Sun path, sometimes also called day arc, refers to the daily (

sunrise Sunrise (or sunup) is the moment when the upper rim of the Sun appears on the horizon in the morning, at the start of the Sun path. The term can also refer to the entire process of the solar disk crossing the horizon. Terminology Although the S ...

sunset Sunset (or sundown) is the disappearance of the Sun at the end of the Sun path, below the horizon of the Earth (or any other astronomical object in the Solar System) due to its Earth's rotation, rotation. As viewed from everywhere on Earth, it ...

) and

season 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 axial tilt, tilted orbit around the Sun. In temperat ...

al arc-like path that the

Sun The Sun is the star at the centre of the Solar System. It is a massive, nearly perfect sphere of hot plasma, heated to incandescence by nuclear fusion reactions in its core, radiating the energy from its surface mainly as visible light a ...

appears to follow across the

sky The sky is an unobstructed view upward from the planetary surface, surface of the Earth. It includes the atmosphere of Earth, atmosphere and outer space. It may also be considered a place between the ground and outer space, thus distinct from ...

as the

Earth Earth is the third planet from the Sun and the only astronomical object known to Planetary habitability, harbor life. This is enabled by Earth being an ocean world, the only one in the Solar System sustaining liquid surface water. Almost all ...

rotates and

orbits In celestial mechanics, an orbit (also known as orbital revolution) is the curved trajectory of an physical body, object such as the trajectory of a planet around a star, or of a natural satellite around a planet, or of an satellite, artificia ...

the Sun. The Sun's path affects the length of

daytime Daytime or day as observed on Earth is the period of the day during which a given location experiences Daylight, natural illumination from direct sunlight. Daytime occurs when the Sun appears above the local horizon, that is, anywhere on the ...

experienced and amount of

daylight Daylight is the combination of all direct and indirect sunlight during the daytime. This includes direct sunlight, diffuse sky radiation, and (often) both of these reflected by Earth and terrestrial objects, like landforms and buildings. Sunlig ...

received along a certain

latitude In geography, latitude is a geographic coordinate system, geographic coordinate that specifies the north-south position of a point on the surface of the Earth or another celestial body. Latitude is given as an angle that ranges from −90° at t ...

during a given season. The relative

position of the Sun The position of the Sun in the sky is a function of both the time and the geographic coordinate system, geographic location of observation on Earth's surface. As Earth's orbit, Earth orbits the Sun over the course of a year, the Sun appears to mo ...

is a major factor in the heat gain of buildings and in the performance of

solar energy Solar energy is the radiant energy from the Sun's sunlight, light and heat, which can be harnessed using a range of technologies such as solar electricity, solar thermal energy (including solar water heating) and solar architecture. It is a ...

systems. 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.

Angles

Effect of the Earth's axial tilt

Sun paths at any latitude and any time of the year can be determined from basic

geometry Geometry (; ) is a branch of mathematics concerned with properties of space such as the distance, shape, size, and relative position of figures. Geometry is, along with arithmetic, one of the oldest branches of mathematics. A mathematician w ...

. The Earth's axis of

rotation Rotation or rotational/rotary motion is the circular movement of an object around a central line, known as an ''axis of rotation''. A plane figure can rotate in either a clockwise or counterclockwise sense around a perpendicular axis intersect ...

tilts about 23.5 degrees, relative to the plane of

Earth's orbit Earth orbits the Sun at an astronomical unit, average distance of , or 8.317 light-second, light-minutes, in a retrograde and prograde motion, counterclockwise direction as viewed from above the Northern Hemisphere. One complete orbit takes & ...

around the

. As the Earth orbits the Sun, this creates the 47°

declination In astronomy, declination (abbreviated dec; symbol ''δ'') 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 ...

difference between the

solstice A solstice is the time when the Sun reaches its most northerly or southerly sun path, 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 ...

sun paths, as well as the

hemisphere Hemisphere may refer to: In geometry * Hemisphere (geometry), a half of a sphere As half of Earth or any spherical astronomical object * A hemisphere of Earth ** Northern Hemisphere ** Southern Hemisphere ** Eastern Hemisphere ** Western Hemi ...

