June 21 2018 – the solstice

This year, the June solstice will fall on 21 June.  In the northern hemisphere, it is the day when there is the most daylight and when the Sun is at its highest in the midday sky.

 

Sunrise at the solstice at Stonehenge, England – image from Wikimedia commons

The origin of the word solstice is from two Latin words:  sol, which means Sun, and sistere, to stand still. This is because, at the time of the solstice, the Sun stops getting higher, appears to stand still at the same height for a few days, and then gets lower in the midday sky.

 

The graph below shows the maximum height, or elevation, of the Sun, measured in degrees above the horizon, during the month of June. The graph is for a location 50 degrees latitude North, which is the same latitude as the southern tip of the British Isles.  

The fact that the Sun’s elevation changes gradually means the amount of daylight also changes very little around the solstice. This is shown in the table below, which gives the sunrise and sunset times and the amount of daylight in hours, minutes and seconds for June in London.

Table of sunrise and sunset times for London (Time and Date 2018).

 

Precise definition of the solstice

The diagram above shows the Earth’s orbit around the Sun. For clarity the sizes of the Earth and Sun have been greatly exaggerated.

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Seasons

 

  • During June, marked as Ain the diagram, the Earth’s North Pole is tilted towards the Sun and the days are longer in the northern hemisphere.
  • During December, marked as Cin the diagram, the Earth’s South Pole is tilted towards the Sun and days are longer in the southern hemisphere.
  • At points Band D, known as the equinoxes, neither pole is tilted towards the Sun and the amounts of daylight in the northern and southern hemisphere are equal.

The precise astronomical definition of the June solstice (also called the summer solstice in the northern hemisphere) is the exact point in time when the North Pole is tilted furthest towards the Sun. The times for this event for the years 2016-2020 are given in the table below – in GMT, in Tokyo time (which is 9 hours ahead of GMT) and in Hawaiian time (which is 10 hours behind GMT).

June Solstice Times

 

 

As you can see, the time of the solstice varies from year to year. It can fall on 20, 21 or 22 June, depending on your longitude (and thus your time zone).

Importance of the solstice to early man

The solstice was of great importance to early man, and many prehistoric sites appear to have been built to celebrate it. The most famous of these is Stonehenge, which is located in Wiltshire, England. It is a set of concentric stone circles built between 4000 and 5000 years ago. It was an amazing feat of construction for stone age man. The stone circle is over 30 metres in diameter. The largest stones are more than 9 metres tall, weigh over 25 tonnes and were hauled over 30 km to the site. It is reckoned that the smaller stones were moved from western Wales, a distance of 225 km (Jarus 2014).

Stonehenge

Image from Wikimedia commons 

At the centre of Stonehenge is a horseshoe arrangement of five sets of arches called triliths, each containing three stones.  The open side of the horseshoe points North East towards a large stone 80 metres away from the main circle. Today this large stone is given the name  ‘The Heel Stone’.

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Stonehenge_Heelstone

Image from Wikimedia commons

The monument is arranged in such a way that, for a few days either side of the June solstice and only at those dates, someone standing in the centre of the horse shoe and facing North East will see the Sun rise over the Heel stone.

Heel Stone Sunrise

How sunrise at the summer solstice at Stonehenge would have looked after the monument’s construction.

It is amazing that prehistoric man built such a large monument to line up with the June solstice. It clearly must have been a major event for a people living outdoors with only natural daylight, and in fact the solstice is still celebrated at Stonehenge today. Modern groups with ancient origins, such as Druids and Pagans, who revere the natural world more than many modern humans, join approximately 30,000 people who flock to Stonehenge to watch the Sun rise at the solstice each year.

Interestingly, to prevent damage to such an important ancient monument it is not normally possible to get right up to the stones. However, the charity which manages the site English Heritage open it up every year for the solstice, giving people a rare chance to get up close.

For the BBC report on the 2017 Stonehenge solstice celebrations click on the link below.

https://www.bbc.co.uk/news/uk-england-wiltshire-40352528

The southern hemisphere

To those of you who live in the southern hemisphere the June solstice is the winter solstice, when the midday Sun is at its lowest in the sky. After the solstice the days start getting gradually longer and the nights gradually shorter, although the change doesn’t really become noticeable until July.

