best times to fish.
Technical Definitions and Computational Details.
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.
During the course of a day the Earth rotates once on its axis
causing the phenomena of rising and setting. Celestial bodies â€“ stars and planets included â€“ seem to appear in the sky at the horizon to the East, then to cross the sky and
again disappear at the horizon to the West.
The most noticeable 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
Sunrise and sunset conventionally 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 moonset times 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
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;
First Quarter Moon transits about 6
hours after the Sun;
Full Moon transits about 12 hours after / before the
Last Quarter Moon transits about 6 hours before the Sun.
Before sunrise and again after sunset there are intervals of time
twilight, during which there is natural light provided by the upper
atmosphere, which does receive direct sunlight and reflects part of it
toward the Earth's surface.
Some outdoor activities may be conducted without
artificial illumination during these intervals, and it is useful to have
some means to set limits beyond which a certain activity should be assisted
by artificial lighting.
The major determinants of the amount of natural
light during twilight are the state of the atmosphere and local
weather conditions in particular.
There are three different twilight Periods.
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.
This is the limit at which twilight illumination is sufficient, under good
weather conditions, for terrestrial objects to be clearly distinguished; at
the beginning of morning civil twilight, or end of evening civil twilight,
the horizon is clearly defined and the brightest stars are visible under
good atmospheric conditions in the absence of moonlight or other
illumination. 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.
Defined to begin in the morning, and to end in the
evening, when the center of the sun is geometrically 12 degrees below the
At the beginning or end of nautical twilight, under good
atmospheric conditions and in the absence of other illumination, general
outlines of ground objects may be distinguishable, but detailed outdoor
operations are not possible.
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, hence the
Defined to begin in the morning, and to end in the
evening when the center of the Sun is geometrically 18 degrees below the
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.
considerable interval after the beginning of morning twilight and before the
end of evening twilight, sky illumination is so faint that it is practically
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
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.
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.
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