Earth in space

We're on a rock whirling around the sun amid other rocks and space debris. It's a nice rock with water and plants and restaurants, but keep in mind that we're surrounded by vacuum and cold and, and space debris.

If you're sitting in your living room looking out your window, you can easily see the motion of that kid bicycling down the street, but what if you're in your car driving down the street. It's not so easy seeing your own motion 

We can see other planets and track their motions. Maybe we shouldn't be too incredulous about our ancestors that thought the Earth was the center of the universe and everything else whirled around Earth.

In a way, they were right. The whole Einsteinian revolution began with the idea that, in an inertial frame of reference it really doesn't matter whose point of view you take.

Hmmm...I'd better explain that "inertial frame of reference" thing. It's really important to modern physics. In an inertial frame of reference, everything is moving at a constant velocity. Different things might be moving at different velocities, but they're not speeding up, slowing down, or changing direction. It's "inertial" because the attribute of inertia is what causes matter to resist changes in velocity.

But Earth isn't in an inertial frame of reference, is it? It's in a circular orbit so it's constantly changing direction 

Well, yes, but it's orbit is huge and, if you look at one segment of it, the orbit looks like a straight line, so it's in an approximately inertial frame of reference locally.

So are we moving around the sun or is everything moving around us. Have you ever been in a vehicle and suddenly had the weird feeling that you and your vehicle was standing still and everything else was moving? You were having an Einsteinian moment.

So how do we choose? That's easy, we choose the most convenient option. Really! Yes! That's what physicists do. And it has proven very inconvenient to see everything as moving around us because if that were the case, Mars can be seen to spin its merry way around the sun, except when it decides to occasionally reverse course and go the opposite direction for a while before turning around and continuing it's journey in the right direction. Mars is a rock. It doesn't "decide".

If we're going around the sun like all the other planets, then we catch up with Mars, pass it and then watch it trail us. That makes a lot more sense.

But it's easy to watch Mars and see what it does, but how can we see what we're doing since it would be really hard for us to look back at us, what with all that vacuum, and cold, and lack of good restaurants.

Well, we have two options. We can watch what other planets are doing and assume that our planet works pretty much the same way, or we can watch what other planets' motions look like and figure out what our motion must be to make their motion look like that.

It's like a big puzzle, but all the pieces are there. We know, for instance, that the sun is in the same place in our sky about every 24 hours. Sunrise yesterday was at 6:49 am. Today it was at 6:48 am. Well, 23 hours, 59 minutes.

So we know that the Earth spins on its axis once every 23 hours and 59 minutes give or take a few seconds.

We also know that the sun takes 31,557,600 seconds (365.25 days of 86,400 seconds per day) for the sun to come back to the same place in the sky. That's how long it takes for the Earth to orbit around the sun.

Wait a minute (or about 60 seconds). How do we know that? Well, it's how we define a second, or how we used to define a second. Now we define a second as "the duration of 9,192,631,770 periods of the radiation corresponding to the transition between the two hyperfine levels of the ground state of the caesium-133 atom" according to Le Systeme international d'unites. Don't worry about it right now. I'm planning a whole blog or two on time later.

But how do I know when the sun is at the same place in the sky? Well, my analemma, of course! Here it is 

Do you see the figure 8?

Let me see if I can help.

I hate drawing on it. It took me a whole year to make it. It looks a little ragged but we moved in the middle of the year and I had to reorient it at the new place but I had the north-south bearing and level values, so it was close. If you want a clean one, a lot of big world globes have analemmas printed on them somewhere in the Pacific Ocean (the only place with enough room). Check your local library or geography classroom 

What I did was build a wooden block to sit astride our back fence. To the top, I tacked a sheet of paper and, in the middle, I drove a nail. On the first and thirtieth of each month (and a few other days), at 1:00 PM, I marked where the end of the shadow of the nail was. The pattern that formed is called an analemma. 

Our analemma looks different than an analemma in Alabama, where I used to live. I was surprised, when I moved to Denver from Selma, Alabama how much more the path of the sun each day lay down toward the southern horizon. We're only 506 miles north of Selma.

The figure 8 pattern tells us an important thing about the Earth. It's not on the level. What I mean is that the axis of rotation is not straight up and down in respect to the sun. We're tilted.

That's what causes the seasons. The sun's light hits us at a different slant at different parts of the globe. That spreads the heating sunlight out more in some places and concentrates it at others.

