Thursday, September 29, 2016

Thinking Of an Experiment

In my last three posts (which have conveniently been combined onto a single page in the tabs), I proposed three tests which anyone with modest resources could perform to show whether or not the Earth is flat. But lately I've been wondering if there is a similarly simple experiment that would show that the Earth is turning.

Not that a moving Earth and a sphere Earth are the same issue; educated people knew that the world was spherical long before they could tell if it moved or not. Some early thinkers, most notably Aristarchus, argued for a heliocentric model thousands of years ago, but it wasn't until the time of Copernicus and Galileo that we started having observation evidence to back it up.

Now, of course, we have lots of evidence; our entire space program depends heavily on the motion of our world and all of our solar neighbors. But flat-Earthers don't believe in any of that.

What I'm more concerned with is thinking of a way that, without the observational skills of an astronomer or sophisticated and expensive equipment, an average person could conduct a test to show that the Earth is turning.

I know of one that I find convincing, involving the Coriolis Effect. These synchronized videos show the experiment. I had another thought, but there is a problem that I'm not sure how to get around.

First, the idea. What if two people, one living very far north or south of the equator, and the other at the equator, were to weigh a standard reference weight at their respective latitudes using an accurate (but inexpensive) jeweler's scale? The precision of the scale is enough to show the difference due to gravity as long as the weight has enough mass.

Let's say that the reference weight is 100 grams. In theory, at either pole the reference weight would weigh 100 grams, and at the equator it would weight about 99.7 grams. That would show that some force is counteracting gravity at the equator. Maybe the flat-Earthers would make something up, but it seems obvious to me that the counteracting force is centrifugal (yes, I know, it's a pseudo-force, but it ACTS like a force, and shows that movement is taking place).

But there is one problem I do not have enough knowledge to overcome: calibration of the scales. When you buy a precision scale, the first thing you normally do is calibrate the scale to a reference weight just like the one I'm talking about. But, of course, when you calibrate the scale, you'd be calibrating it to local gravity, and the comparison would be invalid.

So my question to anyone who understands scales very well is this: why do you calibrate the scale? Is it because no two are exactly the same? Is it because something happens during shipping? Or is it, in fact, because of local gravity? Do you see a way around my little problem?

I'd love to hear from someone with the necessary expertise, because if this could be done with a pair of inexpensive jeweler's scales and reference weights, I think it would make a good addition to the everyman-approach to first-hand knowledge of the shape and motion of the world we live on.

Please leave comments below; I'm truly interested in hearing your thoughts on this.


Wednesday, September 21, 2016

Three Tests, Part Three: Extending Eratosthenes

Since the last experiment involved either getting wet or waiting for lakes to freeze. there is a way to show whether or not the Earth is curved quite easily with the same equipment we used in the sunset experiment (those of us who actually bothered to do it), and some international cooperation.

Around 240 BCE, the librarian at the Library of Alexandria, Eratosthenes, devised a clever way to measure the circumference of the Earth. The method is described here for those who would like to repeat the experiment.

Flat-Earthers have pointed out that this experiment does not prove that the Earth is a sphere, because the same results could have been obtained from a close sun and a flat plane. And they are right about that; the experiment assumed a spherical Earth and a distant sun, because others before Eratosthenes had made compelling arguments to establish those facts, and Eratosthenes was only trying to figure out how big the Earth was.

But one little addition to the experiment would prove the sphericity of the Earth. And it is as simple as adding a third data point. Because the geometry of a curved surface does not match the geometry of a flat surface (see, for example this blog post of mine).

So, through the power of connecting over the Internet, all you need to do is find two people who live a latitudes quite a bit different from your own. More than two is even better. Each of you will need a yardstick, a level, and a measuring tape, and access to Time and Date and Google Maps.

I won't complicate this too much, because the details aren't nearly as important as the basic idea. You and your teammates choose a day, bury the yardsticks to the same depth, and measure the length of the sticks' shadows at solar noon (that's where Time and Date comes in). 

