I had mentioned an example with less math. This isn't so much proving the age of the earth or the solar system, but interesting none the less and relevant in its own fashion. Particularly I would like to hear what you might have to say regarding the motions of the planets and their satellites.
It is generally well accepted today that the earth moves around the sun so let's accept this model. If we regard the sun as being a stationary point of reference, orientate ourselves so that the North Pole is roughly "up", then the earth orbits around the sun in a counterclockwise direction. This is not considered controversial.
Likewise, if we consider the direction of the earth's orbit around the sun, it also spins in a similar counterclockwise fashion. The moon also orbits around the earth counterclockwise, and has a counterclockwise spin. I am not aware of any fringe groups that would claim otherwise, this still remains generally accepted fact. The interpretation of these facts may differ between you and me, however.
From my perspective and theory, the direction and spin of these bodies can be explained simply because "God chose to do it that way" without needing further explanation. After all, I believe in special creation, and although processes may have been used from which these motions would be the inevitable result, it is not a limiting factor. I might expect that you might reason differently. Without an intelligent hand forming the cosmos, you might say that the earth was formed from a solidified mass of matter, and that the spin and orbits of the earth and its moon match the rotation of the sun because of a behavior described as the "preservation of angular momentum." That is, you would say it is that way because it has to be that way and could not have been formed differently.
I apologize if this seems to be putting words in your mouth (or presuming thoughts in your head) but this is the general theory usually adopted by those that rely on a "big bang" theory to explain why we have sun, moon, and stars, of which our earth is but a small part. So here is where the interesting part comes in. If the solar system was formed from a solidified mass of spinning gas, then one would expect the orbits and rotations to all proceed in the same direction. Preservation of angular momentum at work. But... there's an exception. Or two. Or even a few more.
This (non-creationist) site even admits this quickly, in passing, before skipping through to its "big bang" explanation, explaining that the solar system was formed from a pancake of gas and that the directions must be the result of this event, citing "conservation of angular momentum.
http://scienceblogs.com/startswithabang/2010/10/07/counterclockwise-but-there-are/
Were you to reference Wikipedia, what I am describing is found under the entry for "Retrograde motion" Venus rotates backwards (clockwise) for example. Uranus also has a backwards spin while having its own unique axial direction. But this doesn't stop with just planets, because there are various moons of other planets that even orbit in the opposite direction.
I'll just comment that the observed data doesn't seem to fit well within the "God didn't do it" theory. I've seen proposed explanations such as "a giant object must have zoomed in and hit it hard enough to flip it upside down" ... but what are the probabilities? And not just for one planet, but two of them, plus many other moons? Jupiter, Saturn, and Neptune all have moons that travel in opposite directions. To me it looks like a signature, sort of a reminder that "someone did this."
