A universal sundial

A world globe can be used as a sundial that can tell you the time of day anywhere on Earth, time of sunrise and sunset, how the seasons work, and many other things. All you have to do is orient it in the same direction relative to the sun as the Earth. That way, it models Earth in space. Here's how you do it.

You will need a surface that can be tilted (and, possibly a clamp for the base of the globe to keep it from tilting over. Alternately, there are globes that can be tilted in respect to the base.) You will also need a mini-gnomon. A gnomon is just a vertical rod that will cast a shadow in the sun. It has to be small enough to position on the globe's surface. I used a plastic bottle cap and drove a screw through the center from underneath. (The screw should be as near a right angle to the surface of the cap as you can make it. You can test it with a carpenter's angle or even the sides of a sheet of paper.) After using a carpenter's level, or a phone app level to level the surface you will place the globe on, place the cap on the surface and mark the edge at the point north of the screw. Use a magnetic compass or a phone app but don't forget to look up the correction for true north from where you live and add or subtract it from your compass bearing. (Do an Internet search for "magnetic declination".)

With the line between the screw and the edge mark pointing north, make another mark with an erasable marker at the end of the screw's shadow from the sun.

Now, set your globe on the surface with the north pole pointing north (according to your compass with the correction to true north.). Rotate the globe until your position is on top.

Now for the fine tuning. Place the mini-gnomon pointing north directly over your position on the globe. If the sun's shadow on the globe and the sun's shadow on the Earth are oriented the same, they will both be oriented the same in space in respect to the sun, so tilt and rotate your globe until the tip of the screw's shadow touches the mark you made earlier at the shadow's tip. Your globe is now aligned.

What time is it? One way to tell is to watch your mini-gnomon to see when it's shadow is shortest - that's solar noon. During daylight savings, the local time will be an hour behind solar noon.

You can find where on the globe that it's solar noon by moving the mini-gnomon around to find the place where it's shadow is shortest. That will be a line of longitude. Knowing that every 15 degrees of longitude is an hour will allow you to calculate the time anywhere on Earth (at least, while the sun is out.)

You may have heard that the sun is directly overhead on the equator at noon each day. Try it out.

When it's solar noon where you are, place the mini-gnomon directly over your position and slide it straight down your line of longitude to the equator. Does the screw cast a shadow? Not if it's one of the two annual equinoxes. On any other day, the sun will be exactly overhead somewhere north or south of the equator.

You can easily see where sunset and sunrise is by finding the day-night divider line on your globe.

At my current time, here, sunset is slowly creeping off Africa into the Atlantic.

There is a lot you can do with the universal sundial. Can you use a thermometer to measure differences in temperature on the surface of your globe according to the angle the sun is shining on it? That's what causes the seasons.

Once you have a globe oriented, you can use a clamp or clay or some other way to freeze it in position and make a cover to keep it out of the weather. Then you can use it all year.

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. 

--- Notes on time ---

Time is the number of motion with respect to earlier and later.... Not only do we measure the movement by the time, but also the time by the movement, because they define each other. The time marks the movement, since it is number, and the movement the time.

Aristotle

Well, that was Aristotle's conception of time and it is mine - at least my naive conception. That's the time that's in our heads by which we measure our world, but there is also an element in the world, regardless of what we think, or, even, whether we are.

The environment the human mind developed in was shaped in certain ways by certain forces. These, in turn, shaped the human mind. Causal chains are important to survival, so we have been trained over eons to pay attention to causal chains; therefore, time runs in one direction - forward along causality.

What would happen if time ran backward? Things would undo, including our perceptions, and as soon as it ran forward again, it would "redo" and we could never know that time ever ran in any direction but forward.

Physics calls entropy "the arrow of time" because things run from high usable energy states to states in which all the usable energy is used up. But that's not quite right because there are systems that make entropy go in reverse - that increases usable energy in the environment, albeit only temporarily, and we don't see this reversed entropy as time-running-backward. Neither does time run backward in Einstein's world of four dimensions when entropy is reversed.

Currently, unless we cross some barrier that can carry us beyond what we are wired to perceive/conceive the only way to grasp the element of time that is independent of our sense and of us is to trust the mathematics that tells us that there is something out there that we can't grasp but must be there because, otherwise, nothing would work right.

More and more, physics looks strangely like philosophy.