CALCULATION OF THE SIZE OF THE SUN
Unlike stars, which appear as single points of light due to their great distance from the earth, the sun has a visible width to the naked eye.
While it might be thought of as being as big as a quarter, that all depends upon how far the quarter is being held from the eye while making the comparison.
A more scientific approach is to state the size of the sun in terms of the angle it subtends with the eye, that is the angle formed by lines running from the eye to each edge of the sun.
This is easily calculated by the following method:
Apparent Diameter of the sun = approximately 1,400,000 kilometers
Distance of the sun from the earth = 150,000,000 kilometers
(This varies since the orbit around the sun is an ellipse rather than a circle. It varies from a value of 147,100,000 at Perihelion on January 2, the closest approach, to 152,600,000 at the Aphelion on July 2.)
Let x be the angle subtended with the eye as described above.
Then sin x = 1,400,000 / 150,000,000 or simplified, sin x = 1.4/150 = 0.00933
Then from the trigonometry tables we find that the angle whose sine is 0.00931 is 32.1 minutes, where 60 minutes = 1 degree.
This angle varies slightly with the variation of the distance of the sun (from 31.5 minutes to 32.7 minutes).
However, this may be ignored for amateur solstice measurements and for this purpose we shall assume that the angular width of the sun is approximately 0.5 degree.
For comparison, a complete circle is 360 degrees.
At the equator, and at the equinox (hours of daylight = hours of darkness) the sun travels 180 degrees in 12 hours, or 0.25 degrees per minute.