What is solar position?

What is solar position?

Solar position is the Sun's apparent location in the sky as seen from a particular point on Earth at a particular instant, expressed as a pair of angles in the horizon coordinate system. The U.S. Naval Observatory describes the frame directly: "The horizon coordinate system is best suited" for expressing the positions of celestial bodies relative to where the observer stands, and "in the horizon system, positions are expressed using the coordinates azimuth (A) and altitude (a)."¹ The two angles together pin the Sun to a single point on the dome of the sky.

What makes the horizon system intuitive is that it is anchored to the observer, not to the stars. Altitude is measured from the observer's own horizon and azimuth from the observer's own compass, so the same Sun has a different altitude and azimuth for two people standing in different places at the same moment. This is the opposite of the equatorial coordinates astronomers use to catalogue stars — right ascension and declination, fixed to the celestial sphere — which give the same value worldwide. Solar position is the local, observer-centred view: the answer to "where in my sky is the Sun right now?"

Because the Earth turns and orbits, the Sun's altitude and azimuth never hold still. Over a day the Sun sweeps up from the eastern horizon, across the sky, and down to the west; over a year the whole arc rises and falls with the seasons. Wikidata, the structured-data sister of Wikipedia, captures the entity tersely as the "apparent location of the Sun in the sky."⁴ Everything the site reports about the Sun — sunrise, the length of the day, twilight, golden hour, the moment of solar noon — is ultimately a statement about this position at some chosen altitude.

What is the difference between altitude and azimuth?

Altitude and azimuth are the two independent angles that a single position in the sky requires — one vertical, one horizontal. The U.S. Naval Observatory defines each precisely. Altitude is "the angular distance of a celestial body above or below the observer's horizon, measured along a great circle passing through the body and the observer's zenith."¹ It is 0° when the Sun is on the horizon, 90° when the Sun is at the zenith directly overhead, and negative when the Sun is below the horizon. Altitude is also called elevation; the two words mean the same angle.²

Azimuth is "the angular distance measured clockwise along the observer's horizon from a specified reference point (usually true north) to the intersection with a great circle drawn from the observer's zenith through the celestial body of interest."¹ In the convention this site uses — the same one the U.S. Naval Observatory and the National Oceanic and Atmospheric Administration use — azimuth is measured clockwise from true north: 0° is due north, 90° is due east, 180° is due south, and 270° is due west.² A second angle, the solar zenith angle, is sometimes quoted instead of altitude; it is simply the complement, "90° minus the elevation," measured downward from the point straight overhead rather than upward from the horizon.²

The two angles answer different questions. Altitude says how high to tilt your head; azimuth says which way to turn. At sunrise the Sun's azimuth points roughly east and its altitude is near zero; through the morning the altitude climbs while the azimuth swings toward south (for a northern-hemisphere observer); at solar noon the azimuth is exactly due south or due north and the altitude is at its daily maximum; through the afternoon the altitude falls again while the azimuth continues toward west. The Sun rises exactly due east and sets exactly due west only on the two equinoxes, when its declination is zero; on every other date the rising and setting points shift north or south of due east and west.

What determines the Sun's position in the sky?

Three quantities fix the Sun's altitude and azimuth at any moment: the observer's latitude, the Sun's declination on the date, and the hour angle that encodes the time of day. Change any one and the position moves.

Latitude sets the tilt of the whole sky. Near the equator the Sun's daily path runs nearly straight up from the horizon and passes high overhead; near the poles it circles low around the horizon. The Sun's declination — its angular distance north or south of the celestial equator — sets the seasonal part of the geometry. Declination varies smoothly through the year between −23.44° at the December solstice and +23.44° at the June solstice, passing through zero at the equinoxes; the 23.44° figure is the tilt of the Earth's axis itself.² The hour angle measures how far, in angle, the Sun is from the observer's meridian: it is zero at solar noon and changes by 15° for every hour of true solar time, because the Earth turns 360° in 24 hours.

