(This post is part of a long GeoCurrents series aimed at helping parents and teachers instruct students in basic geography. The material at the end of this post is most appropriate for students at the middle- and high-school levels.)
Now that latitude and midday sun angles have been covered, it is time to show how the two concepts are related. The relationship is relatively simple. For any place on Earth, the sun angle at solar noon [1] is found by subtracting the angular distance of the latitude in question from the latitude at which the sun is directly overhead. On the equinoxes, for example, the midday sun is directly overhead at latitude 0° (the Equator), which means that the sun angle there is 90°. At latitude 1°, it will be 89°, at latitude 10° it will be 80°, at latitude 20° it will be 70°, and so on.
Most sources give a more precise but also more complicated, and in my view less explanatory, formula. Here, for example, is how ChatGPT handles the issue:
Question: “How do you calculate the midday sun angle based on latitude?”
ChatGPT Answer: Here’s the basic formula:
Step-by-step explanation:
- Start with 90° — this is the maximum possible angle (directly overhead).
- Subtract the difference between your latitude and the solar declination.
- The solar declination is the angular position of the Sun north or south of the Equator.
- It changes between +23.5° (June Solstice) and −23.5° (December Solstice).
Example: 45° North on the June Solstice
-
Declination = +23.5°
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→ Midday Sun is 68.5° above the horizon.
The relationship between sun angles and latitude is perhaps most easily understood graphically, as is shown in the diagrams that illustrate this post.
The 23.5° tilt of the Earth’s axis relative to the plane on which it orbits the sun determines the latitude belt in which the sun reaches the position directly above the Earth’s surface at different times of the year. This belt ranges from 23.5° north of the Equator to 23.5° south of the Equator, also known as the as the tropics of Cancer and Capricorn, respectively. The same relationship also determines the Arctic and Antarctic circles, which mark the limits of the polar regions in which the sun does not set at certain times of the year. These circles are found at 66.5° north and south of the Equator, which is the same as 23.5° south of the North Pole and 23.5° north of the South Pole. Note that 66.5° and 23.5° are complementary angles, as they add together to form 90°, which is the angular distance from the Equator to the poles.
The 23.5° tilt of the Earth’s axis generates a series of 23.5° and 66.5° angles, as can be seen on the diagram posted below. Another diagram shows that a series of 47° and 43° angles are also formed by the Earth’s tilt. 47° is the angular distance from the Tropic of Cancer to the Tropic of Capricorn (which is derived simply by adding 23.5° with 23.5°). 47° is the angular distance between the Tropic of Cancer and the Arctic Circle, as well as between the Tropic of Capricorn and the Antarctic Circle (66.5 – 23.5 = 43). These angles, along with 0° and 90°, match the midday sun angles at the major latitudes on the solstices, as can be seen in the final diagram . This diagram also shows why the sun does not set on the Arctic Circle on the summer solstice. As can also be seen, on this day and at this latitude the sun angle varies from 47° at solar noon to 0° at midnight. The diagram also shows why the noon sun angle on June 21 is higher at the Arctic Circle than it is at the Tropic of Capricorn.
[1] Because of time zones and daylight savings time, solar noon, or “true noon” – the time at which the sun reaches its highest position – is in most places different from “clock noon.”