The only part of the globe where the sun is ever directly overhead is at the equator, and then only twice a year, solar noon on the equinoxes. As you travel further and further north, the sun "lays down further and further to the south. Notice that my analemma never crossed the nail and it's always on the north side. Above the Arctic Circle, there are times when the sun never sets. It just rides around the horizon. The Arctic Circle isn't fixed but it's currently a little north of 66° latitude.

The same kind of thing happens in the southern hemisphere except the path of the sun slants to the north. That means that, if you build a sundial, you have to take where you are on the globe into account. The analemma was once a very important tool for that reason. The width of the loops of the analemma provides the equation of time that allows a sundial maker to fine-tune their sundials so that they give accurate time.

You can also see the Earth's tilt at night. The path of the sun follows a straight band across the sky called the "ecliptic". It defined a flat platter extending out from the sun. All the visible planets, including us, and the moon "roll" around the platter like marbles on a dinner plate. 

It's tight. Everything stays within about 8° above or below the ecliptic  you can see it at night because that's where the band of constellations called "the zodiac" are.

Go out and find those constellations. If you're not familiar with them, download the Stellarium app. It shows where they are in your sky. You'll see that, although they follow the celestial equator in the night sky (the day sky, too, they're just not bright enough to be seen with the sun), you won't see them around the horizon. They'll be in a band tilting up into the sky unless it's the equinox and you're at the equator.

I could calculate the tilt from my analemma if I could have managed to keep it level and strictly oriented all year. Maybe you could manage that.

By the way, the Wikipedia has a cool article on the analemma with time elapsed photographs of the sun in the sky tracing an analemma and explanations of how it has been used as an astronomer's tool.

We can know a lot about Earth's rotation from direct observation of the sky. What about our orbit around the sun? Well, we already know how long it takes us to get around the sun. What about the shape of the orbit and it's radius?

That'll be in the next blog so stay tuned.

You can learn a lot about us by looking at the sky. The fact that there even is an "us" has a lot to do with where we are in the solar system and in our Milky Way Galaxy. If you haven't already installed Stellarium on your phone, go ahead. It's free. And go out and explore the sky. 

Physics in the playground V: Swinging

What would a playground be without swings? Well, it don't mean a thing if it ain't got that swing (Doo wah, Doo wah, Doo wah).

The Walnut Hills playgrounds have swings (I was tempted to say, "got swings" but this blog is rated S for "science" so….)

Anyway, here are the swings.

My plan was to swing 10 times, first sitting as still as possible, then with my 10 pound pack (I weighed it with a full water bladder), then pumping it to get more energy into the swing, and then pumping it erratically.

This, I think, is our first adventure with a pendulum. It won't be our last because pendulums are surprising.

I recorded all four swingings on one recording. The phone was on the breast pocket of my overalls so the x direction is left-right, the y direction is up-down, and the z direction is forward-backward.

There wasn't a lot of motion left-right, but there was some. That's a problem with studying pendulum motion. You often want the pendulum to swing in only one direction but that's easier said than done. We'll have to deal with that later when we look closer at oscillatory motion.

The y direction shows the up and down motions. Let's look a little closer at that.

That's not what I expected. I thought I would see nice, smooth wave (sine waves, if you're into trigonometry) going from zero (no motion means no acceleration, right?) to maximum acceleration at the bottom of my swings. It's easy to separate the swings because I specifically counted ten.

The reason I never got to zero acceleration is because, even at rest (and, as we will see over and over, nothing is ever really at rest in the universe) gravity is accelerating me downward. Here's a question. Does my phone accelerometers measure the motion of the Earth around the sun, or the sun's gravitational acceleration, or the sun's motion around the Galaxy?

That little dip at the top is a reminder that, try as I might, I could not sit perfectly still on the swing. As the swing began slowing at the bottom of each swing, I wobbled a little. If you've ever seen a chaos pendulum, the crazy swinging was an amplification of the complex motions there in all pendulums.

Noticed that more weight increased the wobble as I tried to sit still against the inertia of my backpack.

When I pumped the swing, the wobble shifted to the top of each swing where I slowed to a stop. I was leaning forward at the end of the forward swing and back at the end of the backward swing with the motion of the pendulum. You can see how this pattern built up.

There was no build up here, but it's hard to separate the wobble from the swing. I was pumping the swing without any particular timing.

The front to back motions showed an interesting thing. Each trial was ten swings. Check the time for each on the line below.

The swings when I tried to sit still took 26.5 seconds. The swings with a ten pound backpack took 26.7 seconds. When I was pumping the swing, it took 28.1 seconds. And when I was pumping erratically, it took 20.7 seconds to complete ten swings.