-specific difference between summer and winter. In the

Northern Hemisphere The Northern Hemisphere is the half of Earth that is north of the equator. For other planets in the Solar System, north is defined by humans as being in the same celestial sphere, celestial hemisphere relative to the invariable plane of the Solar ...

, 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 Solar thermal energy (STE) is a form of energy and a technology for harnessing solar energy to generate thermal energy for use in Industrial sector, industry, and in the residential and commercial sectors. Solar thermal collectors are classified ...

. 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

), 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 In passive solar building design, windows, walls, and floors are made to collect, store, reflect, and distribute solar energy, in the form of heat in the winter and reject solar heat in the summer. This is called passive solar design because, unli ...

. 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 National Oceanic and Atmospheric Administration (NOAA ) is an American scientific and regulatory agency charged with forecasting weather, monitoring oceanic and atmospheric conditions, charting the seas, conducting deep-sea exploratio ...

– the "equator side" of a building is south in the Northern Hemisphere, and north in the Southern Hemisphere, where the peak summer

solar altitude occurs on December 21.

Shadow of a vertical stick at
solar noon Noon (also known as noontime or midday) is 12 o'clock in the daytime. It is written as 12 noon, 12:00 m. (for '' meridiem'', literally 12:00 midday), 12 p.m. (for ''post meridiem'', literally "after midday"), 12 pm, or 12:00 (using a 24-hour clo ...

On the Equator, the noontime Sun will be straight overhead, and thus a vertical stick will cast no shadow, on the

equinox A solar equinox is a moment in time when the Sun appears directly above the equator, rather than to its north or south. On the day of the equinox, the Sun appears to rise directly east and set directly west. This occurs twice each year, arou ...

es. On the

Tropic of Cancer The Tropic of Cancer, also known as the Northern Tropic, is the Earth's northernmost circle of latitude where the Sun can be seen directly overhead. This occurs on the June solstice, when the Northern Hemisphere is tilted toward the Sun ...

(about 23.4°N), a vertical stick will cast no shadow on the

June solstice The June solstice is the solstice on Earth that occurs annually between 20 and 22 June according to the Gregorian calendar. In the Northern Hemisphere, the June solstice is the summer solstice (the day with the longest period of daylight), while ...

(

northern hemisphere The Northern Hemisphere is the half of Earth that is north of the equator. For other planets in the Solar System, north is defined by humans as being in the same celestial sphere, celestial hemisphere relative to the invariable plane of the Solar ...

summer), and the rest of the year its noon shadow will point to the North pole. On the

Tropic of Capricorn The Tropic of Capricorn (or the Southern Tropic) is the circle of latitude that contains the subsolar point at the December (or southern) solstice. It is thus the southernmost latitude where the Sun can be seen directly overhead. It also reach ...

(about 23.4°S), a vertical stick will cast no shadow on the

December solstice The December solstice, also known as the southern solstice, is the solstice that occurs each December – typically on 21 December, but may vary by one day in either direction according to the Gregorian calendar. In the Northern Hemisphere, the ...

( 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.

Duration of daylight

Within the

polar circle A polar circle is a geographic term for a conditional circular line (arc) referring either to the Arctic Circle or the Antarctic Circle. These are two of the keynote circles of latitude (parallels). On Earth, the Arctic Circle is currentl ...

s (north of the

Arctic Circle The Arctic Circle is one of the two polar circles, and the northernmost of the five major circle of latitude, circles of latitude as shown on maps of Earth at about 66° 34' N. Its southern counterpart is the Antarctic Circle. The Arctic Circl ...

and south of the Antarctic Circle), each year will experience at least one day when the Sun remains below the

horizon The horizon is the apparent curve that separates the surface of a celestial body from its sky when viewed from the perspective of an observer on or near the surface of the relevant body. This curve divides all viewing directions based on whethe ...

for 24 hours (on the

winter solstice The winter solstice, or hibernal solstice, occurs when either of Earth's geographical pole, poles reaches its maximum axial tilt, tilt away from the Sun. This happens twice yearly, once in each hemisphere (Northern Hemisphere, Northern and So ...

), and at least one day when the Sun remains above the horizon for 24 hours (on the

summer solstice The summer solstice or estival solstice occurs when one of Earth's poles has its maximum tilt toward the Sun. It happens twice yearly, once in each hemisphere ( Northern and Southern). The summer solstice is the day with the longest peri ...

