Sun path
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. 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. Effect of the Earth's axial tilt. Sun paths at any latitude and any time of the year can be determined from basic geometry. 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. Shadow of a vertical stick at solar noon. On the equator, the sun will be straight overhead and a vertical stick will cast no shadow at solar noon on the equinoxes. Roughly 23.5 degrees north 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 rest of the year, the noon shadow will point to the North pole. Roughly 23.5 degrees south of the equator on the Tropic of Capricorn, a vertical stick will cast no shadow on December 21, the summer solstice for the southern hemisphere, 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 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 north and true south respectively only 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 north nor south (δ☉ = 0°) and solar time noon shadows point NNW north of the equator and SSE south of the equator on the vernal equinox (and point NNE north of the equator and SSW south of the equator on the autumnal equinox). Duration of daylight. 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. Visualization. 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: Visualization for every day of a full year for both daytime and nighttime. A 2021 publication 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.