# Rise, Set, and Twilight Definitions

(For specific rise, set, and twilight computations, see
Complete Sun and Moon Data for One Day or
One Year's table of Sunrise/Sunset, Moonrise/Moonset, or
Twilight Times in **Data Services**.)

**Horizon**: Wherever one is located on or near the
Earth's surface, the Earth is perceived as essentially flat and,
therefore, as a plane. The sky resembles one-half of a sphere or
dome centered at the observer. If there are no visual
obstructions, the apparent intersection of the sky with the
Earth's (plane) surface is the horizon, which appears as a circle
centered at the observer. For rise/set computations, the
observer's eye is considered to be on the surface of the Earth,
so that the horizon is geometrically exactly 90 degrees from the observer's zenith.

**Rise, Set**: During the course of a day the Earth
rotates once on its axis causing the phenomena of rising and
setting. Excluding circumpolar objects, celestial bodies – stars and planets included – seem
to appear in the sky at the horizon to the East of any particular
place, then to cross the sky and again disappear at the horizon
to the West. The most noticeable of these events, and the most
significant in regard to ordinary affairs, are the rising and
setting of the Sun and Moon. Because the Sun and Moon appear as
circular disks and not as points of light, a definition of rise
or set must be very specific because not all of either body is seen to rise
or set at once.

Sunrise and sunsetconventionally refer to the times when the upper edge of the disk of the Sun is on the horizon. Atmospheric conditions are assumed to be average, and the location is in a level region on the Earth's surface.

Moonrise and moonsettimes are computed for exactly the same circumstances as for sunrise and sunset. However, moonrise and moonset may occur at any time of day and, consequently, it is often possible for the Moon to be seen during daylight, and to have moonless nights. It is also possible that a moonrise or moonset does not occur relative to a specific place on a given date.

**Transit**: The transit time of a celestial body
refers to the instant that its center crosses an imaginary line in the
sky - the observer's meridian - running from north to south. For
observers in low to middle latitudes, transit is
*approximately* midway between rise and set, and
represents the time at which the body is highest in the sky on any given day.
At high latitudes, neither of these statements may be true - for
example, there may be several transits between rise and set.
The transit of the Sun is local solar (sundial) noon. The difference
between the transit times of the Sun and Moon is closely related to the
Moon's phase. The New Moon transits at about the same time as the Sun;
the First Quarter Moon transits about 6 hours after the Sun;
the Full Moon transits about 12 hours after/before the Sun; and
the Last Quarter Moon transits about 6 hours before the Sun.

**Twilight**: Twilight is the period of time before sunrise
and again after sunset, during which sunlight is scattered by the Earth’s
upper atmosphere and provides significant illumination. The qualitative
descriptions of civil, nautical and astronomical twilight will match the
computed beginning and ending times for an observer near sea level, with
good weather conditions and a level horizon. Note, however, that the
amount of natural light available at any particular time during the twilight
periods and the actual visibility of objects depends significantly on such
factors as local atmospheric conditions, cloud cover, and visibility of the
horizon. Thus, to determine the actual lighting level, a forensic study
and/or eye witness testimony would be required.

Civil twilightis defined to begin in the morning, and to end in the evening when the center of the Sun is geometrically 6 degrees below the horizon. In the morning before the beginning of civil twilight and in the evening after the end of civil twilight, artificial illumination is normally required to carry on ordinary outdoor activities.

Nautical twilightis defined to begin in the morning, and to end in the evening, when the center of the sun is geometrically 12 degrees below the horizon. During nautical twilight the illumination level is such that the horizon is still visible even on a Moonless night allowing mariners to take reliable star sights for navigational purposes before sunrise or after sunset.

Astronomical twilightis defined to begin in the morning, and to end in the evening when the center of the Sun is geometrically 18 degrees below the horizon. Before the beginning of astronomical twilight in the morning and after the end of astronomical twilight in the evening, scattered light from the Sun is less than that from starlight and other natural sources.

### Technical Definitions and Computational Details

**Sunrise and sunset.** For computational
purposes, sunrise or sunset is defined to occur when the geometric
zenith distance of center of the Sun is 90.8333 degrees. That is,
the center of the Sun is geometrically 50 arcminutes below a
horizontal plane. For an observer at sea level with a level,
unobstructed horizon, under average atmospheric conditions, the
upper limb of the Sun will then appear to be tangent to the
horizon. The 50-arcminute geometric depression of the Sun's
center used for the computations is obtained by adding the
average apparent radius of the Sun (16 arcminutes) to the average
amount of atmospheric refraction at the horizon (34
arcminutes).

**Moonrise and moonset.** Moonrise and
moonset are defined similarly, but the situation is computationally
more complex because of the nearness of the Moon and the eccentricity
of its orbit. If the computations are carried out using
coordinates of the Moon with respect to the Earth's center (the
usual method), then moonrise or moonset is defined to occur when
the geometric zenith distance of the center of the Moon is

90.5666 degrees + Moon's apparent angular radius - Moon's horizontal parallax

Under normal atmospheric conditions at sea level, the upper limb of the Moon will then appear to be tangent with a level, unobstructed horizon. No account is taken of the Moon's phase; that is, the Moon is always regarded as a disk in the sky and the upper limb might be dark. Here again, a constant of 34 arcminutes (0.5666 degree) is used to account for atmospheric refraction. The Moon's apparent radius varies from 15 to 17 arcminutes and its horizontal parallax varies from 54 to 61 arcminutes. Adding all the terms above together, the center of the Moon at rise or set is geometrically 5 to 10 arcminutes above the observer's "geocentric horizon" - the horizontal plane that passes through the Earth's center, orthogonal to the observer's local vertical.

**Accuracy of rise/set computations.** The
times of rise and set phenomena cannot be precisely computed, because,
in practice, the actual times depend on unpredictable atmospheric
conditions that affect the amount of refraction at the horizon.
Thus, even under ideal conditions (e.g., a clear sky at sea) the
times computed for rise or set may be in error by a minute or
more. Local topography (e.g., mountains on the horizon) and the
height of the observer can affect the times of rise or set even
more. It is not practical to attempt to include such effects in
routine rise/set computations.

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. For the same reason, at high latitudes, the effects of observer height and local topography are magnified and can substantially change the times of the phenomena actually observed, or even whether the phenomena are observed to occur at all.

**Twilight.** There are three kinds of
twilight defined: civil twilight, nautical twilight, and
astronomical twilight. For computational purposes, civil
twilight begins before sunrise and ends after sunset when the
geometric zenith distance of the center of the Sun is 96 degrees
- 6 degrees below a horizontal plane. The corresponding solar
zenith distances for nautical and astronomical twilight are 102
and 108 degrees, respectively. That is, at the dark limit of
nautical twilight, the center of the Sun is geometrically 12
degrees below a horizontal plane; and at the dark limit of
astronomical twilight, the center of the Sun is geometrically 18
degrees below a horizontal plane.