Sunrise and sunset: what determines the times?

What astronomers mean by sunrise

In everyday terms, sunrise is the first glimpse of the Sun above the horizon. Calculations need a precise convention: the upper limb of the solar disk touches the mathematical horizon, an ideal level reference with no mountains, buildings or trees blocking the view.

Two effects determine that moment. The Sun has an apparent radius of about sixteen arcminutes, so when its upper limb reaches the horizon, its centre is still below it. The atmosphere also bends light, raising an object’s apparent position. A standard value for this refraction near the horizon is about thirty-four arcminutes, slightly more than a whole solar diameter. You can therefore see the Sun while its geometric disk is still below the horizon.

Together, these give the usual reference altitude of −0.833° for the Sun’s centre at sunrise and sunset. The convention makes astronomical almanacs and calculation programs comparable; it does not turn the atmosphere into a perfectly predictable optical system.

What determines the clock time?

Four main factors govern when the Sun rises and sets at a location.

• Latitude controls the angle of the daily solar path and the length of its above-horizon arc. Seasonal differences grow as you move away from the equator.
• Date determines solar declination, the Sun’s angular distance from the celestial equator. It changes between about +23.4° around the June solstice and −23.4° around the December solstice.
• Longitude shifts solar events within a time zone. For otherwise comparable locations, an eastern site experiences them earlier on a shared clock than a western site. The east–west spread across the New York area and farther across the same time zone illustrates why a single published city time is not universal; latitude also matters when comparing actual cities.
• Time zone and daylight-saving arrangements change the clock reading rather than the celestial event. Compare the correct local date and zone, especially on a trip across state or national boundaries.

The equation of time adds another variation. The Sun does not cross the meridian at the same mean-clock time every day. Its seasonal displacement can amount to roughly a quarter of an hour, so sunrise and sunset are not necessarily balanced around 12:00 on your watch.

The daily arc: latitude and the seasons

The Sun’s daily path is approximately a circle parallel to the celestial equator. The horizon divides it into an above-horizon day arc and a below-horizon night arc. In the simplified picture, rise and set lie symmetrically around local apparent noon, when the Sun crosses the upper meridian. That crossing is towards the south at middle northern latitudes, but not everywhere on Earth.

Solar declination moves the daily circle northward in June and southward in December. For a Northern Hemisphere location, more of the circle lies above the horizon in June; the Southern Hemisphere has the reverse seasons. Latitude determines how strongly this shift changes the visible arc. Near the equator, days remain close to twelve hours; farther towards either pole, the seasonal difference grows. Beyond the polar circles, the whole daily path can lie above or below the horizon for a time.

Even during a single day, solar declination changes a little. Precise software therefore refines the event iteratively rather than relying on a fixed, perfectly symmetric daily circle.

Why a calculated time may differ from what you see

A precise calculation and an actual sighting can differ for understandable reasons.

• Refraction varies. The standard thirty-four arcminutes is a representative value. Temperature, pressure and layers of air over cold water or snow can alter the bending, shifting an observed event by minutes, especially at high latitudes.
• Your visible horizon has a shape. At the Grand Canyon, a ridge can hide the Sun even when it is above the mathematical horizon. City buildings have the same effect. An unobstructed sea horizon gives a different experience.
• Elevation changes the view. From an elevated site with a clear distant horizon, the visible horizon dips below eye level. This horizon dip can make sunrise earlier and sunset later. A high viewpoint does not remove nearby terrain from the line of sight.

Practical observing tips

Sunrise is the end of morning civil twilight, rather than the brightest moment of the morning. If you are planning photographs, allow time on both sides of it. The point on the horizon also changes through the year: at middle northern latitudes the Sun rises north of east in June, south of east in December and approximately due east around the equinoxes. The southern seasonal pattern is reversed.

The earliest sunset does not generally occur on the shortest day, nor the latest sunrise on exactly the same date. The equation of time shifts local apparent noon while the length of the daily arc is changing slowly near a solstice. The dates of those extremes depend on latitude, so a date quoted for northern Europe should not simply be reused for New York, Arizona or a Southern Hemisphere destination.

Never look directly at the Sun without appropriate solar protection, even when it appears dim near the horizon. Binoculars, telescopes and cameras require solar filters designed for the instrument and securely fitted in front of its optics; ordinary eclipse glasses do not make looking through unfiltered optics safe.