Where is the Sun? — Part I (or Bad Science Flummoxes Vacations)

I took a mini-vacation to Brussels a couple of weeks ago, and having to navigate in a new location made me think of a common misconception held, I believe, by a large proportion of adults.

Most students are told that the sun reaches its highest point in the sky (its zenith) at noon. Now, this isn’t exactly true, but it is pretty close for most locations. However, that reasonably accurate principle is often abbreviated to the claim that the sun is directly overhead at noon, a belief many people retain their entire lives.

For the vast majority of Americans, the sun is nowhere near directly overhead at noon except in June and July, and this has several practical consequences.

Three dimensional geometry can be difficult to envision, but let’s look at a single, important case. On the summer solstice, Earth is tilted directly toward the sun. This is why the solstice is the longest day of the year. The angle of tilt is about 23.5 degrees, so someone at that northern latitude (23.5°) will see the sun nearly directly overhead at noon. This latitude is called the Tropic of Cancer. Below I have illustrated this statement and shown why someone standing north of this latitude will not see the sun directly overhead.

Since the entire continental United States lies above the Tropic of Cancer, no one in the extremely misnamed “lower 48” ever sees the sun directly overhead. (Those in Hawaii can.) For most of the year, the noon-time sun is quite far away from directly overhead in the US. For a student on spring break in Kansas City, KS, the inclination of the sun is about 51 degrees, not 90 degrees (which would correspond to the sun being directly overhead).

The above calculation assumes the student’s spring break is near the spring equinox (normally March 20), when it is easy to determine the inclination of the sun based on the latitude of the location. On an equinox Earth’s tilt is perpendicular to the path between Earth to the sun, so Earth’s tilt is irrelevant to the noon-time sun position. Someone standing on the equator (latitude = 0°) sees the sun directly overhead at noon, an inclination of 90 degrees. More generally, a latitude is L°, the inclination will be about 90 – L degrees at noon on an equinox.

Our hypothetical student will see the sun 39 degrees south of the center of her vision when she looks straight up. Because human field of vision is about +/- 50 degrees (vertically), the student in question is barely able to see the sun when looking straight up at noon. The image below gives some impression what the sky looks like to her. The size of the sun has been exaggerated.

Not only is it bad science to think the sun is overhead at noon (that could only occur on a flat, or at least cylindrical, Earth), but it can affect everyday life. For example, many people simply do not know how to tell direction by the position of the sun. This can be a useful tool, especially when vacationing in a new city. If you vacation in any location above the Tropic of Cancer, the sun is very close to directly south at noon. If you vacation to Australia, Argentina, or anywhere else below the Tropic of Capricorn, the sun will always be very close to directly north at noon. This basic information regarding the location of the noon-time sun is often enough to determine directions for most of the day, especially if you are in a city whose streets form a grid coordinated with the four cardinal directions.

This is part I of a two-part series on misconceptions regarding the course of the sun through the sky. In the second part we will discuss more complicated questions that cannot be explained using 2-dimensional geometry. For example, we will take a look at the common claim that the sun rises in the east and sets in the west.