Math of a SunFlower...

The problem with using the time is something that is known (in horological circles at least) as, "The Equation Of Time". This deals with the fact that the Sun is exactly overhead at 12 Noon on only two days of the year. On other days, the Sun can be overhead as much as +/- 20 minutes from Noon.

This is the origin of the "Mean" (or average) in "Greenwich Mean Time"

Sorry - it didn't answer your question - but you might be interested.

I've found some links about Sun's position and would like to share with you;

Excellent.

Now thinking what I can do with it.....

A solar powered robot could certainly benefit.

Is this the information from which you derived the length of the day to be 23H20?

There are a number of steps that need to be performed, converting to and from different calenders and coordinate systems, performing computations, and the converting back. There's a wonderful book called "Practical Astronomy with your Calculator", by Peter Duffet Smith that goes through the calculations in great detail. The book I have is quite old - I got it mid-80s and I used it to implement a simple program to compute the positions of the sun, moon, planets, and other bodies, first on my HP 41CV calculator, and later in C. I still fire it up every now and then to see what's visible at my lat/lon. Good stuff.

-Brian