These three feed a single spherical-astronomy identity for the altitude a at latitude φ, declination δ, and hour angle H:

sin a = sin φ · sin δ + cos φ · cos δ · cos H

The azimuth follows from the same three inputs through a companion formula, taken clockwise from north. The practical upshot is that solar position cannot be read off a single number. Two observers at the same longitude but different latitudes see the noon Sun at different heights on the same day; one observer sees the Sun trace a completely different arc in June than in December. The site computes both angles for any city and date using the position algorithm published by the National Oceanic and Atmospheric Administration, which is accurate "to within a minute for locations between +/- 72° latitude."⁵

How does solar altitude define sunrise, twilight, and golden hour?

Most of the sun events this site reports are not separate phenomena — they are named altitude thresholds that the Sun passes through as it climbs and descends. Reading the events as one continuous ladder of altitudes, from high in the sky down into the dark, makes the relationships between them plain:

• Golden hour — the Sun is above the horizon but no higher than about 6° in altitude, casting warm, low-angle light. Its lower edge is sunrise or sunset; its upper edge is a photographic convention, not a standards-body figure.
• Sunrise and sunset — the Sun's upper limb is on the horizon. For computation the U.S. Naval Observatory places the Sun's centre 0.833° (50 arcminutes) below the horizon at this instant, allowing 34 arcminutes for atmospheric refraction and 16 for the Sun's apparent radius.³
• Blue hour — the Sun is roughly 4° to 6° below the horizon and the sky takes on a deep blue tint, sitting inside the start of civil twilight.
• Civil, nautical, and astronomical twilight — the Sun's centre is 6°, 12°, and 18° below the horizon respectively. Past 18° below, scattered sunlight drops beneath natural starlight and astronomical night begins.³

Each event is simply the moment the Sun's altitude crosses one of these lines. The same thresholds appear in the National Oceanic and Atmospheric Administration's calculator expressed as zenith angles — 96°, 102°, and 108° for the three twilights, equivalent to 6°, 12°, and 18° of altitude below the horizon.⁵ Why the events happen at different clock times in different places is itself a solar-position question: at low latitudes the Sun drops through the altitude lines almost vertically, so the gaps between events are short, while at high latitudes its shallow path can take an hour or more to cross the same few degrees — and above certain latitudes it never reaches the deeper thresholds at all. The same geometry governs day length, which is just the time the Sun spends above the 0° line.

What are solar noon and the subsolar point?

Solar noon is the instant of greatest solar altitude on any given day — the moment the Sun crosses the observer's meridian, with its azimuth pointing exactly due south for a northern-hemisphere observer or due north for a southern one. The height the Sun reaches at that instant follows directly from latitude and declination: the noon altitude equals 90° − |latitude − declination|. At the equator on an equinox both terms are zero and the noon Sun stands at the zenith; outside the tropics it never does.²

The subsolar point is the one place on the Earth's surface, at any given instant, where the Sun is exactly overhead — altitude 90°, zenith angle 0°, a vertical pole casting no shadow. Its latitude is equal to the Sun's declination at that moment, so it travels between the Tropic of Cancer (23.44° N) at the June solstice and the Tropic of Capricorn (23.44° S) at the December solstice, crossing the equator at the equinoxes.² Its longitude is the meridian where it is solar noon at that instant, so the subsolar point sweeps westward around the planet once a day as the Earth turns. Anywhere inside the tropics lies under the subsolar point on exactly two dates each year — the days when the Sun's declination matches the local latitude — and sees the noon Sun pass straight overhead.

How is solar position calculated?

The standard method computes the Sun's declination and the equation of time for the date, derives the hour angle from the observer's longitude and the time, and then applies the spherical-trigonometry formulas for altitude and azimuth. The reference implementation is the one published by the National Oceanic and Atmospheric Administration in its solar calculator, whose algorithms are derived from Jean Meeus's Astronomical Algorithms, the canonical textbook for the field; the documentation states results are "theoretically accurate to within a minute for locations between +/- 72° latitude."⁵ This site uses the same algorithm, with azimuth measured clockwise from true north to match the U.S. Naval Observatory and NOAA conventions.¹

Solar position underlies every sun tool on the site. Each city's sun page reports the Sun's azimuth at sunrise and sunset and its altitude at solar noon for any date, alongside a year-long graph of how those values shift with the seasons, and the solar noon calculator gives the peak noon altitude for a chosen place and day. Whether the question is when the Sun rises, how long the day lasts, or how high the Sun will climb at midday, the answer is read off the same two angles.

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