). In the

middle latitudes The middle latitudes, also called the mid-latitudes (sometimes spelled midlatitudes) or moderate latitudes, are spatial regions on either Hemispheres of Earth, hemisphere of Earth, located between the Tropic of Cancer (latitude ) and the Arctic ...

, the length of

, as well as

solar altitude Solar may refer to: Astronomy * Of or relating to the Sun ** Solar telescope, a special purpose telescope used to observe the Sun ** A device that utilizes solar energy (e.g. "solar panels") ** Solar calendar, a calendar whose dates indicate t ...

and

azimuth An azimuth (; from ) is the horizontal angle from a cardinal direction, most commonly north, in a local or observer-centric spherical coordinate system. Mathematically, the relative position vector from an observer ( origin) to a point ...

, 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 The equator is the circle of latitude that divides Earth into the Northern Hemisphere, Northern and Southern Hemisphere, Southern Hemispheres of Earth, hemispheres. It is an imaginary line located at 0 degrees latitude, about in circumferen ...

Visualization 1

The pictures below show the following perspectives from Earth, marking the hourly positions of the

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 astronomy and navigation, the celestial sphere is an abstract sphere that has an arbitrarily large radius and is concentric to Earth. All objects in the sky can be conceived as being projected upon the inner surface of 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

difference between the solstice suns. In addition, some "ghost" suns are visible below the

, as much as 18° down, during which

twilight Twilight is daylight 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 surf ...

occurs. The pictures can be used for both the northern and the southern

hemispheres of Earth In geography and cartography, hemispheres of Earth are any division of the Earth, globe into two equal halves (hemispheres), typically divided into northern and southern halves by the Equator and into western and eastern halves by the Prime meri ...

. 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 direction The four cardinal directions or cardinal points are the four main compass directions: north (N), south (S), east (E), and west (W). The corresponding azimuths ( clockwise horizontal angle from north) are 0°, 90°, 180°, and 270°. The ...

s. * In the

, north is to the left. The Sun rises in the east (far arrow), culminates in the south (to the right) while moving to the right, and sets in the west (near arrow). Both rise and set positions are displaced towards the north in midsummer and the south in midwinter. * In the Southern Hemisphere, south is to the left. The Sun rises in the east (near arrow), culminates in the north (to the right) while moving to the left, and sets in the west (far arrow). Both rise and set positions are displaced towards the south in midsummer and the north in midwinter. The following cases are depicted: * On the abstract line of the

(0° latitude), the Sun's maximum altitude is great during the entire year, but it does not form a perfect

right angle In geometry and trigonometry, a right angle is an angle of exactly 90 Degree (angle), degrees or radians corresponding to a quarter turn (geometry), turn. If a Line (mathematics)#Ray, ray is placed so that its endpoint is on a line and the ad ...

with the ground at noon every day. In fact it happens two days of the year, during the equinoxes. The solstices are the dates that the Sun stays farthest away from the

zenith The zenith (, ) is the imaginary point on the celestial sphere directly "above" a particular location. "Above" means in the vertical direction (Vertical and horizontal, plumb line) opposite to the gravity direction at that location (nadir). The z ...

but also in those cases it's high in the sky, reaching an altitude of 66.56° either to the north or the south. All days of the year, solstices included, have the same length of 12 hours. * Solstice day arcs as viewed from 20°

. The Sun culminates at 46.56° altitude in winter and 93.44° altitude in summer. In this case an angle larger than 90° means that the culmination takes place at an altitude of 86.56° in the opposite cardinal direction. For example, in the southern hemisphere, the Sun remains in the north during winter, but can reach over the zenith to the south in midsummer. Summer days are longer than winter days, but the difference is no more than approximately two and a half hours. The daily path of the Sun is steep at the horizon the whole year round, resulting in a twilight of only about one hour and 20 minutes in the morning and in the evening. * Solstice day arcs as viewed from 50° latitude. During the winter solstice, Sun does not rise more than 16.56° above the horizon at midday, but 63.44° in summer solstice above the same horizon direction. The difference in the length of the day between summer and winter, from here to the north, begin to be striking – slightly more than 8 hours at winter solstice, to more than 16 hours during the summer solstice. Likewise is the difference in direction of sunrise and sunset. At this latitude at midnight (around 1 a.m. with summer legal hour) the summer sun is 16.56° below the horizon, which means that ''astronomical twilight'' continues the whole night. This phenomenon is known as the '' grey nights'', nights when it does not get dark enough for astronomers to do their observations of the deep sky. Above 60° latitude, the Sun would be even closer to the horizon, only 6.56° away from it. Then ''civil twilight'' continues almost all night, only a little bit of ''nautical twilight'' around the local midnight. Above 66.56° latitude, there is no sunset at all, a phenomenon referred to as the

midnight sun 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 see ...

