how is it possible to have a negative sun angle?
Having a negative sun angle may sound counterintuitive since we typically visualize the sun as being above the horizon. However, it is possible to have a negative sun angle, especially when we use a coordinate system that measures the angle relative to the horizon or celestial equator.
To understand how negative sun angles are possible, we need to consider two coordinate systems: azimuth and altitude.
1. Azimuth: The azimuth angle measures the direction of an object from a specific observer's location. It is typically measured clockwise from north, ranging from 0° to 360°. For example, north is 0°, east is 90°, south is 180°, and so on.
2. Altitude: The altitude angle, also known as the elevation angle, measures the vertical angle between an object and the observer's horizon. It ranges from 0° (on the horizon) to 90° (directly overhead).
When we talk about the sun angle, we usually refer to its altitude angle. At noon when the sun is directly overhead, the altitude angle is 90°. As the sun moves closer to the horizon, the altitude angle decreases. For example, in the afternoon, the sun might have an altitude angle of 45°. In this case, the sun is halfway between the horizon and the zenith (directly overhead).
Now, to explain negative sun angles, let's consider the coordinate system where the azimuth angle is measured relative to north, from 0° to 360°, and the altitude angle is measured above (+) or below (-) the horizon, from 0° to -90°.
A negative sun angle occurs when the altitude angle is below the horizon, or in other words, when the sun is below the horizon. This happens during twilight, before sunrise, and after sunset when the sun is not visible from a particular observer's location.
So, while a negative sun angle may seem contradictory at first, it is a result of using a coordinate system that allows us to measure angles both above and below the horizon.