How Does The Angle Of The Sun Change Throughout The Year

Arc-similar path that the Sun appears to follow across the sky

Sun path polar chart for any location at the latitude of Rotterdam

Sun path, sometimes also called twenty-four hour period arc, refers to the daily and seasonal arc-like path that the Sun appears to follow across the heaven every bit 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 cistron in the heat proceeds of buildings and in the functioning of solar energy systems.^[i] Authentic location-specific knowledge of sun path and climatic atmospheric condition is essential for economic decisions almost solar collector expanse, orientation, landscaping, summer shading, and the cost-constructive utilise of solar trackers.^[2] ^[3]

Effect of the World's axial tilt [edit]

Lord's day paths at any latitude and any time of the year can be adamant from basic geometry.^[4] ^{[ unreliable source? ]} The Earth'south axis of rotation tilts about 23.5 degrees, relative to the plane of Globe'southward orbit around the Sun. As the Globe orbits the Sun, this creates the 47° declination difference between the solstice sun paths, too 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 pinnacle at a depression 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 firm all day long. A vertical window facing south (equator side) is constructive for capturing solar thermal energy. For comparison, the winter sunday in the Southern Hemisphere (May, June, July) rises in the northeast, peaks out at a low angle in the north (more than than halfway up from the horizon in the torrid zone), and then sets in the northwest. There, the north-facing window would allow in enough 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 due south of overhead signal (lower in the south at higher latitude), and and so sets in the northwest, whereas in the Southern Hemisphere in summer (November, December, Jan), the Sun rises in the southeast, peaks out slightly north of overhead indicate (lower in the north at college breadth), and then sets in the southwest. A unproblematic latitude-dependent equator-side overhang can easily be designed to block 100% of the direct solar proceeds from entering vertical equator-facing windows on the hottest days of the year. Scroll-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 lord's day rises due east and sets due w. In the Northern Hemisphere, the equinox sun peaks in the southern half (nearly halfway up from the horizon at mid latitude) of the sky, while in the Southern Hemisphere, that dominicus peaks in the northern half of the sky. When facing the equator, the sun appears to movement from left to right in the Northern Hemisphere and from right to left in the Southern Hemisphere.

The breadth (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.South., 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 n in the Southern Hemisphere, where the acme summer solstice solar altitude occurs on December 21.

Shadow of a vertical stick at solar noon [edit]

On the equator, the lord's day will be straight overhead and a vertical stick will cast no shadow at solar noon on the equinoxes. Roughly 23.5 degrees n of the equator on the Tropic of Cancer, a vertical stick will cast no shadow on June 21, the summer solstice for the northern hemisphere. The balance of the year, the noon shadow will betoken to the North pole. Roughly 23.5 degrees south of the equator on the Tropic of Capricorn, a vertical stick will bandage no shadow on December 21, the summertime solstice for the southern hemisphere, and the rest of the year its apex shadow volition point to the South pole. North of the Tropic of Cancer, the noon shadow will always point due north, and conversely, south of the Tropic of Capricorn, the noon shadow will always point south.

The solar noon shadows of objects on points beyond and below subsolar points will point towards true northward and true due south respectively merely when the solar declination has its maximum positive (δ☉ = +23.44°) or maximum negative (δ☉ = −23.44°) value. On the other hand, on the equinoxes when the sun is neither declined due north nor due south (δ☉ = 0°) and solar fourth dimension noon shadows point NNW north of the equator and SSE due south of the equator on the vernal equinox (and bespeak NNE north of the equator and SSW south of the equator on the autumnal equinox).

Duration of daylight [edit]

Within the polar circles (north of the Chill Circumvolve and south of the Antarctic Circle), each year will experience at least ane day when the Sunday remains below the horizon for 24 hours (on the winter solstice), and at least i day when the Sun remains to a higher place the horizon for 24 hours (on the summer solstice).

In the middle latitudes, the length of daytime, also as solar altitude and azimuth, vary from one day to the next, and from flavor to season. The difference between the lengths of a long summer solar day and of a brusque wintertime day increases as one moves farther away from the Equator.^[2]

Visualization [edit]

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 24-hour interval arcs, the paths along which the Sun appears to follow on the celestial sphere in its diurnal move. The longer arc is ever the midsummer path while the shorter arc the midwinter path. The ii 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, every bit 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 pocket-size isle in the middle of the sea. The light-green arrows represent the cardinal directions.

In the Northern Hemisphere, 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 ascent and set positions are displaced towards the due north in midsummer and the due south in midwinter.
In the Southern Hemisphere, south is to the left. The Sun rises in the east (nigh arrow), culminates in the northward (to the right) while moving to the left, and sets in the w (far pointer). Both rise and set positions are displaced towards the southward in midsummer and the northward in midwinter.

