PHYS 1403 Lab 6: THE CIRCUMFERENCE OF EARTH

PHYS 1403 Lab 6: THE CIRCUMFERENCE OF EARTH

Worksheet

Enter you answers to each question in the data tables and yellow highlighted areas below. When completed, please save and upload this file to the assignment – Lab 6 – in Blackboard.

EXERCISE

For best results, this exercise should be done as close to local noon as possible. If we are on daylight savings time, then local noon will be around 1:00pm. If not, local noon will be around 12:00pm.

Set up the yardstick in a clear area outside where the shadow of the yardstick will lie unobstructed on a flat surface (preferably on a driveway or sidewalk). Using the string and weight, ensure that the yardstick is vertical (when the weight is hung from the string, the string will be vertical). Also make sure the bottom end of the yardstick is resting on the ground and not on another object (such as a rock, your foot, etc.). You can turn the yardstick until the shadow is widest.

Observe the shadow of the yardstick. Since we will be making our measurements close to solar noon, we can assume that the shadow of the meter stick is directed roughly north-south. Use the piece of chalk to mark the bottom of the yardstick and the end of the shadow. Now use the yardstick to measure the length of the shadow (the length between the chalk marks you just made), and record the lengths below.

1. Length of yardstick:

l_m =

2. Length of shadow:

l_s=________________

Note: l_s andl_m must be measured using the same unit! Ifl_m is measured in inches, thenl_s must also be measured in inches. Knowingl_s andl_m, we can calculate the angle of incidence between the rays of sunlight and the surface of the Earth,α. This can be calculated by:

3. From this equation, calculate the value ofα. Be sure that your calculator is in “degree” mode!

α = ________________

At a point directly beneath the Sun, the value forα would be zero, so the value ofα represents the piece of the Earth between us and the point directly beneath the Sun.

4.Divide 360 degrees byα to determine how many times this segment would go into a complete circle.

360°/ α = _______________

Next, we need to find the Sun’s declination,d, for today. To do this, simply start up Stellarium, find the Sun, and click on it. Use the text box that appears in the upper left corner to find the Sun’s declination.

5.Record the sun’s declination below:

d =__________________

Subtractd from the local latitude (use 33°) to obtain the number of degrees between us and the point on Earth directly beneath the Sun.

6. Number of degrees:

Local latitude -d = ________________

There are approximately 111.1 kilometers to one degree of latitude.

7. Multiply your answer to #6 by 111.1 to find the number of kilometers between you and the point directly beneath the Sun.

Distance to the point on Earth directly beneath the Sun = _______________

8. Now, multiply the answer to #7 by the answer to #4 to get the circumference of the Earth.

Circumference of earth = _________________

How does this compare to the accepted value of 40074 km?

9. Compute the percent error using the equation:

Where V_A is the accepted value and V_E is your experimental value (your experimental value is your answer to #8).

% Error = ______________

10. What were your conclusions after performing this experiment?