The difference in measured time between 10 swings without and with a 10 pound backpack was only 2 tenths of a second - for each swing, only 2 hundredths of a second. That difference could have been due to anything: the wind, a nervous twitch. Basically, a difference of 10 pounds didn't make any difference at all.

Pumping the swing did make a difference. When I pumped in time with the swing, each oscillation was longer, so it took 1.3 seconds longer for 10 swings. Still, a tenth of a second (actually, 0.13 second) for each swing is surprisingly small. The swinging of a pendulum is very stable. That's why they used pendulums in clocks for so long.

Did you expect the erratic swinging to take longer? The jerky motion meant that I couldn't get more altitude, I didn't swing as far, so it took less time - 20.7 seconds instead of 26.5 seconds. It did wear me out more, though. Another thing I learned was how out-of-shape I was from sitting around the month before.

Keep in mind how little difference extra weight caused on the pendulum. We'll be looking at more pendulums later and that's an important issue.

Playgrounds are physics laboratories. If you have one nearby, check it out (just don't interfere with the kiddies fun.) 

My heart can't handle the g-forces at an amusement park but, if you like the rides, you might take your smartphone and it's accelerometers for a wild ride. Let us know what you learn!

Physics in the playground-IV: Spinning

The phone clamp I use to mount my phone on things has two ¼" sockets, so I put a nut and lock washer on one of the eye bolts of a cable stretcher. Then I looped a 2 meter long cord through the other eye.

Since the bolt is standard ¼" hardware, it fit into the phone clamp and I fixed it securely with the lock washer.

With the phone, the whole assembly looked like this:

And then I could swing my old phone around my head on a cord. I recorded the process using Science Journal and the accelerometers in the phone and the recordings look like this.

There are some surprising things here, but the acceleration in the z direction isn't one of them. The recording shows that there's a downward acceleration averaging around -7 m/s/s. Since the acceleration due to gravity is 9.8 m/s/s, that's not too surprising considering that there has to be a balancing force keeping it up (the spin).

The acceleration in the x and y directions are a little counter intuitive. Acceleration in the y direction is negative. Velocity is in the positive direction so, frankly, I don't know why there should be a measured deceleration in the phone.

 A lot of people assume that velocity in a circular motion is along the diameter of the circle but that's not right. There's two components of motion. One is straight ahead. If you don't believe it, sling an object on a rope and let go of it. It won't continue in a curve, it will continue straight ahead.

The real shocker is the x recording (this one is correct). That negative 13 m/s/s  acceleration is inward along the cord. It's very tempting to think that the force (and thus the acceleration) on a spinning object is outward, but it's actually inward.

Think about it. If the acceleration were outward, that's where the phone would be going. The phone is constantly being pulled inward by the cord. Like Douglas Adams says, flying is throwing yourself at the Earth and missing. So is orbiting.

Physics textbooks used to talk about a "centrifugal force" which spun things outward in circular motion. If they talk about it any more, they call it an apparent, fictitious, or pseudo-force.

That stuff between seconds 20 and 24 is me pulling the cord in while I continued to spin the phone.

Keep in mind that this is just a preview. We'll be looking a lot closer at all these kinds of motion in future installments.

In the meantime, can anyone suggest why my y acceleration was negative?

I'm sorta stuck with the data until someone replicates it and says,"I got something different. Your phone's messed up." Scientists follow the data. So here's my hypothesis.

I tried to keep the velocity of the phone constant once I got it whirling. Obviously, I failed because constant velocity means zero acceleration. Remember that velocity involves two things, speed and direction. As long as direction is changing, velocity is also changing, regardless of the speed. Also notice that the tracing is spiky at the bottom of the y accelerometer recording. That means that, regardless of my attempt, the phone's speed around the circle wasn't even constant.

In order to keep the phone in motion, I had to pump energy into it, otherwise it would fall. I suspect that, at each revolution, I gave it a jerk forward and each time, it resisted. All these factors together added up to a negative acceleration that I had to work against to keep the phone spinning.

Also notice that the phone accelerometers have a maximum. They clip measurements at -20 m/s/s. 

So, if you have any other ideas, send me a comment. There's a button at the bottom of the blog post that lets you do that. (If you're on a phone, you might have to change to the computer version of the blog.)

Spinning things on cords - gas powered airplanes, slingshot, or just a ball on a rope - can be lots of fun, especially if you pay attention to what's going on, what's pulling what, and where things go when you let go.

