameras are made to produce pretty pictures and bluer skies are prettier. But they're not true blue and science looks for truth.

My son suggested that I use a yellow filter to remove some of the blue coming into the camera and then use the color balance on the camera to get back to true color, and it worked! On the hydrogen spectrum, it worked, but on everything else, it removed so much blue that I couldn't put any back in. blue again!

But recently I bought a packet of Selens Flight Flash Color Strobist Lighting Gel filters. Gels are plastic films. Less expensive than glass photographic filters, they're often used as compensation filters for different light sources. Slipping the ¼ CTO 6500 to 4500 K lightly yellow correction filter over the camera lens, between the phone and it's case did a great job. I used the SnailCamera Pro app, which gives me considerable color balance control to rebalance the picture and I "eyeballed" it until it looked right.

Here's what the camera saw without the picture.


Here's what the scene actually looked like.


Okay, a caveat. The colors were right but I lost some detail. The individual stones in the chimney lost some definition, but right now I'm more concerned with color values. I think some contrast adjustment could get some, if not all, of the definition back.

But I am impressed with the light capturing abilities of modern cell phones. Here are some early evening pictures I took.


A nice sunset


The same shot after the sun had gone away.


A star. Vega. I could not have seen that with my last cellphone camera.

Cell phones offer a lot of power to record your world but know your instrument. It's primary purposes are communication and entertainment. Accurate records require some finagling.

Wednesday, July 1, 2020

Interlude

From the instant of its creation, the universe has been in the process of running down. It's called "entropy". To quote African writer Achinua Achebe and Irish poet William Butler Yeats, "Things fall apart." Except for some miracle - a Big Crunch or the Creator's decision that it's time to wipe the old slate clean and create a new, the inexorable March to uniformity will lead, in a few billion years, to a vast ocean of hydrogen, atoms so far separated that there will be no opportunity for them to crash together to form anything more complex.

But there is turbulence in time. Diversity feeds on itself. As long as things actively fall apart, they also fall together. There are swirls in entropy that pushes it, through sheer momentum against itself. One quality of living things is that they transform. They create order out of disorder. The inert dust and muck around us fall together, against all probability, to form...us.

Life isn't the only builder. There's also chaos. Nature decrees that matter attracts matter and, when enough gas and dust is pulled together, the crushing results begin compacting hydrogen into helium and then larger atoms, under fantastic heat, until the energy is expended. The heaviest element that can be created in a star is iron, but the death throes of a star, the nova, is incredibly energetic, crushing even more atoms together to form brilliant spectacles in the sky, destroying everything in the cosmic neighborhood, and blowing out clouds of element rich dust to settle down on the universe.

The dust we see in a sun beam is mostly the detritus of life - dead microorganisms, and in our homes, skin cells sloughed off our own bodies and the tiny creatures that eat them. But a significant portion is micrometeorites, much of it, that fine dust blown out by dying stars. Over millions of years it has settled on Earth along with the usual products of erosion and, in the molten mix of tectonic plates, heavy elements concentrate in globs of magma to be extruded in cracks near (in geological terms) the surface where it can cool into rich veins of ore.

It might have happened in the crash of two such plates in the Earth's crust that buckled, what would be North America, thousands of feet upward to form the Colorado plateau. Or maybe before. That wasn't the first time the crust had been buckled around here. The Appalachians once rivaled the Himalayas in grandeur but, over time, they were worn down to the narrow band of mountains they are today. The Ozarks had their time.

But time has been working on the Wild West, too, eroding the smooth skyland of Colorado into deep ravines between towering mountains, dissolving ore veins into acidic, carbon dioxide rich lakes (the product of acid rains and dying organisms) where lead precipitated out into insoluble lead carbonate, cerussite, carrying other heavy elements with it, including silver. 

Nature values nothing. She just acts. But the new (in geological terms) animal invading the continent of North America brought a brain that valued much, especially that which is rare and that which glitters...and silver is both rare and glittery. Those that came from the east recognized the white sands below the highest mountain of the North American Rockies, Mount Elbert, to be composed of cerussite and understood that it often carries silver.

