Day Lab - Step 1: Determine the Angular Size of the Sun

From the lab: 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.

 
In our case, the "sundial" is created from focussing an image of the sun through a lens in a window onto an easel. To measure the angular diameter of the Sun, we marked the right edge of the Sun's image and timed how long it took for that image to cross that marking (basically, how long it takes the sun to traverse its diameter).

Our results were:

• 2:17.59 minutes  = 137.59 seconds
• 2:14.46 minutes = 134.46 seconds
• 2:21.45 minutes = 141.45 seconds
• 2:17.51 minutes = 137.51 seconds

This data set has a mean of 137.75 seconds and a standard deviation of 2.86 so average time is: $$\bar{t} = 137.75 \pm 2.86$$

So what can we do with this information? We can find the angular diameter of the sun because we know the sun traverses about 360 degrees in our sky each day. 

Source

We examined a fraction of that day and can therefore set up the proportion below: $$\frac{\theta}{\bar{t}} = \frac{360^{\circ}}{1 \: day}$$  Rearranging the equation and converting days to seconds gives: $$\theta = \frac{\bar{t} \times 360^{\circ}}{8.64 \times 10^4 s}$$ which with our result is:  $$\theta = \frac{137.75 \pm 2.86 \times 360^{\circ}}{8.64 \times 10^4 s}$$   $$\theta = \frac{137.75 \pm 2.86 \times 360^{\circ}}{8.64 \times 10^4 s}$$    $$\theta = .5750^{\circ} \pm 0.01192^{\circ}$$ The most accurate measurement of the angular size of the sun I could find online was .573 degrees. Our results did not quite match up, but they came close, only a 0.35% error.

Acknowledgements: I worked with Corey, Daniel, Richard, Sean, and Jonathan.