# dusk

Counter-twilight with counter-twilight arch ( Venus belt ) over the blue-gray earth shadow arch .
Twilight over the nautical horizon with a waxing moon; the earth shades the sky almost all around.

As dusk is called the smooth transition of lighting conditions at the beginning and end of the bright day in exchange for the night , due to the sun's position in the light scattering and the atmosphere created. The perceived light as dusk or twilight referred.

## Terms

One distinguishes between

By definition, sunrise is the moment when the top of the sun's disk crosses the geocentric or true horizon . This means that dawn ends with the appearance of the uppermost edge of the solar disk over this horizon. Conversely, dusk begins with the disappearance of the top edge of the solar disk below this horizon. The period of time during which the solar disk appears or sinks therefore belongs to the day and not to twilight, even if the brightness of the sun is still increasing or already decreasing during this period.

In the course of twilight, phases can be differentiated and then differentiated how deep the sun is below the horizon . For this, the position of the sun below the horizon is specified as the depth angle of the center of the sun disk. According to the depth of twilight, a distinction is usually made between three twilight phases, each of which ends at a certain angle, i.e. in the evening

Twilight phases
• civil twilight - reading outdoors possible (depth angle up to 6 degrees)
• nautical twilight - horizon ( chiming line ) still / already recognizable and already / still some stars visible and based on which there is the possibility of nautical navigation (depth angle up to 12 degrees)
• astronomical twilight - up to the maximum darkness of deep night (depth angle up to 18 degrees)

The duration of the three twilight phases depends on the inclination of the apparent path of the sun when rising or setting, and thus on the geographical latitude of the location and the time of year. The period of civil twilight is contained in that of nautical twilight, this in turn in that of astronomical twilight. Twilight lasts shortest near the earth's equator on the equinox and then ends 20 minutes after sunset in civil terms, 45 minutes in nautical terms and 70 minutes in astronomical terms. At the 50th parallel, the three twilight phases last around 2 hours, provided the astronomical end is reached at all, because in the short nights around the summer solstice , evening twilight turns into morning twilight ( midnight twilight or " white nights "). In regions of around 66 ° latitude, such as the Arctic Circle , the sun does not set on this date ( midnight sun ).

As a result of numerous terrestrial sources of illumination, in many places no completely black night sky can be experienced after the end of astronomical twilight; this brightening is also known as light pollution .

## Definition and cause

As a result of its atmosphere , the boundary between the light and the shadow side is blurred on Earth (taken at an altitude of around 390 km, from the ISS )

Physically, twilight means the time span in which scattered residual light from the sun, which is below the horizon, is visible from one location. It lasts as long as the day-night boundary, which has been widened towards the zone of twilight at night, extends across this location. There are twilight zones on all planets with an atmosphere. On the other hand, the Earth's moon or atmospheric planets like Mercury do not have twilight; the bright day is suddenly followed by the dark night.

The scattering of sunlight in high layers of the earth's atmosphere is the reason for the transition phase of twilight. This scattering occurs both in the air itself and in any particles ( aerosols ) that may be present . Since dawn and dusk are the same in their cause and only differ in their course, only dusk is considered here initially.

Above an observer for whom the sun has just set, the higher air layers are illuminated by the sun for a longer period of time. These layers of air scatter part of the penetrating sunlight in the direction of the observer, to whom they therefore appear more or less brightly shining. Most of the scattered light is only slightly deflected from its original direction, and the observer therefore sees the brightest (predominantly reddish) glow when he looks in the direction in which the sun is just below the horizon. Light that reaches the observer from other directions in the sky has been scattered at larger angles, which happens with less intensity and more blue content. Regions of the sky further away from the sun therefore appear increasingly darker.