When that was confirmed, the new town of Leadville, Colorado, founded in 1860, began attracting miners and miners attracted other civilized creatures like the faro dealing Doc Holliday, fellow Georgian turned Coloradan (he's now buried in Glenwood Springs), and the unsinkable Molly Brown...

and myself. Yesterday, two friends and I, taking a break from stargazing and pendulum watching, traveled to this interesting little village below Mount Elbert to look at saloons and city halls preserved for posterity and tiny homes. And here are some pictures.


Mine dumps and mountains
The Old Church on Harrison Avenue and Mount Elbert.
Lake in the mountains

My personal transportation for several years has been the trains and buses around Denver but with Covid-19, I've avoided them since they require a mask and it's hard for me to get enough air through a mask.

I still walk to the shops in the area. There are always interesting things on the way.

One of my favorite wildflowers, the common milkweed, is blooming now.
Purple seems to be in vogue. This is Colorado and thistles are everywhere.

These rare gems are a variation of the Mallows that are everywhere. They're called "cowboy's delight" or "copper Mallows." It's strange to think of them so closely related to hollyhock, hibiscus, and marsh mallow (yes, marshmallows were originally a plant product, made by whipping up the thick, starchy solution from marsh mallow roots.)

We've been having moist air coming over the Rockies, giving us occasional rain storms to cool off our afternoons.
The public library has been closed for remodeling and now, with Covid 19, will it ever open? Stay tuned.

Much of our weather has a lot to do with the jet stream that shifts like an injured snake over us and the Rocky Mountains to the west. I've flown over the Rockies in a jet and from up there, they don't look quite so big and, after all, what's 14,000 foot mountains when the atmosphere is well over a million feet thick.

But when a tsunami is far out at sea, you can only measure a small change in the surface of the ocean. It's only when the depth changes that the sea turns into a great wall of water.

When air masses flow over the mountains and then out over the plains, they can set up vibrations. As the moist air moves upward, it cools off and water condenses out in the form of clouds. The air at the bottom of the waves is clear.  We get interesting rows or hatches of clouds. Sometimes, they're said to look like UFOs. Technically, they're called "lenticular clouds" for their resemblance to lenses.


Little Dry Creek is up now. It's not a mountain Creek, so it's not from snow melt. It's being fed by the afternoon showers and there seems to be a lag time between the rain and the rise in water level. I'll have to check that out sometime.

All walks are interesting. If you stay aware of your surroundings, there will be plenty to engage you.


Sunday, June 14, 2020

Critical Thinking for Voters update

For those following the Critical Thinking for Voters Ebook, I have corrected some past typos and added a chapter about fallacies. It isn't a manual on fallacies, basically a "what to look for" briefer with references to deepen your knowledge. I try not to be partisan or judgmental and try to stay away from contemporary illustrations (but sometimes it's just to tempting.)

Actually, fallacy watching would make a great family hobby right now. Turn on the latest political debate, pull up the wikipedia List of Fallacies article and start marking them off as you hear them.

"That's a red herring."
"Ah, too common. Not worth many points. That one was an interesting slippery slope, though."
"Wait a minute. Was that a fallacy of ambiguity? I think it was!"
"What kind is it?"
"Wait. I'll check.....Equivocation......That's an ambiguity in the middle term! Wow! That's an ambiguity in the middle term! That's gotta be worth 75 points at least! High five everybody!"

They ought to have a television kit for sale somewhere!

Friday, May 29, 2020

Can I trust my phone?

Recently, I was checking some of my past measurements and I found the latitude and longitude I recorded at The Bluffs to be off by about 130 miles. (I checked the GPS recording from the Physics Toolbox Pro with the latitude and longitude from Google Maps.) That's a tiny error in respect to the circumference of the earth. I still calculated that to within 1.01% on the same hike. But it would be pretty bad if I were telling someone where to meet me!

