Next in my series of empyrical demonstrations about FE failing to explain common events in the nature, let's demonstrate that full eclipses that project a shadow umbra over a region of the earth, are impossible with the FE model.

I'm talking about this:

http://apod.nasa.gov/apod/image/0106/tse1999_kobusch_big.jpg**Not** about this:

http://images.fineartamerica.com/images-medium-large/total-eclipse-allen-lefever.jpgIf you didn't noticed, when the Moon/Shadow Object moves between the Sun and the Earth, it proyects a shadow, but a shadow has different parts, that you can see in the next diagram:

http://upload.wikimedia.org/wikipedia/commons/2/2e/Diagram_of_umbra,_penumbra_%26_antumbra.pngI will demonstrate that eclipses where the whole Solar disc is hidden by the Moon/Shadow Object, are impossible according to FE model, but the real thing is that we can see a lot of eclipses of this type along the history of the earth, as well as predicting when, where and how they will happen.

So, lets get into matter.

First, let me pressent you a simple diagram of how FE illustrates the Earth, Sun and Shadow Object.

In this image, you may note that the Shadow Object (blue small circle) is not in the same plane as the Sun (yellow circle) orbyts around the Arctic.

This is because if the Shadow Object is in the same plane as the Sun, then eclypses won't be possible at all since we will be seeing the Sun from a lower angle that the Shadow Object can cover part of the Sun.

Now, for umbra eclipse (we will call "umbra eclipse" to those eclipses where the whole solar disc is hidden by the Moon/Shadow Object), we need to stay observing from the umbra zone.

Everyone can agree that if we have a source of light and an object obstructing the light (this object is smaller than the source of light) rays falling upon a surface, we can change the umbra, penumbra and antumbra by moving closer and further the blocking object.

Actually, when the blocking object is close to the light source, the umbra length becomes smaller, and when we move farther from the light source the blocking object, the umbra length becomes longer.

You can experiment this in your own house using a light bulb and a iron marble or any other similar opaque object tied to a thin thread.

So, translating this to a Sun-Moon-Earth scale, the Earth is our "wall", the Moon/Shadow Object is the obstructing object and the Sun is the source of light.

To see an eclipse where the Moon/Shadow Object covers the whole Solar disk, we need to stay in the Umbra zone.

Let's then calculate, using the FE model sizes and distances, the length of the Umbra zone, to see if it is possible that the Shadow Object predicted by the FE, allows or not a Umbra Eclypse in the earth surface.

From now on, lets call "Moon" to the Shadow Object, for the sake of abbreviaton.

What we need to calculate is B distance, in the previous image (note that the previous image may not be at a correct scale).

Using some basic school trigonometry, we know that:

B = R

_{Moon}/Sin(α)

Where R

_{Moon} is the Radius of the Moon/Shadow Object.

R

_{Moon} (remember, Shadow Object), we know it's value according to FE theory: from 4 to 8 kilometers. Because FE scientists doesn't seem to reach an agreement, lets take the medium size: 6 kilometers.

But we need to calculate the angle "α".

For this, we will use again simple school maths:

α = Arcsin(R

_{Sun} - R

_{Moon} / D

_{Sun} - D

_{Moon})

Where R

_{Sun} is the Radius of the Sun (25.74 Km in the FE model), D

_{Sun} is the distance from the Earth to the Sun and D

_{Moon} the distance from the Earth to the Moon (obtaining here the distance from the Sun to the Moon, again basic school Maths).

According to FE model, the distance Sun-Earth is 4828 kilometers.

The distance from the Shadow Object to the Earth or the Sun is unknown, so we need to "invent" a distance. Since we know "the Shadow Object is very close to the Sun", then lets say the Shadow Object is at 4728 Kilometers from the Earth (which is then 100 kilometers from the Sun. Please note that "very close" is a subjective description, but for a 4828 Km distance, it could be agreed that 100 kilometers is very close.

So giving numbers to all of this, we get:

α = Arcsin(25.74 - 6 / 4828 - 4728) = Asin(0.19) = 10.95º

Now, we can calculate the length of the umbra zone for the FE model, given the case that the Shadow Object is 100 kilometers away from the Sun:

B = 6 / Sin(10.95) = 6 / 0.18 = 33 Km

So, we have that the umbra zone is only 33.33 kilometers long.

But according to the FE model, the Sun is at a distance of 4828 kilometers above the earth surface, and given the Shadow Object that is "very" close to the Sun (we supposed 100 kilometers), then we have an umbra zone that goes from 4728 Km to 4694.67 Km above our heads.

So actually, this means that we will have to travel 4694.67 Km up in the sky and firmament to enter the umbra zone, or what is the same, the distance from the Shadow Object to the Sun is so low that the umbra zone projected doesn't even come any close to the Earth Surface.

In either case, this calculation we just made, is actually invalid, since we don't know the distance from the Shadow Object to the Sun. It was stated as "very close", but this is a subjective description. I can say very close when it is 1 milimeter away, and other may say very close for 1 centimeter away.

So what we need to find is a distance A (in the image above) that gives a distance B enought to reach the earth surface.

Getting back to α (alpha), we have:

α = Arcsin(25.74 - 6 / 4828 - Y)

Being X the distance from the Shadow Object to the Earth, which we want to find.

If we take Y as 1000 Kilometers above the Earth Surface, we have:

α = Arcsin(25.74 - 6 / 4828 - 1000) = Asin(0.0051) = 0.29º

And finally: B = 6 / Sin(0.29) = 1185 Km

So having the Shadow Object at a distance of 1000 Km above the Earth Surface, will be slightly enough to allow the surface to enter the umbra zone.

We can conclude then that the Shadow Object must be roughtly 3828 Km away from the Sun, which, for me and most of the humans in the earth is not a "very close" to the sun, if we compare that "very close" with the distance from the Earth to the Sun.

Actually, if we draw an illustration to scale, we have the next (Sun and Shadow Object diameters are not at correct scale respect distances, it would be impossible to draw in a small image like the next):

Which for the Flat Earth model, seems wrong.

Conclussion: following the FE model, and even when there is no a complete source of distances information, the FE models seems to fail when explaining Solar eclipses, since in a FE world won't exist full solar disk eclipses.