# LTE: Letters to the Editor

### Is This a Surveying Problem?

Shelly,

My name is Michael Rice, and I am a professional engineer/professional land surveyor working in a small private firm in New Bern, North Carolina.

As the most recently licensed land surveyor in the office (there are two other dual licensees and a PLS in charge of our survey crew) I enjoy the few opportunities I have to look through your magazine. The problem corner questions are often interesting, and I like talking them over with the survey crew chief.

I have a question/comment about problem 215. Being stumped by Dr. Bloch’s question, I visited the website to view the solution. Having done so, I’m still not sure I understand the logic behind asking the question or desiring its solution.

The solution implies that light emitted from the sun is tightly focused on the center of the earth. It implies that the sunlight forms a circle of light on the earth’s surface that is dependant upon the earth’s radius and surface arc length subtended by two earth radii that are tangent to the sun’s circumference.

If my understanding of the solution is correct, I wonder why the question was asked? Other than being an exercise in trigonometry, I perceive the question as having no application to surveying. Am I correct or am I missing something?

With a radius of approximately 695,500 km, the sun is considerably larger than the earth, and if the question were presented with the “sun” and “earth” labels reversed, an angle AOB subtended on the sun, tangent to the earth is approximately 0.005 degrees. This puts sunlight “beams” reaching the earth nearly parallel, and covering nearly 1/2 of the earth’s surface at all times, yielding a “diameter of sunlight” approximately equal to the earth’s diameter.

Just curious,
Michael L. Rice, PE, PLS
New Bern, NC

Mr. Rice,

This problem relates to the angle that the sun subtends when it is centered directly over the earth. The apparent size of the sun as seen from a fixed point on the earth subtends a mere ½ degree. It is also the same apparent size subtended by the moon.

The answer to part a is further clarified by the question in part b. Since both the sun and the moon subtend the same angle at the earth, there can be a full solar eclipse.

Furthermore, a full solar eclipse cannot be seen simultaneously over most of the earth. Indeed researchers must travel great distances to actually record a full solar eclipse. It is precisely this full eclipse footprint on earth that is the core of the problem.

To the ancient Egyptian surveyors this sun footprint was extremely important not only in locating surveying bench marks but for locating the Tropic of Cancer and its importance for determining the flooding times of the Nile.

And yes, this is an exercise in trigonometry, which is the fundamental mathematical basis for surveying. Problem #217 answers more fully the applications of these problems to surveying.

—Ben