The moment the sun disappears below the horizon is a daily phenomenon that has captivated observers. Determining the sun’s precise position at this instant requires understanding celestial mechanics and specifying which angular dimension is being measured. The answer varies continuously based on geography and time, as sunset is a dynamic astronomical calculation influenced by the geometry of the Earth-Sun system.
Understanding Angular Measurements of Sunset
The sun’s position is defined by two angular coordinates relative to an observer. The first is azimuth, the horizontal direction measured as a compass bearing clockwise from true North. For reference, \(0^\circ\) is North, \(90^\circ\) is East, \(180^\circ\) is South, and \(270^\circ\) is West. Azimuth dictates the specific point on the horizon where the sun sets.
The second measurement is altitude, the vertical angle of the sun above the local horizon, where \(0^\circ\) is the horizon line and \(90^\circ\) is directly overhead. Although many assume the altitude at sunset is \(0^\circ\), the sun is actually already below the horizon when it visually vanishes due to the physics of Earth’s atmosphere.
How Latitude and Season Determine the Setting Point
The horizontal angle of sunset (azimuth) is highly variable, depending on the observer’s latitude and the date. The sun sets exactly due West (\(270^\circ\) azimuth) only on the vernal and autumnal equinoxes. On these days, the Earth’s axis is not tilted toward or away from the sun, causing the sun to appear directly over the equator.
On all other days, the setting point shifts dramatically along the horizon. In the Northern Hemisphere, the sunset position moves progressively north of West after the spring equinox, peaking on the summer solstice. Conversely, the point shifts south of West after the autumnal equinox, reaching its southernmost extreme on the winter solstice. This seasonal migration is reversed in the Southern Hemisphere.
The magnitude of this shift from the due West point is directly proportional to the observer’s latitude. Near the equator, the setting point varies minimally, shifting only about \(23.4^\circ\) north or south of West annually. For observers farther north, such as at \(40^\circ\) latitude, the position can shift by more than \(30^\circ\) from the West point, setting at \(300^\circ\) (Northwest) in the summer and \(240^\circ\) (Southwest) in the winter.
Near the polar circles, the variation is extreme, leading to the midnight sun phenomenon where the sun does not set for part of the summer. The Earth’s \(23.4^\circ\) axial tilt causes this annual cycle by dictating the sun’s declination, which determines the setting azimuth. Since declination changes daily, the setting point on the horizon is in constant, predictable motion.
The Effect of Atmospheric Refraction
While azimuth changes seasonally, the altitude of the sun at official sunset is a near-constant, negative value due to atmospheric refraction. Light from the sun bends as it passes through layers of air that increase in density closer to the surface. This refraction acts like a lens, making the sun’s image appear higher in the sky than its true geometric position.
At the horizon, this bending is significant, generally amounting to about \(0.5^\circ\) of angular displacement. Official astronomical sunset is defined as the moment the upper edge (limb) of the sun disappears below the horizon. Since the sun has an apparent diameter of about \(0.5^\circ\), the standard definition requires the geometric center of the solar disk to be \(0.833^\circ\) below the horizon to account for both size and refraction.
When the sun visually touches the horizon, it has already sunk below the true horizontal plane. Refraction allows an observer to continue seeing the sun for several minutes after it has geometrically set. While \(0.833^\circ\) is the standard value for official calculations, the exact degree of refraction can vary depending on local atmospheric pressure, temperature, and humidity.