### Civil, nautical, astronomical twilight

The sunset lasts around 2 minutes near the equator, in Central Europe around 3–4 minutes from the first contact of the sun disk with the horizon to its complete disappearance. In astronomy, three phases are distinguished for the subsequent twilight. Assuming sunset, evening twilight runs as follows:

The twilight phases after sunset run faster with a steeper path of the sun
• The civil twilight , also civil twilight , takes an average of about 40 minutes in Germany. While the sky is slowly decreasing, the bright planets first become visible, especially Venus and Jupiter . Towards the end of civil twilight, a good eye can already see the brightest stars up to the 1st magnitude . Civil twilight begins with sunset and, according to the astronomical definition, ends when the center of the solar disk is 6  degrees below the true horizon. The end of civil twilight is referred to in aviation with the abbreviation ECET , the beginning of civil dawn with BCMT .
• The nautical twilight or medium twilight lasts longer than the civil twilight. In the course of this twilight phase, stars up to the 3rd magnitude and thus also the trains of constellations can be recognized, while at sea the notch is still clearly visible as a line between sea and sky. This provides the conditions for a nautical position determination with the sextant , in which the height of certain stars above the horizon is measured. According to the astronomical definition, nautical twilight ends when the center of the sun is 12 degrees below the true horizon.
• The astronomical twilight lasts longer than the nautical twilight. It includes the subsequent phase of twilight, until it doesn't get darker any more, and ends when the center of the sun is 18 degrees below the true horizon. Only then does the actual night begin in an astronomical sense - that is, the sky background would have become completely dark without residual light from artificial light sources.

The point in time at which the respective twilight phase begins depends on the degree of longitude and thus on the true solar time . The earth needs around 24 hours for a rotation of 360 ° around its own axis, equivalent to around 4 minutes per degree of longitude and around 15 ° in one hour. For example, twilight sets in about 30 minutes earlier in Berlin than in Cologne , which is about 7 ° more west.

At the end of the night, when sunrise is approaching, the twilight phases run through in reverse order until sunrise.

The definitions of the twilight phases refer to the so-called geometric height of the sun below the horizon. The refraction and other influences on the observed sun position are therefore not taken into account. For the individual calculation of times at which the sun reaches certain heights, see position of the sun .

### Duration

The duration of twilight initially depends on the latitude of the observation location. At the equator , the apparent path of the sun stands steeply on the horizon and dusk only lasts for a short time. Towards the poles , the path of the sun cuts the horizon at a flatter angle and twilight lasts longer. As the distance from the equator increases, the twilight phases can lengthen so much that an evening turns into a morning. In the northern zones of Europe, Asia, North America and the southern tip of South America, at certain times of the year, a twilight phase lasts without interruption and a lower phase is no longer reached.

Zones of twilight in Europe on June 21st

At a given latitude , the angle at which the sun sets also depends on the season, so that the duration of twilight varies slightly over the course of a year. The longest twilight times are reached at the two solstices . The shortest twilight times occur near the equinoxes.

Depending on the season and latitude, the duration of twilight phases is different. As a rough guide for latitudes below the Arctic Circle, civil twilight or civil twilight lasts about half an hour, nautical twilight or medium twilight more than one and astronomical twilight about one and a half to three hours - if the twilight phases are passed through.

#### Duration of twilight at different latitudes

Sun in the sky at dusk and sunrise (SR)

The tables show how many minutes after sunset the twilight phase in question ends or how many minutes before sunrise it begins. The longest twilight times at the two solstices are also reached at the equator. The shortest twilight times coincide with the equinoxes .

The duration of the three twilight phases can be calculated, similar to the calculation of the azimuth of the rising sun , with the side cosine law of spherical trigonometry . To do this, one considers the triangle that is spanned in the sky by the north pole , the zenith of the observer and the position of the sun. is the geographical latitude of the observer and the current declination of the sun. is the zenith distance of the sun as seen from the observer. The three sides of the triangle are thus and . At sunrise the zenith distance of the sun is 90 °. For the limits of the three different twilight phases, the sun, which is below the horizon, has a zenith distance , being 6 °, 12 ° or 18 °. ${\ displaystyle (NP)}$ ${\ displaystyle (Z)}$${\ displaystyle \ varphi}$${\ displaystyle \ delta}$${\ displaystyle c}$${\ displaystyle a, b, c}$${\ displaystyle a = (90 ^ {\ circ} - \ delta)}$${\ displaystyle b = (90 ^ {\ circ} - \ varphi)}$${\ displaystyle c}$${\ displaystyle c = 90 ^ {\ circ} + \ sigma}$${\ displaystyle \ sigma =}$