Google Maps will help determine the distances between the parallels from each location. Now, you can map out the triangulations on a flat plane, and then on a sphere and compare, but you can simplify it. Just assume a flat plane and try to use the triangulations to determine the distance to the sun. If the Earth is flat, and the sun is close, then the distances to the sun should be consistent. If they are not, then the assumptions of a flat plane and a close sun are incorrect.

Having determined that, you can then extend the math to conclude that the Earth is, indeed, a sphere, and that it was pretty close to the size that Eratosthenes worked out over 2200 years ago.

Saturday, September 17, 2016

Three Tests, Part Two: Revisiting Wallace

Maybe my little test with the sunset hasn't convinced you, although as I write this, no one has come up with even an attempt at a flat-Earth explanation for the results. But here's another test, which requires quite a bit more time and effort than the last, but directly indicates that standing water curves, and even gives you a way to approximate by how much.

It is a variation on the test performed by biologists Alfred Russell Wallace at the Old Bedford Level in 1870. You can read more about that event here. But it requires a long stretch of relatively still water with a line of sight over at least five miles. And if the water is not shallow, the process can be rather harrowing.

So, I'm calling on flat-Earthers who live in very cold climates to try a simpler variation. You'll need a sufficiently large body of water that freezes over so that it's perfectly safe to walk on. You'll also need three stepladders that are at least 10 feet high (Gorilla or Little Giant ladders would work well), two targets big enough to see from miles away with a telescope, some hardware to affix the targets to the top of the ladders, and a telescope. A spotting scope would be easier to use than the type designed for astronomy.

Set up the ladders so that one is about 2-1/2 to 3 miles away from the first. Affix a target to that ladder and measure its distance from the frozen surface. Set up another ladder so that it forms a line of sight with the other two, and is the same distance from the second as the second is from the first. Affix a target to it at the same height.

Now go back to the first ladder and set up the scope so that it is also the same height above the surface as the two targets. Aim the scope at the furthest target. If the Earth is flat, the first target will be in the way of the second. In the Earth is concave, as "Lord" Steven Christ claims, the first target will be below the second target. And if the Earth is convex (and it is), the first target will be higher than the second.

If you measure how much higher, by having someone with a cell phone move another target until it is centered in your scope, you can use that information to estimate to circumference of the Earth, not with any great accuracy, but close enough to know that the "official" circumference is definitely in the ball park.

Have I done this experiment? No. First, the sunset tells me what I need to know, and I don't feel the need to go to the trouble. Second, Wallace did this in 1870 and I have no reason to doubt his veracity. And third, if I did the experiment and published the results, the flat-Earthers would only reward my efforts by declaring them fake. See, for example, what happened to Wallace.

That said, when the lakes in my area freeze over this winter, I may suggest to one of the science teachers at the local high school that this would make an interesting project to show that direct evidence is available to anyone willing to access it and evaluate it with an unprejudiced eye.

The question is, are any flat-Earthers willing to go out into the cold and do the same?

Tuesday, September 13, 2016

Three Tests, Part One: Shadows At Sunset

Flat-Earthers will, it seems, go to great lengths to prove that the Earth is not a globe. They will try to raise money, unsuccessfully, to travel to Antartica, perhaps in order to demonstrate that they will be turned away at gunpoint for the attempt.

They will buy fairly expensive cameras with powerful zoom lenses and use the zoom to somehow prove that the ships don't go over the horizon, or that faraway skylines are visible when they shouldn't be, or that stars are really blurry undulating masses.

They will shoot lasers across lakes in an attempt to debunk a similar (but notably not identical) experiment performed on the series Genius recently.  And they will measure the temperature, so they say, of moonlight compared to moon shade which, somehow, is supposed to prove that the Earth is flat. But what they won't do is perform a few simple, definitive tests that show whether or not the Earth is flat.

So, if you seriously think that the Earth is flat, forget about high-tech, GoFundMe campaigns, and vague, badly designed experiments. Be prepared to get out, reach out, and find out. Warning: there's math involved.

