What Is the Zenith Angle?

The zenith angle is the angle between a point of interest and the zenith — the point directly overhead. In a three-dimensional coordinate system, the zenith is the axis perpendicular to the horizontal plane. Zenith angle is measured from a local zenith, meaning that it changes based on the location of the person or device making the measurement. Solar zenith angle, the angle between the zenith and the sun, is useful in determining whether the sun is rising or setting and in predicting solar effects on radio communications.

Mathematically, the zenith corresponds to the z-axis on a set of spherical coordinates. This type of three-dimensional coordinate system describes positions on a sphere. The x- and y-axes, which are horizontally perpendicular to each other, form a flat plane. The third axis, or z-axis, is vertically perpendicular to this flat plane in the third dimension. If the Earth were plotted on spherical coordinates with the center of the Earth as the point of origin, the z-axis would run through the center of the Earth from the north to the south pole.

When zenith angle is measured, the point of origin is defined based on the location at which the measurement is taking place. For example, a person standing on the ground creates a vertical axis that runs from the center of the Earth through his or her head up into the sky. This line is the local zenith. If that person were to observe the sun and measure the angle between its position in the sky and the local zenith, he or she would have found the solar zenith angle.

This measurement can be useful in determining position, as it can be measured from any celestial object. Satellites and stars, as well as the sun, can be pinpointed with the zenith angle. The angle between the local zenith and a point such as a satellite is sometimes known as the viewing zenith angle.

The smaller the solar zenith angle, the higher the sun is in the sky. As the sun rises, the angle gradually decreases until midday. The position of the sun can be important in navigation as well as in radio communications, where it is used to predict the level of interference from solar flares. When the angle is low, and the sun is high in the sky, it is more likely that radio signals may be attenuated or lost due to solar flare activity.