Day Lab Part 1: Measuring the Angular Size of the Sun

The sun appears to move all the way around the Earth (360 degrees) in 24 hours. If we measure how long (minutes and seconds) the sun takes to move its own diameter along the sundial in our lab, we can measure its angular diameter, in degrees. 

To conduct this portion of the lab, we focused the sun's light with a lens onto a large white sheet of paper. This acted as our sundial. Below is a diagram of the setup: 

As a group, we then marked the two extremes of the sun, with a corresponding time. We then allowed the sun to pass one full diameter, and again noted the time. After conducting these measurements several times, we were then able to determine the suns angular diameter using some simple geometry. The average time we measured for one diameter to pass was: 2 min 15 seconds, or 135 seconds. 

From this, we were then able to calculate the angular diameter of the sun, \( \theta\). \[ \frac{24 \, hours}{360 \, degrees} = \frac{diameter \, time}{ \theta }\] \[ \frac{24 \, hours}{360 \, degrees} = \frac{135 \, seconds}{ \theta }\] 
\[ \theta = \frac{135 \, seconds \times 360 \, degrees}{ 24 \, hours \times \, 60 \, minutes \times 60 \, seconds} = 0.56 \, degrees \]