So I wondered how my other phone sensors perform. After all, the inside of a smartphone is a noisy place with so much electronics packed into such a tiny space building up heat, and so much energy swirling around in my urban setting. I decided to check my magnetometer so I set my phone in a quiet place (in my bedroom) using the Science Journal to record magnetic fields and left it for about an hour.

Here's the recording.


Not a lot of detail here but there are a few things that jump out at me. The first, oh, 23 minutes are rather "fuzzy" and then the tracing settles down into a nice flat line. After that, there are a few spikes somewhat larger than the earlier fuzz; then, at the end (maybe give minutes), the tracing drops and suddenly jumps up).

I don't see any drift. In other words, the tracing doesn't seem to drift up or down over time.

I am going to guess that the early fuzziness is internal noise as my magnetometer adapts to internal noise in the phone. Is the noise enough to worry about? Well, all instruments have errors, even manual tools like rulers and scales react to environmental noises like changes in heat and drafts. To check how much the tracing moved around, I saved the tracing as a comma separated values (cvs) file and loaded it into my DANSYS statistical spreadsheet. All I needed to check was the range of values in a section of the tracing.

The range here is 0.0165 μT. The average field strength is 52 μT (these figures are x10). The standard deviation is 0.028 μT. That last figure indicates that 66% of the samples will deviate from the average of 52 μT by only 0.028 μT, and 98% will deviate by 0.056 μT. I can live with that!.

The 52 μT background field strength is very close to what I found and reported in the Earth Specs blog. That's pretty close to the normal field strength of the Earth's magnetic field (25 to 65 μT).

By the way, background magnetism isn't constant over the Earth's surface. Dense rock and metal content in the Earth's crust can concentrate the magnetic field in certain areas much like iron cores in transformers and electromagnets can concentrate the magnetic field produced by an electric coil. This fact can be used by prospectors to find ore deposits and the magnetometer has long been in the prospector's tool chest. This close to the Front Range of the Rocky Mountains, it doesn't surprise me that the magnetic field strength is toward the upper range of Earth's background magnetism.

As for the spikes in the last half of the tracing, those do not surprise me either. The air system clicked on a couple of times while I was recording and electric relays and motors can kick out some heavy fields.

You always have to be concerned about the accuracy and reliability of your instruments. Different phones will have different sensors and driver circuits. You might want to check out your sensors. NASA has a cool book called "A Guide to Smartphone Sensor." It's a free download and you can get it here:



Monday, May 18, 2020

Earth's specs

Somewhen in the 200s BC, a Greek named Eratosthenes measured the circumference of the Earth. He worked and lived in Alexandria, Egypt and knew of a place in Syrene, Egypt where, on the summer solstice, the image of the sun could be seen in a deep well, meaning that the sun was directly overhead. That placed Syrene on the equator. 

Eratosthenes assumed the Earth to be a sphere. If that were true, he reasoned that, if he stuck a rod in the ground vertically, it's line could be extended straight to the Earth's center to form an angle with a similar line from Syrene and that angle could easily be calculated. All he had to do was measure the angle formed of the line from the tip of the sun's shadow to the tip of the rod with the ground, subtract that from the 90° angle of the vertical rod with the ground, and he would have it...and "it" would also be Alexandria's latitude. It worked out to be about 7°.

By that time, everybody knew that the Earth was round and that the angular measure of any circle was 360°, and Eratosthenes knew that Alexandria was 5000 stadia from Syrene, he could figure out the circumference of a great circle on the Earth and, therefore, the Earth. His result was 250,000 stadia, or 39,385 kilometers, which is 1.4% off from the accurate circumference, 39,941 kilometers. Not too shabby!

So, on my recent hike to The Bluffs, I decided to do a modernized version of Eratosthenes' calculation.

The summer solstice was still a ways in the future so, not trusting nature to provide me with a good shot of the sun on demand, I measured the latitude and the distance between Arapahoe and Ridgegate Stations on the RTC southern light rail lines. I used Veiyra Software's Physics Toolbox Pro for the measurements. Here are the readouts.

