This is the start of things that should make you go hmmm… There are nearly innumerable things about the place that we live that are just downright improbable. Earth seems perfectly suited for life in that if you change almost anything about Earth or the laws of the universe it is no longer capable of supporting the life we see all around us. There are several major theories to explain this amazingly ideal arrangement of things. The Weak Anthropic Principle states that anywhere life pops up under those ideal conditions that would allow for intelligence that life would wonder at the amazing improbability of its situation, thus the life and its improbability are linked. Intelligent Design says that the world is the way it is because it was made that way by someone smart. A new theory I ran across from Lynn Margulis is the Gaia theory which points out that the environment and its life-forms are inseparable and that life creates an environment that is naturally suitable to it.
I chose solar eclipses because they just don’t fit the anthropic mold to me. They aren’t necessary to life, they can’t be affected by life forms living on the planet, and it doesn’t fit the Christian view very well either because the Sun has almost no place in the Judeo-Christian tradition. In fact, solar eclipses (pictured here by Govert Schilling) are often used in various pagan religions. So why are solar eclipses so improbable and unnecessary? It’s because the only reason people can see the corona is because the ratio between the moon’s diameter and its distance from Earth is exactly the same as the Sun’s diameter over the Sun’s distance from Earth. That means that from Earth, the moon and sun look exactly the same size, even though they are in reality hugely different. The sun’s surface is millions of times brighter than the corona, so if the sun isn’t fully blocked you have no chance of seeing its dazzling display. (ref)
To understand why this is not necessary you only 
need to picture two other scenarios. If the moon were more dense, it could weigh the same at the same distance and same gravity but it would appear as simply a black dot traveling across the sun. Conversely, if we were orbiting a gas giant we would see the Sun disappear behind the monstrously huge planet.
So with a bit of math I think I can calculate the sun’s diameter without ever looking at it based solely on the characteristics of the moon and earth. Based on Wikipedia we find that the moon has an average diameter of 3,474 km (0.273 Earths). It orbits between 363,104 km to 405,696 km from Earth. Now, I think I need to subtract the radius of the earth so we’re calculating from the surface, but with the earth being only 6,373km thick, the 42,000km variance in the moon’s orbit probably negates that. The ratio of average distance/diameter then is 110.651. We should be able to divide the distance to the sun. 149,597,887 km is the average distance to the sun so I would calculate the sun’s diameter at 1,351,979 km. I’ve purposely not looked at the correct answer up until this point, so I’m really hoping my math is right. For example, I didn’t add the radius of the sun to the distance from Earth. So let’s look to Wikipedia for the correct answer. And the answer is… 1.392 x 10^6 km or 1,392,000 km.
Wow, that’s pretty close on astronomical terms. Let’s see what answer I get when I compensate for the radius of earth and the sun… ratio of 108.816 and the distance to the sun would be 150,593,887 gives me a diameter of 1,383,930 km. So, with a bit of sloppy math, I can calculate the diameter of the sun based on the diameter of moon, because of how perfectly solar eclipses line up. I don’t see any reason why this is ‘necessarily true’.
I’m not really assigning any meaning to this. Facts by themselves don’t truly have a deeper meaning, it takes a human observing them to appreciate that. I can show any number of possible arrangements that leave all the tides on earth untouched while ruining the specific improbable beauty of a solar eclipse but I think I’ve drowned you with enough math for now. So I’d just encourage you to look at some photos of solar eclipses and the sun’s corona.
P.S. If someone who is better at math than me (astronomer?) would like to calculate the tolerance range on perfect solar eclipses I’d be delighted to post it. I know that if you make the graphs ‘to scale’ the rays from the sun are nearly parrallel.
(Next: Something prettier, smaller, and infinite)
I have a question for you, and honestly I didn’t know the question to this until I lost 3 months of my life to Ultra Fractal. Are Fractals painted, drawn or discovered? Probably a question you’ve never asked, that’s what I’m here for. Well, for a full explanation of how fractals are calculated check out David Dewey’s Introduction to the Mandelbrot Set. The short answer is that the Mandelbrot equation is Z = Z2 + C. That should tell you the answer to my question right there. I can’t really express the infinte depth of fractals, you’re going to have to see it for yourself. Just consider this, when browsing around and zooming in on fractals like Mandelbrot the area is so big that after only a few minutes you could be looking at a scene no one has ever seen even though the Mandelbrot was discovered in 1977.
