Sunrise Time Lapse Video

Although the Sun appears to "rise" from the horizon, it is actually the Earth's motion that causes the Sun to appear. The illusion of a moving Sun results from Earth observers being in a rotating reference frame; this apparent motion is so convincing that many cultures had mythologies and religions built around the geocentric model, which prevailed until astronomer Nicolaus Copernicus formulated his heliocentric model in the 16th century.[3]

Architect Buckminster Fuller proposed the terms "sunsight" and "sunclipse" to better represent the heliocentric model, though the terms have not entered into common language.

Beginning and End

Astronomically, sunrise occurs for only an instant: the moment at which the upper limb of the Sun appears tangent to the horizon.[1] However, the term sunrise commonly refers to periods of time both before and after this point:

Twilight, the period in the morning during which the sky is brightening, but the Sun is not yet visible. The beginning of morning twilight is called astronomical dawn.
The period after the Sun rises during which striking colors and atmospheric effects are still seen.[2]

Angle Edit
The stage of sunrise known as false sunrise actually occurs before the Sun truly reaches the horizon because Earth's atmosphere refracts the Sun's image. At the horizon, the average amount of refraction is 34 arcminutes, though this amount varies based on atmospheric conditions.[1]

Also, unlike most other solar measurements, sunrise occurs when the Sun's upper limb, rather than its center, appears to cross the horizon. The apparent radius of the Sun at the horizon is 16 arcminutes.[1]

These two angles combine to define sunrise to occur when the Sun's center is 50 arcminutes below the horizon, or 90.83° from the zenith.[1]

Time of Day Edit
The timing of sunrise varies throughout the year and is also affected by the viewer's latitude and longitude, altitude, and time zone. These changes are driven by the axial tilt of Earth, daily rotation of the Earth, the planet's movement in its annual elliptical orbit around the Sun, and the Earth and Moon's paired revolutions around each other. The analemma can be used to make approximate predictions of the time of sunrise.
In late winter and spring, sunrise as seen from temperate latitudes occurs earlier each day, reaching its earliest time near the summer solstice; although the exact date varies by latitude. After this point, the time of sunrise gets later each day, reaching its latest sometime around the winter solstice. The offset between the dates of the solstice and the earliest or latest sunrise time is caused by the eccentricity of Earth's orbit and the tilt of its axis, and is described by the analemma, which can be used to predict the dates.

Variations in atmospheric refraction can alter the time of sunrise by changing its apparent position. Near the poles, the time-of-day variation is exaggerated, since the Sun crosses the horizon at a very shallow angle and thus rises more slowly.[1]

Accounting for atmospheric refraction and measuring from the leading edge slightly increases the average duration of day relative to night. The sunrise equation, however, which is used to derive the time of sunrise and sunset, uses the Sun's physical center for calculation, neglecting atmospheric refraction and the non-zero angle subtended by the solar disc.

Neglecting the effects of refraction and the Sun's non-zero size, whenever sunrise occurs, in temperate regions it is always in the northeast quadrant from the March equinox to the September equinox and in the southeast quadrant from the September equinox to the March equinox.[4] Sunrises occur approximately due east on the March and September equinoxes for all viewers on Earth.[5] Exact calculations of the azimuths of sunrise on other dates are complex, but they can be estimated with reasonable accuracy by using the analemma.

The figure on the right is calculated using the solar geometry routine in Ref. [6] as follows: 1.) For a given latitude and a given date, calculate the declination of the Sun using {\displaystyle 0^{\circ }}{\displaystyle 0^{\circ }} longitude and solar noon time as inputs to the routine; 2.) Calculate the sunrise hour angle using the sunrise equation; 3.) Calculate the sunrise time, which is the solar noon time minus the sunrise hour angle in degree divided by 15; 4.) Use the sunrise time as input to the solar geometry routine to get the solar azimuth angle at sunrise.

Hemispheric symmetry Edit
An interesting feature in the figure on the right is apparent hemispheric symmetry in regions where daily sunrise and sunset actually occur.

This symmetry becomes clear if the hemispheric relation in sunrise equation is applied to the x- and y-components of the solar vector presented.