Physics in the playground III: Crash on a spiral slide

There was a spiral slide in the playground - in fact, this spiral slide.

I sent this cart:

(remember it?) with my old phone clamped to it, down the slide. Of course, being top heavy, it turned over when it hit the first twist.

The old phone also has Science Journal on it, so I recorded it's disastrous descent. Here's the recording.

It's pretty obvious that there were two big crashes and you can probably guess where they were by looking at the top photo. 

Remember that the x direction is left-right. If you were in the cart, you would have been thrown to one side when the cart hit the side of the slide but, when it flipped, you would have been on the other side and would have been thrown that way. The tracings show those spikes, first in the positive direction, and then in the negative.

The y (forward-back) tracing shows a lot of deceleration, but gravity is still working so, as soon as the cart comes away from the side, it continues it's downward acceleration.

The z direction is the direction of spin and, what might confuse some folks is that most of the acceleration is toward the center of spin. Wait and see what happens when I put the phone on a rope and spin it around my head!

A nice thing about these tracings is that they can be spread out to see details. Let's look at the second crash from the x tracing.

There's a lot of vibration happening here on the order of about five spikes per second.

This is the kind of data that engineers get when they study things like crash tests and black boxes from planes that have crashed.

We'll be looking a lot closer at these motions in future blogs. This is just a preview!

Keep in mind that I'm not crashing my new phone - the one I use for a phone - down crash courses, but it's nice to have an old smartphone that I can still use as a pocket computer. It's holding up well under the abuse, but I'm also pretty careful not to overdo it. For instance, I won't just throw it as hard as I can against a tree.

Next time, we'll see what happens when something spins around at the end of a rope. Expect g-forces.

Physics in the playground II: The tree

There's a tree standing in the Walnut Hills Park playground ( one of the playgrounds, that is). I think it's some kind of fruit tree but there are no leaves on it and I'm not a tree identification expert. Here's the tree.

The real reason I did this was the new app I downloaded. Dioptra is a software version of my surveyor's compass. It gives me all the angles utilizing the accelerometers and the magnetometers in my phone.

We looked at the accelerometers last time.

Phones that have  built-in magnetometers use them for an onboard compass. Apps like Science Journal can use them to directly measure magnetic and electric fields.

Magnetometers in phones usually sense changes in conductivity in tiny electronic devices when they are exposed to a magnetic field. 

The phone has three magnetometers in one and they're aligned, just like the accelerometers along the x, y, and z planes, so the phone can sense the direction of a magnetic field.

Here's what the Dioptra screen looks like.

I aim with the crosshairs and the scales tell me directions. The curved scale on the left is a level. It tells me how much the phone is tilting. The data above it gives me my position in space and time: date and time, latitude and longitude, altitude, and error (CEP stands for circular error probable. For those in statistics, it's a 50% confidence interval for measurements within a circle.) I can set the app for different units.

The scale at the bottom is the compass reading for line-of-sight and the numbers above it makes it explicit. Those are the azimuth and bearings. Azimuth is the degrees of the angle between line-of-sight and due north. The bearing is the same in compass directions.

The scale to the right is the incline of the sight-line to horizontal. So, here's my sight-line to the tree top.

The phone is 4 degrees off level...ah, who cares. The location data is not important to what I'm doing, so I'll ignore it.  The GPS data could be as much as 30 feet off. That won't affect the accelerometers. My line-of-sight, just in case you're interested, is nearly southwest, 232 degrees from North and 52 degrees southwest,

but that won't play in our calculations either.

What I need is the inclination, which is 43.6 degrees from horizontal. You might have noticed that I have a tape measure in the first photo above. I was 20 feet from the base of the tree when I shot this line. That means that I have a right triangle with a base (adjacent side to my position) of 20 feet and the angle where I stood was 43.6 degrees. What I want is the length of the opposite side (height of tree). I can get that in several ways but I think I'll go with tan(angle)=opposite side/adjacent side. That shuffles around to opposite side=tan(angle) times adjacent side, or the length I want is the tangent of 43.6 degrees times 20 feet.

The height of the tree above my eye level is 19.05 feet. My eye level is 5.5 feet off the ground so that makes the tree 24.5 feet high.

I did the calculations on my MC50 calculator app.

The Dioptra app is put out by Workshop512 and the MC50 calculator by Walter Stubbs.

It's pretty impressive what phone apps will do. If you need your phone to do something that it doesn't already do, check your app store. Check out the rating, reviews, and app description before downloading. Advertisements are not usually a big problem but some of these apps are clogged up with ads. Some of the apps have a price and some are free but have a better version that you can buy. The prices are usually very reasonable.