Arapahoe Station

Ridgegate Station.

The distance, measured as the crow flies using Google Maps, is 5.6 miles or 9 kilometers.

"As the crow flies" is another way of saying "along a great circle on the globe," so I now have a way of converting degrees along the circumference of the Earth to kilometers and vice versa. By the way, I have it from a reputable source, namely, a crow, that crows do not always fly in straight lines.

The two stations are at almost the same longitude, so I can ignore that. The difference in latitude is .08 degrees.

But what about the stick in the ground? Well, that's another thing. It's called a gnomon and was a primary tool of ancient astronomers. It simply measured the angle of inclination of an astronomical object. Today we have astrolabes (basically a protractor with a plumb bob and a pointer) and the more advanced theodolite used by surveyors. I have a theodolite on my phone, the Dioptra app by Workshop512.

Since I really had all the information I needed, and I didn't know how far I was from the equator, I just wanted to do a modern version of Eratosthenes' trick to find my latitude by the sun. True to course, it was so cloudy on the summer equinox that I couldn't even tell which quadrant of the sky the sun was in, but I slapped a welder filter on my phone and took this shot from Dioptra the next day.


The angle of inclination was 51.1°, which was close to the actual measure on the equinox taken from the Time and Date website:


Solar noon was at 1:07.

Angle of inclination was 50.5°, which placed my latitude at 90°-50.5°=39.5° . Looking at the Toolbox measurements above, I'm off by less than a tenth of a degree. The Dioptra measurement, which is also GPS is 39.58, so it's close.

But back to the real thing. The difference in measured latitude was 0.08° which is 4 minutes and 48 seconds (There are 60 minutes in a degree and 60 seconds in a minute). If 0.08 degrees is the same as 9 kilometers, 1 degree is 112.5 kilometers.

Okay, breath held, the moment of truth….112.5 kilometers times 360 degrees is 40,500 kilometers. The actual value is 39,941 kilometers. I was off by 1.01% Wow! I just impressed myself!

Of course, along with all the measurement error and such, the Earth is only approximately a sphere. The radius at the equator is larger than the radiuses at the poles.

We know the circumference of the Earth. The approximate volume is easy. The volume of a sphere is π\6 times the diameter cubed. The diameter is the circumference divided by π. Working backward, the diameter is 12,714 kilometers. So the volume is right at 10 to the 12th power cubic kilometers.

Okay, mass...mass is a bear. You measure mass with a balance and standard mass (remember the blog about mass and weight?) But Earth does have a mass. How in Sam Hill would you figure it out?

Well, obviously, you can't use a balance so any measurement has to be indirect. The first measurement to within 1% was made in 1798 by Henry Cavendish as a spin off of his accurate measurement of the gravitational constant. He used a torsion balance to do that and I can't even approach that kind of precision at home, so I'll just tell you how he did it. 

Isaac Newton figured out that the force of attraction (gravity) between any  two masses is directly proportional to the difference between their masses, and inversely proportional to the square of the distance between them. But to come up with an actual measurement, a proportionality constant was needed. He called it the Universal Gravitational Constant and never found it's value.

About 70 years later, Cavendish did it. Imagine a long, vertical, thin, flexible rod. At the bottom end is another rod forming an inverted T. At the end of that rod are two balanced heavy masses. His masses were  .73 kilograms each. He could set the bottom rod spinning back and forth and measure a slight force inhibiting the motion by comparing the frequency of oscillation with and without the force. The force, of course, would be another large mass close to one of the chunks of lead on the torsion balance. He knew the masses he was working with, the separation between them, and Newton's formula, so he was ready to calculate the Universal Gravitational Constant.

It was 6.67408 x 10^-11 m^3kg^-1s^-2 .

Believe it or not, that's what we need to calculate the mass of the Earth. Using Newton's formula we need the acceleration due to gravity (we found that approximately fooling around with the smartphone's accelerometer), multiplied by the radius of the Earth squared (we know that), divided by the Gravitational Constant.