${\ displaystyle \ gamma}$is the angle at the North Pole between the meridian of the observer and the current meridian of the sun for a certain twilight limit . (SR = sunrise) is the corresponding angle at sunrise, i.e. at a zenith distance of 90 °. From the moment the sun is just below the horizon until sunrise, the earth rotates by an angle of . The earth needs for the rotation around the angle${\ displaystyle \ sigma}$${\ displaystyle \ gamma _ {SR}}$${\ displaystyle \ sigma}$${\ displaystyle \ Delta \ gamma = \ gamma - \ gamma _ {SR}}$${\ displaystyle \ Delta \ gamma}$

${\ displaystyle t_ {D} = {\ frac {\ Delta \ gamma} {360 ^ {\ circ}}} \ cdot 24}$Hours  or: minutes.  ${\ displaystyle t_ {D} = {\ frac {\ Delta \ gamma} {360 ^ {\ circ}}} \ cdot 1440}$

The angles and are calculated as follows: ${\ displaystyle \ gamma}$${\ displaystyle \ gamma _ {SR}}$

 The side cosine law is: ${\ displaystyle \ cos \ gamma}$ = ${\ displaystyle {\ frac {\ cos c- \ cos a \ cdot \ cos b} {\ sin a \ cdot \ sin b}}}$ So follows for : ${\ displaystyle \ gamma}$ ${\ displaystyle \ gamma}$ = ${\ displaystyle \ arccos \ left [{\ frac {\ cos c- \ cos a \ cdot \ cos b} {\ sin a \ cdot \ sin b}} \ right]}$ Replacing the three sides of the triangle follows: ${\ displaystyle a, b, c}$ ${\ displaystyle \ gamma}$ = ${\ displaystyle \ arccos \ left [\ sec \ delta \ cdot \ sec \ varphi \ cdot (- \ sin \ sigma - \ sin \ delta \ cdot \ sin \ varphi) \ right]}$ At sunrise is: ${\ displaystyle (\ sigma = 0 ^ {\ circ})}$ ${\ displaystyle \ gamma _ {SR}}$ = ${\ displaystyle \ arccos \ left [- \ tan \ delta \ cdot \ tan \ varphi \ right]}$

and thus:

${\displaystyle t_{D}(\varphi ,\delta ,\sigma )={\frac {\arccos \left[\sec \delta \cdot \sec \varphi \cdot (-\sin \sigma -\sin \delta \cdot \sin \varphi )\right]-\arccos \left[-\tan \delta \cdot tan\varphi \right]}{360^{\circ }}}\cdot 1440\quad min}$


With this formula the duration of the three twilight phases is calculated as a function of latitude and declination . ${\ displaystyle \ sigma = 6 ^ {\ circ}, 12 ^ {\ circ}, 18 ^ {\ circ}}$${\ displaystyle \ varphi}$${\ displaystyle \ delta}$

##### Examples
Observer at the equator ( ) ${\ displaystyle \ varphi = 0 ^ {\ circ}}$
Day date civil nautical astronomic
Winter solstice 21st December 26 min. 52 min. 79 min.
equinox March 19-21 and
September 22 or 23
24 min. 48 min. 72 min.
Summer solstice June 21st 26 min. 52 min. 79 min.
Observer at 30 ° north latitude (e.g. Cairo )
Day date civil nautical astronomic
Winter solstice 21st December 31 min. 61 min. 90 min.
equinox March 21st and
September 22nd or 23rd
28 min. 56 min. 84 min.
Summer solstice June 21st 32 min. 65 min. 101 min.
Observer at 50 ° north latitude (e.g. Vancouver , Frankfurt am Main , Kiev )
Day date civil nautical astronomic
Winter solstice 21st December 45 min. 87 min. 126 min.
equinox March 21st and
September 22nd or 23rd
37 min. 75 min. 115 min.
Summer solstice June 21st 51 min. 117 min. (not reached)

For large geographical latitudes and certain times of the year it may happen that some twilight phases are not reached. The formula for calculating the twilight duration does not provide a real value for these latitudes and declinations.