Next time, I send a phone down a spiral ramp on a crash course.

Although the Dioptra app does everything my surveyor's compass does, I'm not ready to get rid of the compass. In the first place, it's very small. Also, it will never need a battery change or charge.

Physics in the playground, part 1

Pendulums, ramps, levers, towers - what better place to see physics in action than a playground? It's a veritable mechanics laboratory!

This playground is nearby in Walnut Hills Park so I threw my pack of gadgets on and headed out to do some light demonstrations of motion and how to measure it using a smartphone.

[Playground at Walnut Hills Park]

First, I hiked up Davies Street to Yosemite. I needed an approach to the playground, not to make a grand entrance, but to measure linear motion on the trail. I have several apps on my phone to do that, but I chose the AllTrails and Science Journal apps. AllTrails uses GPS information to record a lot of information about a hike, and the Science Journal taps the phone's accelerometers to measure...well, acceleration.

The path through Walnut Hills Park and, consequently, the Little Dry Creek Trail begins at Yosemite Street between Davies Street and Briarwood Street. I started there, recording my progress downhill to the playground.

In physics, there are three fundamental measurements - position, time, and number (count). Everything else: force, temperature, voltage, current, illumination, ultimately boils down to those three. 

Distance is established by two points. It has direction and time might also (have direction, that is.) You establish direction by setting up an arbitrary frame of reference. It can be any frame of reference, but the best is the most convenient. When you're working with geographic positions and distances, the most convenient is usually the longitude-latitude system used by mariners and surveyors.

Here are some pictures.

Science Journal uses the sensors in my phone to record things. Here, it's recording my motion as I walk down the trail. Note! It's not recording distance, and it's not recording speed. It's recording acceleration. It's limited to the sensors available in the phone and it can receive signals from a Bluetooth instrument like my Arduino, Bluetooth multimeter, or camera shutter release. What it has to record motion is the accelerometers in my phone. Accelerometers measure acceleration...period.

Some phones have gyroscopes to measure motion - mine doesn't. 

Acceleration is the rate at which velocity changes. Say you're traveling at 30 miles per hour in a car down a city street. 30 miles per hour is your speed. In one hour, you'll have traveled 30 miles (assuming your speed doesn't change). 30 miles per hour north, north west is a velocity. Velocity is a vector quantity which means that there's two things to keep up with - speed and direction. If you change speed from 30 miles an hour to 40 miles and hour, you have accelerated. Acceleration is measured as distance per time (velocity) per time. If you keep a speed of 30 miles per hour but you turn a corner and at now going due north, you have still accelerated. Direction matters.

You might have heard of nanotechnology, machines that you have to use a powerful microscope to see? Well, phone accelerometers are nanotechnology. But they work the same way you feel a change in speed or direction in a car. When the phone's motion changes, a tiny weighted arm in the accelerometer leans a little, just like you do, and the electronics can pick up that tilt and translate it into a measurement of how big a change there was.

There are three accelerometers in a phone. They measure acceleration in three directions. They're used to tell the phone if you're holding it right side up, sideways, or upside down.

The accelerometers are usually labeled x, y, and z. Do you remember high school algebra and all those graphs you had to draw? That can help you remember which accelerometer is which. Picture a graph on the face of your phone. The x accelerometer measures motion in the direction along the x axis. The y accelerometer measures direction along the y axis. And the z accelerometer measures directions at a right angle to the face of the phone..

I had my phone in the front breast pocket of my overalls so x was left-right, y was up-down, and z was forward-backward. I just show the output of the y and z accelerometers here because x is boring. I just went straight ahead.

Scientists (and the Science Journal) measures acceleration in meters per second per second (meters per second squared or m/s2). That means that, if I'm walking a meter per second (a decent clip) and I speed up in a second to two meters per second, I will have accelerated one meter per second squared.

My smallest acceleration in the y direction on the walk was -5.7 m/s2. That's -5.7 m/s2  downward. My maximum y acceleration was 39 m/s2 . That jolt will be explained in a minute. My average acceleration was 8.9  m/s2 . Why was I moving up and down at all?

Let's spread out the tracing and see what it looks like.

That's the up and down motion of my steps. Those double blips are the profiles of my steps and they are how pedometer apps can count my steps to figure out how far I've walked.

My forward and backward motion ranged from -12 to 18 m/s2 . Those spikes in the middle of the tracings (and in the y direction) was when I started walking backwards and then started walking forward again. See acceleration is directional!

