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Sun path, sometimes also called day arc, refers to the daily and seasonal arc-like path that the Sun appears to follow across the sky as the Earth rotates and orbits the Sun. The Sun's path affects the length of daytime experienced and amount of daylight received along a certain latitude during a given season.
The relative position of the Sun is a major factor in the heat gain of buildings and in the performance of solar energy systems. [1] Accurate location-specific knowledge of sun path and climatic conditions is essential for economic decisions about solar collector area, orientation, landscaping, summer shading, and the cost-effective use of solar trackers. [2] [3]
Sun paths at any latitude and any time of the year can be determined from basic geometry. [7] [ unreliable source? ] The Earth's axis of rotation tilts about 23.5 degrees, relative to the plane of Earth's orbit around the Sun. As the Earth orbits the Sun, this creates the 47° declination difference between the solstice sun paths, as well as the hemisphere-specific difference between summer and winter.
In the Northern Hemisphere, the winter sun (November, December, January) rises in the southeast, transits the celestial meridian at a low angle in the south (more than 43° above the southern horizon in the tropics), and then sets in the southwest. It is on the south (equator) side of the house all day long. A vertical window facing south (equator side) is effective for capturing solar thermal energy. For comparison, the winter sun in the Southern Hemisphere (May, June, July) rises in the northeast, peaks out at a low angle in the north (more than halfway up from the horizon in the tropics), and then sets in the northwest. There, the north-facing window would let in plenty of solar thermal energy to the house.
In the Northern Hemisphere in summer (May, June, July), the Sun rises in the northeast, peaks out slightly south of overhead point (lower in the south at higher latitude), and then sets in the northwest, whereas in the Southern Hemisphere in summer (November, December, January), the Sun rises in the southeast, peaks out slightly north of overhead point (lower in the north at higher latitude), and then sets in the southwest. A simple latitude-dependent equator-side overhang can easily be designed to block 100% of the direct solar gain from entering vertical equator-facing windows on the hottest days of the year. Roll-down exterior shade screens, interior translucent-or-opaque window quilts, drapes, shutters, movable trellises, etc. can be used for hourly, daily or seasonal sun and heat transfer control (without any active electrical air conditioning).
Everywhere around the world during the equinoxes (March 20/21 and September 22/23) except for the poles, the sun rises due east and sets due west. In the Northern Hemisphere, the equinox sun peaks in the southern half (about halfway up from the horizon at mid latitude) of the sky, while in the Southern Hemisphere, that sun peaks in the northern half of the sky. When facing the equator, the sun appears to move from left to right in the Northern Hemisphere and from right to left in the Southern Hemisphere.
The latitude (and hemisphere)-specific solar path differences are critical to effective passive solar building design. They are essential data for optimal window and overhang seasonal design. Solar designers must know the precise solar path angles for each location they design for, and how they compare to place-based seasonal heating and cooling requirements.
In the U.S., the precise location-specific altitude-and-azimuth seasonal solar path numbers are available from NOAA – the "equator side" of a building is south in the Northern Hemisphere, and north in the Southern Hemisphere, where the peak summer solstice solar altitude occurs on December 21.
On the Equator, the noontime Sun will be straight overhead, and thus a vertical stick will cast no shadow, on the equinoxes. On the Tropic of Cancer (about 23.4°N), a vertical stick will cast no shadow on the June solstice (northern hemisphere summer), and the rest of the year its noon shadow will point to the North pole. On the Tropic of Capricorn (about 23.4°S), a vertical stick will cast no shadow on the December solstice (southern hemisphere summer), and the rest of the year its noon shadow will point to the South pole. North of the Tropic of Cancer, the noon shadow will always point north, and south of the Tropic of Capricorn, the noon shadow will always point south.
Within the polar circles (north of the Arctic Circle and south of the Antarctic Circle), each year will experience at least one day when the Sun remains below the horizon for 24 hours (on the winter solstice), and at least one day when the Sun remains above the horizon for 24 hours (on the summer solstice).
In the middle latitudes, the length of daytime, as well as solar altitude and azimuth, vary from one day to the next, and from season to season. The difference between the lengths of a long summer day and of a short winter day increases as one moves farther away from the Equator. [2]
The pictures below show the following perspectives from Earth, marking the hourly positions of the Sun on both solstice days. When connected, the suns form two day arcs, the paths along which the Sun appears to follow on the celestial sphere in its diurnal motion. The longer arc is always the midsummer path while the shorter arc the midwinter path. The two arcs are 46.88° (2 × 23.44°) apart, indicating the declination difference between the solstice suns.
In addition, some "ghost" suns are visible below the horizon, as much as 18° down, during which twilight occurs. The pictures can be used for both the northern and the southern hemispheres of Earth. A theoretical observer is supposed to stand near the tree on a small island in the middle of the sea. The green arrows represent the cardinal directions.
The following cases are depicted:
A 2021 publication [8] about solar geometry first calculates the x-, y-, and z-component of the solar vector, which is a unit vector with its tail fixed at the observer's location and its head kept pointing toward the Sun, and then uses the components to calculate the solar zenith angle and solar azimuth angle. The calculated solar vector at 1-hour step for a full year for both daytime and nighttime can be used to visualize the Sun path effectively.
In the following figures, the origin of the coordinate system is the observer's location, x-positive is East, y-positive is North, and z-positive is upward; at North Pole, y-negative is tangent to the prime meridian; at South Pole, y-positive is tangent to the prime meridian; z-positive is daytime, and z-negative is nighttime; the time step is 1 hour.
Each "8" pattern in all figures is an analemma corresponding to a specific hour of every day of the year; all the 24 hours on a specific day of the year depict the sun path of that day.