. * Solstice day arcs as viewed from 70° latitude. At local noon the winter Sun culminates at −3.44°, and the summer Sun at 43.44°. Said another way, during the winter the Sun does not rise above the horizon, it is the

polar night Polar night is a phenomenon that occurs in the polar regions of Earth, northernmost and southernmost regions of Earth when the Sun remains below the horizon for more than 24 hours. This only occurs inside the polar circles. The opposite phen ...

. There will be still a strong twilight though. At local midnight the summer Sun culminates at 3.44°. Said another way, it does not set; it is the polar day. * Solstice day arcs as viewed from either pole (90° latitude). At the time of the summer or winter solstices, the Sun is 23.44° degrees above or below the horizon, respectively, irrespective of time of day. Whilst the Sun is up (during summer months) it will circle around the whole sky (clockwise from the

North Pole The North Pole, also known as the Geographic North Pole or Terrestrial North Pole, is the point in the Northern Hemisphere where the Earth's rotation, Earth's axis of rotation meets its surface. It is called the True North Pole to distingu ...

and counter-clockwise from the

South Pole The South Pole, also known as the Geographic South Pole or Terrestrial South Pole, is the point in the Southern Hemisphere where the Earth's rotation, Earth's axis of rotation meets its surface. It is called the True South Pole to distinguish ...

), appearing to stay at the same angle from the horizon, therefore the concept of day or night is meaningless. The angle of elevation will gradually change on an annual cycle, with the Sun reaching its highest point at the summer solstice, and rising or setting at the equinox, with extended periods of twilight lasting several days after the autumn equinox and before the spring equinox. ;Solstice day arcs as viewed from selected latitudes File:solstice-0.jpg, 0° latitude (the

) File:solstice-20.jpg, 20° latitude File:solstice-50.jpg, 50° latitude File:solstice-70.jpg, 70° latitude File:solstice-90.jpg, 90° latitude ( either pole)

Visualization 2

A 2021 publicationZhang, T., Stackhouse, P.W., Macpherson, B., and Mikovitz, J.C., 2021. A solar azimuth formula that renders circumstantial treatment unnecessary without compromising mathematical rigor: Mathematical setup, application and extension of a formula based on the subsolar point and atan2 function. ''Renewable Energy'', 172, 1333-1340. DOI: https://doi.org/10.1016/j.renene.2021.03.047 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 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 Solar time#Mean solar time, mean solar time over the course of a year. The change of position is a result ...

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. File:Wreath_of_Analemmas_Rotterdam.png,

Rotterdam Rotterdam ( , ; ; ) is the second-largest List of cities in the Netherlands by province, city in the Netherlands after the national capital of Amsterdam. It is in the Provinces of the Netherlands, province of South Holland, part of the North S ...

, the Netherlands File:Wreath_of_Analemmas_Equator.png,

Prime Meridian A prime meridian is an arbitrarily chosen meridian (geography), meridian (a line of longitude) in a geographic coordinate system at which longitude is defined to be 0°. On a spheroid, a prime meridian and its anti-meridian (the 180th meridian ...

File:Wreath_of_Analemmas_North_Pole.png,

File:Wreath_of_Analemmas_South_Pole.png,

References

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External links

* U.S. Naval Observatorybr>Sun or Moon Altitude/Azimuth Table

Sun path calculation and visualization on Android

Sun path in augmented reality

Sun path by location and date

Sun positions, diagram and paths around the world by location and date

Seasonal and Hourly Sun Path Design Issue Tutorial

Sun path on map, charts and table, sun position for every location and date

Sun position by location and date
Meteorological quantities Observational astronomy Solar design