#### Polar day and night

Blue twilight during the polar night in Longyearbyen , Spitsbergen (78.21 ° N, 15.61 ° E)
• On the day of the summer solstice , the sun does not set in the polar regions , but can still be seen as midnight sun . Because of the atmospheric refraction, this can be the case from around 65.7 ° latitude, a little below the Arctic Circle . During this time there is no twilight at all. Above the Arctic Circle, this is the case at higher latitudes over an increasingly longer period of time. Finally, near the geographic poles , the sun does not set during the entire summer half-year, between the spring and autumn equinoxes . This period is known as polar day .
• In contrast, polar night is the period when the sun stays below the horizon in regions close to the polar. During this period of time, only twilight light occurs at higher latitudes. Twilight is at its darkest around the day of the winter solstice , at the pole it is dark night.

#### Midnight twilight

White night - midnight solstice in Helsinki (24 June 2005)
Twilight in Germany on June 21st
Midnight twilight on the southern edge of the North German Lowlands (June 29; 52.28 ° N, 8.59 ° E)
• At all latitudes greater than 60.561 ° (60 ° 33 '40 ”) there are nights in the summer when civil twilight changes to civil dawn, i.e. no nautical twilight is reached because the sun is less during the whole night than 6 degrees below the true horizon. One speaks of white night or of midnight twilight .
• At all latitudes greater than 54.561 ° (54 ° 33 '40 ”) there are nights in the summer when nautical twilight changes to nautical dawn, i.e. no astronomical twilight is reached because the sun is less during the whole night than 12 degrees below the true horizon. This only happens in northern Germany (northern Schleswig-Holstein, northern tip of the island of Rügen). Here too, one speaks of midnight twilight .
Midnight twilight and
noctilucent clouds (beginning of July; 53.94 ° N, 10.67 ° E )
• At all latitudes greater than 48.561 ° (48 ° 33 '40 ”) there are nights in summer when astronomical twilight does not end because the sun is less than 18 degrees below the true horizon throughout the night. Therefore it does not become dark night , but remains at a midnight twilight . This happens in almost all of Germany; only in the area south approximately of the Strasbourg-Passau line is no midnight twilight to be experienced.

## Optical phenomena

During twilight, typical twilight colors and other optical phenomena develop. These are phenomena at dawn and dusk of an atmosphere-bearing planet or moon . On earth there is an abundance of optical phenomena and luminous phenomena.

Optical phenomena at civil twilight depending on weather and observation conditions can be:

• Earth shadow arc : When the sky is clear, the shadow of the earth is projected over the horizon into the opposite twilight sky.
• Purple light : Is caused by small dust particles in the atmosphere and makes parts of the sky appear purple.
• Counter-twilight : colored reflection of the rising or setting sun in the opposite segment of the sky.
• Alpenglow : colored scattered light of the sunset and sunrise on mountain ranges or mountain ranges.
• Mother-of-pearl clouds : Acid ice clouds in the stratosphere which, as a result of the diffraction of sunlight on the crystals, make correspondingly pure interference colors visible.
• Blue Hour : The deep blue sky during twilight is almost entirely caused by the upper ozone layer.
• Green lightning : The wavelength-dependent refraction of sunlight creates a briefly visible green beam.
Luminous night clouds and colored horizontal
stripes over the Drentschen Bargerveen (June 23; 52.65 ° N, 7.17 ° E )

Optical phenomena at nautical twilight can be:

• Colored horizontal stripe: A colored, mostly glowing red stripe above large areas of the horizon, which can be up to 180 degrees.
• Post-purple light: A rare faint purple afterglow of the sky when the sun is more than 12 degrees below the horizon.
• Luminous night clouds : A whitish, cloud-like accumulation of ice crystals above the mesosphere in the mesopause at an altitude of 81 to 85 kilometers

Wilhelm von Bezold described in detail the typical course of twilight in Central Europe in the 19th century and the variety of phenomena to be observed .

## literature

• Herbert Smutek: The clear-sighted recognition of stars close to the zenith at dusk . In: Hermann Mucke (Hrsg.): Modern astronomical phenomenology. 20th Sternfreunde Seminar, 1992/93. Zeiss Planetarium of the City of Vienna and Austrian Astronomical Association 1992, pp. 209–220.