Sunday, 13 December 2009

A Few Clarifications.

In my entry before the last there was a lot going on behind the scenes which I didn't explain. For the benefit of my scientifically inclined readers I am going to explain the the chain of reasoning I went through to arrive at the final answer and why my answer was as accurate as it was. One of my friends had sent me an email with an inquiry of  how I reasoned it out. Here I present my reply. I hope it clears all doubts.

To do this calculation I had to make an assumption.

First of all, I had to assume that the earth is tilted as far as possible away from the sun. Since It is December Which is winter time in the northern hemisphere, this is a pretty good approximation. But I couldn't be sure. However something else partially cancels this effect(namely, the latitude of my position).

I reasoned that since it was only the 8th of December, the earth could not have reached this maximum position(In actual fact, maximum is reached on December 22). So the angle that I calculate must be smaller than 23.45 degrees. I the checked the location of the city I stay in and I found out that it was on the 5 degree North latitude. So I reasoned that even if the angle would be smaller this smaller angle I get would be larger than the original tilt by five degrees (Since I'm 5 degrees above the equator). So if the earth was not at this maximum position, my angle would be made larger by roughly 5 degrees and my answer would therefore be closer to the correct answer.

And most importantly I made this calculation at exactly 12 noon, a time when the sun should have been directly above my head making an angle of 90 degrees. If I made the calculation at this time, then any deviation suffered by the sun from normal must be the tilt of the earth.

So I have taken into account the Latitude (5 degrees greater), and the time of the day. I do not need to worry about the longitude because all places on the same longitude will experience midday at exactly the same time. I think that covers everything.
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