The following cases are depicted:

On the abstruse line of the Equator (0° breadth), the Lord's day's maximum altitude is great during the entire year, but it does not form a perfect right angle with the ground at apex every solar 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 but anyway also in those cases information technology's high in the sky, reaching an distance of 66.56° either to the due north or the due south. All days of the year, solstices included, have the same length of 12 hours.
Solstice twenty-four hour period arcs as viewed from 20° breadth. The Sun culminates at 46.56° altitude in wintertime and 93.44° altitude in summer. In this instance an angle larger than 90° means that the culmination takes identify at an altitude of 86.56° in the reverse cardinal management. For example, in the southern hemisphere, the Sun remains in the north during wintertime, but can reach over the zenith to the south in midsummer. Summertime days are longer than winter days, but the deviation is no more than approximately two and a half hours. The daily path of the Sun is steep at the horizon the whole twelvemonth circular, resulting in a twilight of only most one hour and 20 minutes in the forenoon and in the evening.
Solstice twenty-four hour period arcs every bit viewed from l° latitude. During the winter solstice, Sunday does not ascension more than than 16.56° above the horizon at midday, but 63.44° in summer solstice in a higher place the same horizon direction. The difference in the length of the day between summertime and winter, from here to the north, brainstorm to be striking – slightly more than 8 hours at winter solstice, to more than than 16 hours during the summer solstice. Also is the difference in direction of sunrise and sunset. At this breadth at midnight (effectually 1 a.grand. with summertime legal 60 minutes) the summer sun is 16.56° below the horizon, which means that astronomical twilight continues the whole night. This miracle is known as the grey nights, nights when it does not get nighttime enough for astronomers to do their observations of the deep sky. Above 60° breadth, the Sun would be even closer to the horizon, but six.56° away from it. And then civil twilight continues almost all night, simply a little bit of nautical twilight effectually the local midnight. Above 66.56° latitude, there is no sunset at all, a phenomenon referred to as the midnight sun.
Solstice day arcs equally viewed from 70° latitude. At local noon the winter Sun culminates at −iii.44°, and the summer Sun at 43.44°. Said another way, during the wintertime the Sun does not rise above the horizon, it is the polar nighttime. There will be however a strong twilight though. At local midnight the summer Sunday culminates at three.44°. Said some other way, it does not set; it is the polar day.
Solstice day arcs as viewed from either pole (90° breadth). At the fourth dimension of the summer or wintertime solstices, the Sun is 23.44° degrees above or below the horizon, respectively, irrespective of time of twenty-four hour period. Whilst the Sun is upward (during summertime months) it will circle effectually the whole sky (clockwise from the North Pole and counter-clockwise from the South Pole), appearing to stay at the aforementioned bending from the horizon, therefore the concept of twenty-four hours or night is meaningless. The angle of top volition gradually change on an annual cycle, with the Lord's day reaching its highest point at the summertime solstice, and ascent or setting at the equinox, with extended periods of twilight lasting several days after the autumn equinox and earlier the spring equinox.

Solstice day arcs as viewed from selected latitudes

20° latitude
l° latitude
70° latitude

Visualization for every day of a full year for both daytime and night [edit]

A 2021 publication ^[5] about solar geometry offset calculates the x-, y- and z-component of the solar vector, which is a unit vector with its tail fixed at the observer'south location and its head kept pointing toward the Sun, and so uses the components to summate the solar zenith angle and solar azimuth bending. The calculated solar vector at 1-hour step for a full yr for both daytime and dark can be used to visualize the Sunday path effectively.

In the following figures, the origin of the coordinate system is the observer'due south location, x-positive is East, y-positive is Due north, and z-positive is up; at Due north Pole, y-negative is tangent to the prime number meridian; at Due south Pole, y-positive is tangent to the prime tiptop; z-positive is daytime, and z-negative is nighttime; the time step is 1 60 minutes.

Each "eight" pattern in all figures is an analemma corresponding to a specific hour of every twenty-four hours of the year; all the 24 hours on a specific 24-hour interval of the twelvemonth depict the lord's day path of that day.

Encounter likewise [edit]

Ecliptic
Passive solar design
Solar access
Pyranometer
Pyrheliometer
Heliostat
Daylighting
Analemma
Effect of Sun angle on climate
Position of the Dominicus
Equinox
Solstice

References [edit]

^ "Solar Resources Information". National Renewable Free energy Laboratory. Retrieved 2009-03-28 .
^ ^a ^b Khavrus, Five.; Shelevytsky, I. (2010). "Introduction to solar motion geometry on the basis of a elementary model". Physics Education. 45 (6): 641. Bibcode:2010PhyEd..45..641K. doi:ten.1088/0031-9120/45/6/010.
^ Khavrus, V.; Shelevytsky, I. (2012). "Geometry and the physics of seasons". Physics Educational activity. 47 (half-dozen): 680. doi:10.1088/0031-9120/47/6/680.
^ Librorum, Helluo (2012). "Notes from Noosphere: The uncomplicated geometry of sun, moon, and star paths". notesfromnoosphere.blogspot.com . Retrieved September xix, 2013.
^ Zhang, 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 betoken and atan2 function. Renewable Energy, 172, 1333-1340. DOI: https://doi.org/10.1016/j.renene.2021.03.047