Directly North of Syene at Alexandria sticks do cast shadows. Dividing the circumference by the number 3.1415926 . In this figure we demonstrate why sidereal time is about 4 minutes of solar time fast compared to the Sun clocks. This is also equal to the angle that the Earth must rotate through before the observer has the Sun due South again from the time the fixed star is due South. Thus the time from one sidereal noon to the next is 4 minutes shorter than the corresponding solar passage.
Stars rise and set four minutes earlier each day.
Altlitude is the angular elevation of a celestial object from the horizon. In the figure it is angle HON,denoted by h here. Recall from geometry that intersecting sets of perpendicular lines generate equal angles. This means we can determine our latitude by measuring the altitude of the North Star. Remember that, at arm s length, each knuckle subtends an angle of about 2 degrees, a clenched fist about 10 degrees and a spread hand about 20 degrees, so the arm can be used as a crude quadrant.