RADIUS OF THE EARTH
We are going to figure out the radius of the Earth using trigonometry but first we need to learn how to measure the angle of elevation to the Sun. What is an angle of elevation?
The angle of elevation for an object is the angle between the horizontal and the line of sight to the object.
The angle of elevation for an object is the angle between the horizontal and the line of sight to the object.
There are several different techniques we can use to find this angle. Ask your teacher for the equipment needed to try each of these methods.
Shadows and Trigonometry
Start with an object that has a known height and is at 90º to the horizontal (something like a retort stand would work well). Place it in the Sun and measure the length of it's shadow as accurately as possible.
Draw a diagram and use pythagoras' theorem to calculate the angle of elevation.
Shadows and String
Start with an object that has a known height and is at 90º to the horizontal (something like a retort stand would work well). Place it in the Sun and attach a string from the top of the object to the end of the object's shadow to create a right angled triangle. Use a protractor to measure the angle of elevation where the string meets the ground.
Inclinometers
Use an inclinometer to point at the Sun and find the angle of elevation. Safety Warning: shield your eyes to protect them from the Sun's glare.
Choosing a Method
Now that you have tried the three different techniques you need to decide which one you think is most reliable.
You could try repeating the experiment several times using the different techniques to see which gives the most consistent results.
You could look up the expected angle of elevation for your location and time of day using software such as Starry Night and then compare that to your experimental results.
Consider too whether some techniques are better for sunny days and other techniques for cloudy days.
Once you are confident that you are able to collect the angle of elevation data accurately you can progress to the next page and commence the experiment to find the radius of the Earth.
You could try repeating the experiment several times using the different techniques to see which gives the most consistent results.
You could look up the expected angle of elevation for your location and time of day using software such as Starry Night and then compare that to your experimental results.
Consider too whether some techniques are better for sunny days and other techniques for cloudy days.
Once you are confident that you are able to collect the angle of elevation data accurately you can progress to the next page and commence the experiment to find the radius of the Earth.