Test One: Measure a Sunset, Watch the Moon Set
I've talked about sunrise and sunset before, and gotten a lot of excuses about perspective. But perspective is a visual phenomenon, and we're going to ignore it. Instead, we are going to cast and measure some shadows, and do some trigonometry. If you're not particularly good at trig (it's okay, I'm not either), I'll point you to an online calculator that you can use to help out.

It helps to be on an ocean beach that faces west for this. A beach that faces east also works, but then you should watch the moon rise and measure the sunrise. And if you don't have access to a beach, any big field without any really tall surrounding mountains will work almost as well. I'm going to assume a west-facing beach.

Pick a clear evening when the moon is full or nearly full. It will be easier to see. For tools you'll need a yardstick, a tape measure, a compass, a small level, binoculars, and paper and pencil. Get yourself a spot at least an hour before sunset. Plunge the yardstick into the sand until two feet are sticking up. Use the level to make sure it's straight up and down.

Half an hour before sunset, measure the shadow cast by the stick, and use the compass to work out the direction of the shadow. Believe it or not, that's all the data you need to gather. After the sun has fully set and no longer casts any usable light, try to bring it back into view with the binoculars.

Bring the binoculars back to the beach half an hour before the moon sets. Watch the moon sink below the horizon, note it's apparent size, and whether the horizon cuts it off as it sinks. When it's out of sight, try to bring it back into view with the binoculars.

Now it's time to go home and do some evaluation of what you just did.

Evaluation
Get out your simple data on the shadow. First, let's start with the length of the shadow. Open this triangle calculator. Erase any data already provided. In the box for side x, put the height of your stick, or two feet. In the box for angle a, put 90, since your stick formed a right angle with the ground. In the box for side z, put the length of the shadow, and click on "Calculate."

The key number is the angle that will show as opposite side 1 (the calculator should show side x and angle b; I don't know why it doesn't). This is the angle above the ground that the sun was when it cast it's shadow. In my test, it was 6.71 degrees. What does this say about the flat Earth? Well, let's apply this math in reverse.

The most common flat-Earth model has the sun 3000 miles above the "plane." Let's plug that back into the calculator: put 3000 into side x, erase side z, and put 6.71 into angle b. Calculate. Look at the figure for side 3. In my test, the stick cast a 17-foot shadow; if the sun were 3000 miles over a flat plane, it would be over 25,000 miles away at sunset. In other words, off the disc of the flat-Earth model.

Not a problem, you say? We know that when it's sunset where you're standing, it's noon somewhere else. Where else on Earth is 25,000 miles away? The model is breaking down.

Okay, what if the sun is not 3000 miles high? If the sunset happens when the sun is about 6000 miles away, which is one of the implications of the model, then how high would it be? Erase side x, put 6000 in side z (leaving the original figures for angles a and b). Calculate.

In my test, the sun would have to be 706 miles high to create that shadow. If you think that's possible, then it's time to go out and try to measure the height of the sun. I give you some idea of the difficulties of that task if you assume a flat Earth in this blog post. But before you go to the trouble, let's think about your other observations.

Get out your favorite azimuthal equidistant map projection, or another flat-Earth map if you have one. You can get the Gleason Map here.  Find yourself on the map. Then chart the angle of the sun based on the shadow angle you jotted down. Does it make any sense? In some lucky circumstances it might, but in most locations on most days, it won't match up.

When you watched the moon go down, it didn't shrink in size. It may have even looked a little larger as it came close to the horizon. And it moved down into the horizon, the horizon cutting through it until it sank out of sight. And you couldn't bring it back into view with the binoculars. So it wasn't just moving away from you. Relative to the ground, it was actually behind the ground. Same with the sun. Behind the curve. Because the Earth is curved.

I know of no other way to explain these observations. You're welcome to bring your own interpretation, but if it's vague, prepare to be challenged. Because on something as important as the truth, especially when you deign to rebuke a couple of thousand years of established scientific thought, you'd better be specific, or you'd better go home.

And if this doesn't convince you, the next experiment (in this post) is designed to directly indicate that water does, contrary to flat-Earth myth, curve over the surface of the Earth.