Otherwise, I kept my velocity pretty constant. My average acceleration was only 2.7 m/s2 .

A nice thing about the Science Journal recording is that I can go back to it and do things like move my stylus along the tracing to see exactly what the measurement was at any particular time in the recording.

The AllTrails app recorded my distance, the time of the walk, and the elevation. How did it do that!? The phone can keep track of time, certainly. It has a clock, like all computers, but distance?

Some phones have a barometer built in that keeps up with atmospheric pressure (for weather measurements) and because pressure decreases predictably as altitude increases, it can measure altitude. My phone doesn't have a barometer, but it can receive signals from the Global Positioning System satellites orbiting the Earth - the same satellites that send signals to the GPS system in some cars. It can pinpoint the position of the phone to within a few feet. Altitude is a little less accurate, but okay for my purposes.

I walked 0.3 mile in 5 minutes and 23 seconds for a speed of about 0.05 miles a minute or 3.3 miles an hour almost due west (see the mountains below? In Denver, the mountains are west.). That's a fast walk. I usually walk 2 or 3 miles/hour. I had an altitude loss of about 40 feet. Those are 40 foot contours on the map. The elevation profile shows a loss of 50 feet. There's an error of about 10 feet. 

After arriving at the playground, I measured the height of a tree, crashed a cart on a spiral slide, and swang on a swing. What fun! To be continued!

If you have a cellphone, you probably have accelerometers and the Science Journal is a free download developed by the folks at Google. There are also free pedometer apps online. AllTrails cost (not much) but it also gives you descriptions of trails you might want to hike and puts you in touch with other hikers.

Terminus: Boulder

It was a nice day to take a walk.

This terminus hike was different in that it wasn't a train terminal. There is a fleet of buses that run regularly from Union Station in Denver to Downtown Boulder Station in Boulder. Designated FF1 through FF7, they make different stops on the way. FF2 is the express, so I took it out. "FF" stands for "Flatirons Flier" named after the huge outcrop of iron laden sandstone that looms over Boulder.

[Flatirons from downtown Boulder]

Unlike the commuter buses that run in Denver, the Flatiron Fliers are comfy cross country buses. I almost expect a steward to come out on the way and offer little cups of soda and peanuts. It's a long ride, but a nice one through the mesa country north of Denver.

The Fliers run through the first area I lived in when I moved to Colorado, Broomfield. Looking back through the blogs, you can find past hikes I took near Superior, Colorado and Flatiron Junction.

Downtown Boulder looks a little "small town" but the city is home to a very big school, the University of Colorado, and it's a major Colorado tourist destination. Situated at the mouth of Boulder Canyon, it's a gateway to the Rockies known for its shopping and nightlife.

Watch the traffic - it's also known for reckless drivers.

From the bus station, I walked down to the little bandshell amphitheater located on Boulder Creek. Boulder Creek Trail parallels the creek through town and into the canyon. It's well traveled by students, tourists, and resident joggers, but not such that it's not a corridor for wildlife. The town loves its animals. It's the first place in the US to give pets the status of personhood.

Boulder Creek Trail is a nice walk, ending at the west end in Eben G. Fine Park. Eben Givens Fine was a community builder who moved to Boulder from Missouri in 1886 and took a job as a pharmacist in a local drug store.

[Boulder Public Library from Boulder Creek]

[Boulder Creek]

[Boulder Creek at Eben Fine Park]

A tunnel under Canyon Road connects Eben Fine Park with Settlers and Red Rocks Park. "Red Rocks" may sound like plagiarism. After all, Red Rocks Park is near Morrison, but, in fact, it's the same Red Rocks, known also as the Fountain Formation, that pops up in places along the Front Range from Wyoming to New Mexico. The red rock is arkose conglomerate and the "red" is mostly iron rich feldspar that was recrystallized under pressure from stuff washed out of the mountains after the uplift that formed the Rockies. [Correction. It was debris from the Ancestral Rockies. ]

(By the way, if you're curious, the word "plagiarism" is from the Latin word "plagiarius" which means "kidnapping".)

[Red Rocks at Red Rocks Park in Boulder]

I returned to the bus station along Pearl Street, especially known for its shops, restaurants and nightlife.

[Pearl Street]

Since I was in no hurry to get back home (I needed a rest and the hike was short - it was just a little after noon when I left Boulder.) I took the first Flatirons Flier to leave, the FF1, which stops at pretty much every stop along the route.