In astronomy, declination is one of the two angles that locate a point on the celestial sphere in the equatorial coordinate system, the other being hour angle. The declination angle is measured north (positive) or south (negative) of the celestial equator, along the hour circle passing through the point in question.
A solar equinox is a moment in time when the Sun crosses the Earth's equator, which is to say, appears directly above the equator, rather than north or south of the equator. On the day of the equinox, the Sun appears to rise "due east" and set "due west". This occurs twice each year, around 20 March and 23 September.
A solstice is the time when the Sun reaches its most northerly or southerly excursion relative to the celestial equator on the celestial sphere. Two solstices occur annually, around 20-22 June and 20-22 December. In many countries, the seasons of the year are defined by reference to the solstices and the equinoxes.
In astronomy, an analemma is a diagram showing the position of the Sun in the sky as seen from a fixed location on Earth at the same mean solar time, as that position varies over the course of a year. The diagram resembles a figure eight. Globes of the Earth often display an analemma as a two-dimensional figure of equation of time vs. declination of the Sun.
A circle of latitude or line of latitude on Earth is an abstract east–west small circle connecting all locations around Earth at a given latitude coordinate line.
In observational astronomy, culmination is the passage of a celestial object across the observer's local meridian. These events are also known as meridian transits, used in timekeeping and navigation, and measured precisely using a transit telescope.
Sunrise is the moment when the upper rim of the Sun appears on the horizon in the morning. The term can also refer to the entire process of the solar disk crossing the horizon.
Sunset is the disappearance of the Sun below the horizon of the Earth due to its rotation. As viewed from everywhere on Earth, it is a phenomenon that happens approximately once every 24 hours, except in areas close to the poles. The equinox Sun sets due west at the moment of both the spring and autumn equinoxes. As viewed from the Northern Hemisphere, the Sun sets to the northwest in the spring and summer, and to the southwest in the autumn and winter; these seasons are reversed for the Southern Hemisphere.
Dawn is the time that marks the beginning of twilight before sunrise. It is recognized by the appearance of indirect sunlight being scattered in Earth's atmosphere, when the centre of the Sun's disc has reached 18° below the observer's horizon. This morning twilight period will last until sunrise, when direct sunlight outshines the diffused light.
Midnight sun, also known as polar day, is a natural phenomenon that occurs in the summer months in places north of the Arctic Circle or south of the Antarctic Circle, when the Sun remains visible at the local midnight. When midnight sun is seen in the Arctic, the Sun appears to move from left to right. In Antarctica, the equivalent apparent motion is from right to left. This occurs at latitudes ranging from approximately 65°44' to exactly 90° north or south, and does not stop exactly at the Arctic Circle or the Antarctic Circle, due to refraction.
Twilight is sunlight illumination produced by diffuse sky radiation when the Sun is below the horizon as sunlight from the upper atmosphere is scattered in a way that illuminates both the Earth's lower atmosphere and also the Earth's surface. Twilight can also refer to the periods when this illumination occurs.
The solar zenith angle is the zenith angle of the sun, i.e., the angle between the sun’s rays and the vertical direction. It is the complement to the solar altitude or solar elevation, which is the altitude angle or elevation angle between the sun’s rays and a horizontal plane. At solar noon, the zenith angle is at a minimum and is equal to latitude minus solar declination angle. This is the basis by which ancient mariners navigated the oceans.
The September equinox is the moment when the Sun appears to cross the celestial equator, heading southward. Because of differences between the calendar year and the tropical year, the September equinox may occur from September 21 to 24.
Meridian altitude is a method of celestial navigation to calculate an observer's latitude. It notes the altitude angle of an astronomical object above the horizon at culmination.
A lunar standstill or lunistice is when the Moon reaches its furthest north or furthest south point during the course of a month. The declination at lunar standstill varies in a cycle 18.6 years long between 18.134° and 28.725°, due to lunar precession. These extremes are called the minor and major lunar standstills.
The amount of heat energy received at any location on the globe is a direct effect of Sun angle on climate, as the angle at which sunlight strikes Earth varies by location, time of day, and season due to Earth's orbit around the Sun and Earth's rotation around its tilted axis. Seasonal change in the angle of sunlight, caused by the tilt of Earth's axis, is the basic mechanism that results in warmer weather in summer than in winter. Change in day length is another factor.
Daytime or day as observed on Earth is the period of the day during which a given location experiences natural illumination from direct sunlight. Daytime occurs when the Sun appears above the local horizon, that is, anywhere on the globe's hemisphere facing the Sun. In direct sunlight the movement of the sun can be recorded and observed using a sundial that casts a shadow that slowly moves during the day. Other planets and natural satellites that rotate relative to a luminous primary body, such as a local star, also experience daytime, but this article primarily discusses daytime on Earth.
The equator is a circle of latitude that divides a spheroid, such as Earth, into the Northern and Southern hemispheres. On Earth, the Equator is an imaginary line located at 0 degrees latitude, about 40,075 km (24,901 mi) in circumference, halfway between the North and South poles. The term can also be used for any other celestial body that is roughly spherical.
A season is a division of the year based on changes in weather, ecology, and the number of daylight hours in a given region. On Earth, seasons are the result of the axial parallelism of Earth's tilted orbit around the Sun. In temperate and polar regions, the seasons are marked by changes in the intensity of sunlight that reaches the Earth's surface, variations of which may cause animals to undergo hibernation or to migrate, and plants to be dormant. Various cultures define the number and nature of seasons based on regional variations, and as such there are a number of both modern and historical definitions of the seasons.
The Rayleigh sky model describes the observed polarization pattern of the daytime sky. Within the atmosphere, Rayleigh scattering of light by air molecules, water, dust, and aerosols causes the sky's light to have a defined polarization pattern. The same elastic scattering processes cause the sky to be blue. The polarization is characterized at each wavelength by its degree of polarization, and orientation.