This video: http://www.youtube.com/watch?v=pa8zGYStrXM
It raises a question, a simple question, really, about the motion of the Sun in the sky. How come the sun can shine on one side of the wall in the morning, and again in the evening?
The creator of the video however thinks that this explanation is insufficient. Since he hasn't noticed the same thing happen on this wall before, it must have come to be just recently.
So the natural explanation is that the Earths axial tilt is changing.
As far as I know (what I've been told), it does change. Just not by more that 2 degrees with a period of 40,000 years, and 7 arcinutes with a period of 18.6 years.
Finding that wobble insufficient to cause so drastic changes, I set out to see if my explanation could at least get the same results as shown in the video.
Wikipedia tells me that the angle of the earth is currently 23 degrees plus frosting.
The video tells me that it's shot at 35 degrees North latitude.
Please pardon my awful skill with MSPaint.
Okay, so now we know where we are, and where we will be during the 24 hours. Our latitude doesn't change, so we'll be somewhere on that dark blue line, this side, or the other, of earth.
Where are we, when the sun sets?
Already we can see, that we've gone around the axis quite a bit more than 90 degrees. But how much is quite a bit?
To find that out, we need to bust out trigonometry.
It's easy to see that x = r * sin(c). r here being the radius of the earth, and c our latitude, we get x = 6378km * sin(35deg) = 6378km * 0.5736 = 3429 km.
Now we can find y: y = x * tan(a) = 3429km * tan(23deg) = 1456km.
What does that got to do with the angle of the sun setting? To see that, we need a new drawing (no more copypasta for me...)
Here A is the point where we rotate out of the suns light (gotta remember, it's us moving, not the sun), and B is the point where we again start seeing it over the horizon.
Now, what we want to find is angle f. That's the angle over 90 degrees that the earth has rotated, when the sun sets on the solstice at 35N latitude.
To find that angle, however, we need the length of k. We get that, when we see that the angle CNA is a right angle (k is in the plane of 35N, and x colinear with the earth's axis) and that r is, again, the earth's radius. We know x: 3429km, and we know r: 6378km. Meaning k is equal to k = sqrt(r^2 - x^2) = 5378 km.
So at last, we can calculate: f = asin(y/k) = asin(1456/5378) = 15.7 degrees.
We can now also calculate the time of sunrise and sunset. If midday is 1 PM (summer time is weird), then sunrise occurred at 1PM - (90deg+15.7deg)/180deg * 12 hours = 1PM - 7.05 hours = 1PM - 7hr3min = 5:57 AM and sunset will occur at 1PM + 7hr3min = 8:03PM
These results are accurate only to the units digit, I rounded off anything higher. Times should be accurate to around 10 minutes.
If that wall is East-West, then I think I can say that the Earth's axial tilt is sufficient to explain it's current state of being lit on the north side both in the morning and in the evening. It not being so earlier I cannot fit in current models, but to dismiss the observation as faulty without having proof thereof would be just as bad as dismissing the model as faulty.
And now I'm going to sleep. Dawn is fast approaching on this side of the globe. If my calculations are wrong somewhere, blame this guy:
