What are sunrise and sunset?

What are sunrise and sunset?

The U.S. Naval Observatory states the everyday convention plainly: "Sunrise and sunset conventionally refer to the times when the upper edge of the disk of the Sun is on the horizon."¹ The two events are the symmetric morning and evening halves of the same astronomical phenomenon — the Sun's apparent path carries it above the horizon at sunrise and below it again at sunset. Wikidata, the structured-data sister of Wikipedia, gives the same definition for sunrise as the "instant at which the upper edge of the Sun appears over the eastern horizon in the morning" and for sunset as the "daily disappearance of the Sun below the western half of the horizon."⁶⁷

The "upper edge" qualifier matters. If the convention used the Sun's centre, sunrise and sunset would be visibly later and earlier than the actual disappearance and reappearance of the Sun. The choice of the upper limb instead — the topmost point of the apparent solar disc — keeps the published times faithful to what an observer with a flat horizon actually sees.

For the calculation that produces the time, the convention is converted into an angle of the Sun's centre below the horizon. The U.S. Naval Observatory states it as: "for computational purposes, sunrise or sunset is defined to occur when the geometric zenith distance of center of the Sun is 90.8333 degrees" — equivalently, when the Sun's centre is 0.8333° (50 arcminutes) below the geometric horizon.¹ The same threshold appears in NOAA's solar calculator and every modern sun-position library.²

Why 0.8333° below the horizon?

The 50-arcminute figure is the sum of two physically independent corrections that happen to point the same way at the moment of rising and setting.¹

• 16 arcminutes of solar semidiameter. The Sun is not a point. Its apparent radius, the angle from the Sun's centre to its edge as seen from Earth, averages about a sixteenth of a degree. When the upper limb is on the horizon, the centre is 16 arcminutes below it.
• 34 arcminutes of atmospheric refraction. Light from the Sun crosses Earth's atmosphere on its way to the observer, and the atmosphere bends it. Refraction is strongest where the path is most oblique to the air — at the horizon — and lifts the Sun's apparent position by roughly 34 arcminutes there. NOAA's glossary states the cause directly: "as light from the sun (or another celestial body) travels from the vacuum of space into Earth's atmosphere, the path of the light is bent due to refraction."³

The two corrections add. The Sun's centre has to climb (or fall) the full 50 arcminutes from the geometric horizon before its upper limb reaches the visible horizon, so the formula uses the Sun's centre at 0.8333° below the horizon as the trigger event.¹ One consequence is that the Sun is observable above the horizon while it is still geometrically below it. Another is that day length, defined between observed sunrise and observed sunset, is always slightly longer than the time the Sun's centre actually spends above the geometric horizon — a few extra minutes near the equator, more at high latitudes.

The 34-arcminute figure is a long-term average. Real-world refraction varies with air temperature, pressure, and humidity. Any actual sunrise or sunset is therefore observed a minute or two earlier or later than the computed time — usually less than a minute at low and middle latitudes, occasionally several minutes near the poles, where the Sun's path skims the horizon at a very shallow angle and small refraction differences translate into large time differences.¹

How are sunrise and sunset calculated?

The textbook procedure is to compute the Sun's geometric altitude — its angle above an idealised, refraction-free horizon — for the location and instant of interest, then find the moments at which that altitude crosses the −0.8333° threshold in each direction. Solar position is derived from the day's solar declination δ (the Sun's angular distance north or south of the celestial equator) and the observer's latitude φ; the two combine through the spherical-astronomy identity for the hour angle H₀ at sunrise and sunset:⁸

cos H₀ = (sin h₀ − sin φ · sin δ) / (cos φ · cos δ)

Here h₀ is the apparent altitude convention — −0.8333° for sunrise and sunset. The hour angle is converted to a time of day by adding it to (or subtracting it from) solar noon: sunrise is solar noon minus H₀ converted to hours, sunset is solar noon plus H₀. Solar noon itself depends on the observer's longitude and the day's equation of time, which together shift the moment of meridian transit away from civil 12:00 by up to roughly an hour.⁴

The standard implementations are NOAA's solar calculator and the formulas in Jean Meeus's Astronomical Algorithms — the canonical reference textbook for the field. NOAA states: "The calculations in the NOAA Sunrise/Sunset and Solar Position Calculators are based on equations from Astronomical Algorithms, by Jean Meeus."²⁹ The U.S. Naval Observatory publishes a parallel approximate algorithm that it claims is "essentially the same as that found on page C5 of The Astronomical Almanac" and accurate to roughly one arcminute within two centuries of the year 2000.¹⁰

The textbook implementation is more accurate than most readers expect. NOAA states: "The sunrise and sunset results are theoretically accurate to within a minute for locations between +/- 72° latitude, and within 10 minutes outside of those latitudes."² The accuracy ceiling is set by the constant 34-arcminute refraction assumption rather than by the solar-position formula — a single calculation cannot know the actual atmospheric profile above any particular observer at any particular moment.

Why does the Sun look bigger and oranger at the horizon?

Two unrelated effects combine to make the rising and setting Sun look different from the noon Sun. Neither has to do with the Sun itself; both are properties of the air the light passes through.

The colour shift is the easier of the two to explain. At the horizon, sunlight reaches the observer through a much longer column of atmosphere than it does at midday. Air molecules scatter shorter wavelengths preferentially (Rayleigh scattering), so the longer path strips blue and green light from the beam and leaves the warmer reds and oranges to reach the eye.¹¹ The Wikipedia article on sunset gives the chain of cause directly: "the shorter wavelength components, such as blue and green, scatter more strongly, these colors are preferentially removed from the beam."¹²

The shape change is more interesting. The same atmospheric refraction that lifts the Sun's apparent position also varies across the disc — light from the bottom of the Sun is refracted more than light from the top, because the bottom rays travel a slightly longer path through the densest part of the atmosphere. The differential lift compresses the disc vertically. The Wikipedia sunrise article describes the geometry precisely: "Light from the lower edge of the Sun's disk is refracted more than light from the upper edge. This reduces the apparent height of the Sun when it appears just above the horizon. The width is not affected, so the Sun appears wider than it is high."¹¹ The flattening is easily noticeable in any clear-horizon photograph.

The "bigger" sensation is largely a perceptual illusion rather than an optical one. The Sun's actual angular diameter changes very little through the day; the apparent size at the horizon is a cousin of the Moon illusion, in which familiar reference objects on the horizon — distant trees, hills, buildings — make the disc look larger than it does isolated against an empty sky overhead.

How do latitude and season change sunrise and sunset?

Three things vary with latitude and time of year: the time at which sunrise and sunset occur, the direction along the horizon at which they occur (the azimuth), and the speed at which the Sun crosses the horizon.

The azimuth changes most dramatically with the seasons. At the equinoxes, the Sun rises due east and sets due west everywhere on Earth. Through the rest of the year the rise and set points sweep north and south of east and west, with the maximum excursion on the solstices. At mid-latitudes the maximum excursion is several tens of degrees from due east and west; in the tropics it is smaller; near the polar circles it grows large enough that on midsummer day the Sun "rises" in the north-northeast and "sets" in the north-northwest, having crossed the entire eastern, southern, and western sky between them.

The angle at which the Sun crosses the horizon governs the duration of the rise and set events themselves — the time the disc takes to clear or be eclipsed by the horizon — and the duration of twilight on either side. Near the equator, the Sun's daily path is nearly perpendicular to the horizon, so the disc cuts down through the rising-Sun, twilight, and night thresholds quickly; sunrise and sunset each play out in only a couple of minutes. Near the polar circles, the path is nearly parallel to the horizon, so the same thresholds are crossed slowly and the disc can take many minutes to clear or be eclipsed by the horizon at midsummer.

Time of day shifts with latitude through the equation-of-time and longitude offsets that already separate solar noon from civil noon. Within a single time zone, sunrise can fall tens of minutes apart between observers at the eastern and western edges of the zone, even on the same day at the same latitude, because the same civil clock covers up to fifteen degrees of longitude — a full hour of solar-time difference.

Why don't earliest sunset and latest sunrise fall on the solstice?

The shortest day of the year — for an observer in the Northern Hemisphere — is the December solstice, the date on which the Sun reaches its lowest noon altitude. Day length is at its annual minimum on that date. The earliest sunset and the latest sunrise of the year, however, do not fall on the same day. Earliest sunset arrives a week or two before the solstice; latest sunrise lands a week or two after it. The Sun is at its lowest in the middle of December, but it is not at its earliest-setting until early December, and not at its latest-rising until early January.

The asymmetry comes from the equation of time, the difference between apparent solar time (what the Sun in the sky shows) and mean solar time (the steady time scale a clock keeps). The U.S. Naval Observatory states the link directly: "The Equation of Time moves the date of earliest sunset to before the solstice and the date of latest sunrise to after the solstice."⁴ On dates near the December solstice, the equation of time is moving rapidly through its early-November maximum; the Sun is "running fast" relative to the clock by roughly half a minute per day, biasing the entire daily clock pattern of solar events earlier. Earliest sunset therefore lands a week or two before the solstice. By early January, the equation of time has turned and the Sun is "running slow" relative to the clock; latest sunrise lands a week or two after the solstice for the same reason.

The mid-southern-latitude observer experiences the mirror version around the June solstice: earliest sunset before, latest sunrise after. The asymmetry is built into apparent solar time, not an artefact of the calculation.

What about high latitudes and altitude?

At sufficiently high latitudes the Sun fails to rise or set on at least some dates of the year. The boundary is the Arctic Circle in the Northern Hemisphere and the Antarctic Circle in the Southern, both at approximately 66°34′ from the equator — Earth's axial tilt of 23.44° subtracted from 90°. Above the Arctic Circle, on the December solstice the Sun never climbs above the horizon (polar night); on the June solstice it never falls below it (the midnight Sun). The duration of each phenomenon grows with latitude, lengthening from a single day at the polar circle itself to a continuous stretch lasting most of a half-year at the geographic poles.

NOAA's solar calculator handles the polar case explicitly: "For locations above the Arctic Circle and below the Antarctic Circle, when a sunrise or sunset does not occur on the given day the program locates the local time and date of the most recent sunrise or sunset, and the next sunset or sunrise."⁵ On a polar-summer date inside the Arctic Circle, the calculator therefore returns the previous sunrise (sometimes weeks earlier) and the next sunset (sometimes weeks later), with the Sun continuously above the horizon in between.

USNO warns that even at sub-polar high latitudes the published times become uncertain: "The accuracy of rise and set computations decreases at high latitudes. There, small variations in atmospheric refraction can change the time of rise or set by many minutes, since the Sun and Moon intersect the horizon at a very shallow angle."¹ At a high-latitude observatory in northern Norway or northern Canada, a sunrise computed for a particular date can shift by many minutes if the actual atmospheric refraction differs even modestly from the standard 34-arcminute average — and the same warning applies to anything that depends on a sharply-defined horizon, such as the timing of the first solar glimmer above mountains, sea, or local terrain.

Observer altitude shifts the times in the opposite direction from latitude. An observer on a mountain or in an aircraft sees the geometric horizon depressed below the local horizontal — the dip angle from the horizontal grows with altitude. The Sun therefore rises a little earlier and sets a little later than it does for an observer at sea level on the same plumb line. The effect is small at modest altitudes but grows visibly large for an observer aboard a high-altitude aircraft, where the apparent sunset can run well past the time it would have arrived for the ground beneath.

How are sunrise and sunset used?

Sunrise and sunset times are the foundation of every "sun event" calculation an ordinary user might want — day length, civil/nautical/astronomical twilight, golden hour, blue hour, the times at which the Sun reaches a particular altitude or azimuth. Most software computes solar noon first, derives sunrise and sunset as offsets from it, and derives every other event as a separate altitude threshold against the same hour-angle equation.

The legal and operational uses follow the practical pattern. Many jurisdictions reference vehicle-headlight requirements, the boundaries between day and night for hunting and fishing, and the timing of religious observances to local sunrise and sunset (or to the closely-related civil twilight thresholds). Aviation and maritime regulations usually rely on the same times. Photographers, astronomers, and outdoor recreationists use them to plan around the visible Sun.

For pages on this site, the sunrise/sunset calculation drives the entire sun-and-moon section. Pick a city and a date in the sunrise & sunset calculator to see the local times, day length, and a year-long sun graph. The dedicated city sun pages — Sydney, London, and so on — quote the same numbers along with twilight, solar noon, and the seasonal context, all derived from the same NOAA-flavoured solar-position formula.

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