Theoretical analysis of sun-moving
in different time zones.

Let's find out, how do the light time hang from the time zone, latitude you live and from the season.

So imagine yourself you are in the center of the sky sphere. The sphere is divided in two parts with the blue circle - math horison - in visible and invisible part. The red circle shows a way of sun in the day. Points E and W show rising and setting places. The line P'P is the polar line the Earth spins around.

The time the sun is over the math horison we may find so:

Let's figure out, how do the angle β hangs from the angle α between directions on the north and the sun at rising

The max value of angle N'QO is 23°33'. Let's find value of angle α, if the N'QO is 23°33'. Sinus-theorem by:

While OQ = OW as radiuses of the sphere, the angle O'N'O = 90 - φ, and in threeangle N'OW: N'O = OW cos α, then:

With help of this equation we can find the values-diapason of the angle α by the yearly moving of the sun and, with help of equation (*), we can calculate changing of the light time of a day in a year.