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This post talks about two interesting effects to do with the way it get dark after the Sun has set.  The first one, which anyone who has travelled to places lying at different latitudes will have seen, is that the closer you are to the equator the quicker it gets dark after the Sun has set. The second effect which many of you may have noticed now that we are well into Autumn (if you live in the northern hemisphere) is that at this time of year it gets dark more rapidly after sunset compared to the long evenings in June and July when not only does the Sun set much later but the sky is quite light for over an hour afterwards. This post explains how these two effects are due to the way that the Sun appears to move through the sky at different latitudes and at different times of the year.

Twilight

To explain them properly we first need to understand the process of how it gets dark. As discussed in a previous post, twilight is the period of time in the evening or early morning when although the Sun is below the horizon (because it has set or not yet risen) its rays hit the upper atmosphere causing the sky to glow faintly, so it isn’t completely dark. The table below shows the progression from daylight through all the stages of twilight into darkness as the Sun moves further and further below the horizon.  It also gives the ‘official’ names for each period of time – for more information about these names, see my previous post here.

twilight-stages

 

How the Sun moves at different latitudes

The series of diagrams below shows how the Sun appears to move through the sky on 22 September, the equinox, at a number of different latitudes .

 

sun-manchester

In Manchester, England (latitude 53.5 degrees North), assuming that there is no cloud cover, which for those of us who live here is a very rare occurrence ;-), the Sun rises in the east and moves in a westerly direction climbing through the sky. At  midday it is due south and is at its highest point in the sky at an angle of 36.5 degrees above the horizon. After midday it moves downwards and it sets in the west approximately 12 hours after it has risen. After the Sun has set it continues to gets lower in the sky and, about 1 hour 16 minutes later, it is 12 degrees below the horizon. This is the end of nautical twilight and at this point it is quite dark.

sun-equator

For someone situated at the equator, the Sun rises in the east, moves upward in the sky and is directly overhead at midday. From there it moves downwards and sets in the west approximately 12 hours after it has risen. The diagram below shows that after it has set, because the Sun is moving directly downward, it drops to 12 degrees below the horizon much more rapidly than in Manchester. In fact it only takes 44 minutes to move from sunset to the end of nautical twilight.

 

sun-point-barrow

For someone situated at Point Barrow at the northern tip of Alaska (latitude 71.5 degrees North) the Sun rises in the east and moves in a westerly direction gradually climbing through the sky at a shallow angle. At  midday it is due south and is at its highest point in the sky, at a height of only 18.5 degrees above the horizon. From there it gradually moves downwards  and it sets in the west approximately 12 hours after it has risen. The diagram below shows that, because the Sun is moving at such a shallow angle, it takes a long time to drop 12 degrees below the horizon. In fact the end of nautical twilight is not achieved until two and a half hours after the Sun has set.

The times and duration of civil and nautical twilight are summarised in the table below (see note 1).

twilight-at-diff-places

 

How quickly it gets dark at different times of year

The diagram below shown why it takes much longer to get dark at around the time of the summer solstice than at other times of year.

sun-different-days

 

It shows the path of the Sun through the sky in Manchester at the summer solstice (Jun 20) and at a date early November. At the summer solstice the Sun rises in the north east and climbs up steadily in the sky to reach a a maximum height of 60 degrees at midday. It then descends, setting in the north west at 9:42 pm. As it sinks below the horizon it is moving at a very shallow angle compared to other times of year and it takes a longer time to drop to -12 degrees, the end of nautical twilight, than at other times of the year. This is shown in more detail in the chart below, which shows how the height of the Sun in the sky changes at the time of sunset at different times of year.

 

 

sunset-paths

Some actual values are shown in the table below:

manchester-darkness

 

Notes

Note 1 Although post focuses on the way it gets dark in the evening, the duration of morning twilight when the Sun has not yet risen but it is starting to get light is also much longer at higher latitudes for the same reason.

Note 2 For the more mathematically inclined of my readers, the elevation of the Sun is given by the following relationship:

sin(EL) = sin(DEC)*sin(LAT)+cos(DEC)*cos(LAT)*cos(HA)

where

  • EL is the elevation or height of the Sun measured in degrees
  • DEC is the declination of the Sun in celestial coordinates, or to look at it another way the “latitude” of the Sun as seen from the Earth with respect to the stars. This changes throughout the year as the Earth moves around the Sun in its orbit. At the June solstice the Sun has a declination of +23.5 degrees, at the equinoxes it is zero and at the December solstice it is -23.5 degrees
  • LAT is the latitude of the observer
  • HA is the hour angle. it the number of hours since the solar noon (when the sun is highest is sky) multiplied by 15. So 2 hours after the solar noon is an Hour Angle of 30 degrees, 3 hours before the solar noon is an hour angle of -45 degrees

At the equinoxes n the declination of the sun is 0 degrees so:

  • sin(DEC)=0
  • and cos (DEC)=1.

Therefore the relationship simplifies to

sin(EL) =cos(LAT)*cos(HA).

Using this formula the diagram below shown the elevation of the Sun changes throughout the the day on the September Equinox at three places at different latitudes: Singapore (1.5 degrees N), New York (40.5 degrees N), Reykjavik, Iceland (64 degrees N)

sun-diffs-places

 

 

 

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