So let's do it. Square the Earth first. The diameter is 12714 km so the radius is 6357 km. We need that in meters so 6357 x 10^3 meters. Square that to get 4.04 x 10^13 meters squared. The acceleration due to gravity is 9.18 meters per second square so the numerator is 3.71 x 10^14. Now we divide that by our Gravitational Constant, 6.67408 x 10^-11 m^3kg^-1s^-2  to get 5.56 x 10^24 kg (the accurate figure is 5.972 x 10^24 kg).

Actually, Cavendish didn't report the mass of the Earth. He stopped one step short by publishing the density of Earth which was 5.45 grams per cubic centimeter. He probably figured that, from there, it was easy to multiply that times the volume of Earth so, eh, let someone else do the easy part. 

If we look around and figure out what proportion of Earth is made of light rocks, heavy rocks, water, air... and come up with an average density we would say that it's around (and people before Cavendish had done just that) 2.7 grams per cubic centimeter, so where does all that mass come from?

Well, obviously, there's more underneath our feet than meets the eye. In fact, the deepest we've ever been is 12,262 meters and, although that's pretty deep, it barely scratches the surface. Still, the researchers expected temperatures around 212 degrees Fahrenheit and what they got was 356 degrees. It's hot down there.

But two things convince us that the core of the Earth is iron-rich molten metal. One is the surprising density of Earth. The other is something you don't see a lot of in the solar system...magnetism.

Earth is a magnet. The sun and gas giants like Jupiter and Neptune have strong magnetic fields. Mercury has a weak field. Some of the moons (but not ours) seem to be magnetic, but most of the smaller planets are magnetically inert.

We've used compasses that rely on the Earth's magnetic field for a long time. It wasn't until 1600 that William Gilbert proposed that Earth is a magnet. In fact, Earth is not a permanent magnet. It's an electromagnet.

Moving electrons (current) generates magnetic fields and our rotating molten metal outer core is one humongous magnetic field generator.

Our planet is special. We are just the right size. If we were too big, gravity would squash us. Too small and we wouldn't have enough gravity to hold onto our atmosphere. We get just enough sunlight for a healthy biosphere. We have plenty of that rare commodity - water. A nice balance of plants and animals conditions our air. And we have an effective magnetic shield that shunts dangerous solar radiations around the planet and out into space.

When I bought my current phone, I made sure it had a magnetometer in addition to the other regular sensors. Phones with GPS receivers will provide fairly accurate compass readings, but a magnetometer is more accurate and you can use it to measure both magnetic fields and electrical currents.

My Android has a AK09918 triaxial magnetometer. Since it's triaxial, it measures field strength in three directions (like the accelerometers). There are two common kinds of magnetometers in smartphones: magnetoresistive and Hall Effect. The AKM is a Hall Effect sensor that uses a flat conductive plate. A magnetic field causes electrons to deviate from their path and polarizes the plate. That can be sensed as a potential difference across the plate.

About a week ago, I hiked down a mile of  Little Dry Creek trail and used the Physics Toolbox Pro to record magnetic fields. I walked almost due west so I was cutting across the magnetic field lines.

The strength of a magnetic field is measured in teslas (in this case, in microteslas). A tesla is equal to a weber per square meter, and a weber is a kilogram per square second. If you understand induction (it makes transformers work), webers involve how much voltage you can crank out with a magnetic field. So with microteslas, don't expect geomagnetic electric generating stations any time soon.

I recorded the magnetic field in three directions at a rate of one measurement per second. Since I had the phone in my shirt pocket, the x direction was right-left, y was up-down, and z was forward-backward. I then saved the several thousands readings in a csv (comma separated values) file that I could pick up with DANSYS, my statistical spreadsheet.

Here's a graph of the tracings.

The tracings are pretty fuzzy, indicating a lot of noise. The inside of a smartphone has lots of electrical components crowded together and heat from those and the outside. Noise is to be expected and when you're measuring on the order of micro-anything, you can expect noise to blur the lines. 

All the lines have big spikes but the z component has the most. That is my forward and backward direction and I was walking in an urban environment, so power lines, underground cables…. yeah. So that's not the Earth's magnetic field, right? 

Many scientists call this the anthropocene epoch because the biggest influence on the Earth's environment, for the first time, is a single species - humanity. Every stray magnetic field alters Earth's magnetic field locally. Have you ever tried to get a compass to work in a house? You're likely to find it somewhat off the magnetic north.

But, we can sense some trends. There is a noticeable difference between the start of my recording and the latter part. That's because I started at my home and walked a ways more or less north before turning west on the trail.

The green line gives us the total field strength. It's measuring around 50 to 75 microteslas. The normal background magnetic field strength runs around 25 to 65 microteslas, so we're well within that range (once we get away from the houses.) The local residue from residences doesn't seem to spread out very far. The trail is generally about 200 to 300 feet (as measured by Google Maps) from the nearest houses.

Geophysics is the study of the physical attributes of our planet. After the barriers between East and West came down in 1957, scientists took the opportunity to focus on Earth and instituted the International Geophysical Year. You can learn a lot more with a team than you can alone. Perhaps you can join with some interested neighbors and have a Geophysical Year of your own!

Friday, April 3, 2020

Critical Thinking for Voters

I don't and never have intended this blog as a place for political commentary, but the last presidential election and local elections since then have caused me concern on several points not the least being the disturbingly low turnout of eligible voters in the 2016 presidential election, evidently because voters in the United States do not believe that their votes matter.

I believe that their votes do matter - or can if they vote critically, and am working on an ebook, Critical Thinking for Voters. It's a work in progress but I am making it available as I finish chapters. It can be downloaded via the link in the sidebar of this blog.

Let me know what you think.

Wednesday, March 25, 2020

Photos during the time of ...

(With apologies to Mr. Gabriel Garcia Marquez)

Avoiding everything is getting old and is certainly cramping my style, but slowing the transmission of a novel virus has its points.

I've mostly been wandering around close to home. People are out socially distancing. It is certainly a time to be out observing social behavior under atypical circumstances.

How are people behaving around you? How are you reacting to the different situations?

I've been back to Fiddler's Green to see more of the statues and I walked down Little Dry Creek Trail to look at Holly Reservoir. Here are some photos.

A reminder of the old west in modern Arapahoe County.
That odd little mound near Arapahoe Station.
An ensemble at Plaza Tower One, Village Center. A bear, plates falling down and some logs.

The elephant puzzled me until I saw the mouse on the pavement in front of it.
Denver likes murals.
This wild boar looks like a matching statue over near Englewood Station. Much of the art in this area is also part of the Denver Museum of Open Air Art. 
This piece of modern art...well, I'll let the artist explain it….

Giraffes!
They're still working on Marjorie Park.

There are extravagant water features all around Denver. This one is at the apartments called "The Cascades". I suspect there's a little nose twerking of nature here in the high desert.


Pike's peak from Quebec.
Another consequence of the virus.
A photo I took of the sun through a welder filter. You know that photographing the sun directly will damage your digital camera, right?
Interesting tunnel under Arapahoe on Little Dry Creek Trail. It's blocked now but maybe later...
Little Dry Creek at Holly Park
Mount Evans from Holly Park. They're done nice views from this little park on Little Dry Creek Trail.
Holly Park
Although Little Dry Creek is almost never dry, Holly Reservoir usually is. Like many stream constructions in the area, Holly Reservoir is a buffer in case of flash floods.

If you want to hike the whole thing, Little Dry Creek Trail begins at Yosemite near Briarwood and Davies Streets and runs about 4 miles to the Highline Canal. It's a well maintained trail, easy at sections but the stretch along Arapahoe is a constant grade that can wear you out after a time. It grades up toward the east.

One of the socially acceptable activities during the time of The Virus is hiking. If you're into biking, that's okay, too.