Note

Strictly speaking it isn’t true that for the whole northern hemisphere the midday Sun is at its highest in the sky on the solstice. At the Tropic of Cancer, which is 23.5 degrees north, and is shown as the upper red line in diagram below, the Sun is directly overhead at midday on the June solstice. At low latitudes between the equator and the Tropic of Cancer the Sun is directly overhead at midday on two dates either side of the solstice. For example, in San Juan, Puerto Rico, which lies 18.5 degrees North of the equator, the Sun is overhead at midday on May 13 and July 30.

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Tropic of cancer

References

Jarus, O (2014) Stonehenge: Facts & Theories About Mysterious Monument, Available at: http://www.livescience.com/22427-stonehenge-facts.html(Accessed: 10 June 2016).

 

Time and Date (2018) London, ENG, United Kingdom — sunrise, sunset, and daylength, June 2018, Available at: http://www.timeanddate.com/sun/uk/london(Accessed: 4 June 2018).

 

20 March 2018 – the equinox

Now that we are in the month of March, it is only a short time until 21 March, the first day of spring (or first day of autumn if you’re one of my readers in the southern hemisphere).

There is a commonly held view that 21 March is an equinox and that the equinoxes are the two days in the year when all places on the Earth have exactly 12 hours of daylight and 12 hours of darkness. In fact, as I’ll explain later, both these statements are only approximately correct.  In reality the situation is as follows.

  • 21 March can sometimes be the date on which the spring equinox falls but its date varies from year to year and also depends upon where you are located.  In 2018 it will fall on 20 March for most places in the world.
  • At the equinoxes there is actually nowhere on the Earth where there are exactly 12 hours of daylight and 12 hours of darkness.

What is an equinox?

The origin of the word equinox comes from two Latin words aequus (equal) and nox (night). This definition suggests that at an equinox the length of the day and night are equal. However the precise astronomical definition of an equinox is slightly different.

Earths Orbit

The diagram above shows the Earth going around the Sun in its orbit

  • At the December solstice (point A in the diagram) the North Pole is tilted further away from the Sun than at any other time of the year, and the South Pole is tilted nearest the Sun.  In the northern hemisphere the period of darkness is longest compared with the period of daylight, and in the southern hemisphere the reverse applies.
  • At the summer solstice in June (point C) it is exactly the opposite of the winter solstice – it is the North Pole which is now tilted nearest to the Sun so the northern hemisphere experiences the longest period of daylight.
  • There are two times a year (B and D in the diagram) when the neither the North Pole nor the South Pole are tilted towards the Sun and these times are the equinoxes.  If we take two places with the same latitude, one of which is North of the equator and the other one South of the equator, (for example Istanbul, Turkey 41oand Wellington New Zealand 41oS ) they will both have the same amount of daylight at the equinox.

On what date do the equinoxes occur?

The diagram also shows that the Earth moves in an elliptical orbit around the Sun. This means that it has further to travel in its orbit between the March equinox and the September equinox than in the return leg of its journey from September to March. The two equinoxes are therefore not exactly half a year apart: from the March equinox to the September equinox is around 186 days, whereas from the September equinox to the March equinox is only 179 days.

The tables below give the times of the two equinoxes from 2016 to 2021  for three Locations: London (Greenwich Mean Time or GMT), Honolulu (GMT -10 hours) and Tokyo (GMT +9 hours).  As you can see, the northern hemisphere spring equinox can occur on 19, 20 or 21 March and the autumn equinox on 22 or 23 September.

spring equinox times

autumn equinox times

(Data TimeandDate.com 2016a)

On what dates in a year are there are exactly 12 hours of daylight?

The first thing we need to think about when we answer this question is what do we mean by the word ‘daylight’? Do we consider twilight, the time just after sunrise or just before sunset when it is not completely dark, to be daylight? Or do we consider daylight as being the time when the Sun is above the horizon?

If we use the definition of ‘daylight’ as being the interval between sunrise and sunset then there are actually slightly more than 12 hours of daylight at the equinox everywhere in the world.  The first reason for this is that the definition of sunrise is the time when the first light from the Sun’s rays reaches above the horizon, not when the centre of the Sun is above the horizon. The diagram below shows the path of the Sun’s disc around sunrise at the equinox in London.  In the early morning, the time when the half of the Sun is above the horizon and half below the horizon is 6:03 am, shown as B in the diagram, but sunrise is about a minute before this time.

Sun path sunrise

Similarly, in the early evening the time when half of the Sun is above the horizon and half below the horizon is 6:13 pm,  B in the diagram, but sunset is when the last light from the Sun’s rays are above the horizon and is about a minute after this time.

Sun path sunset

The second reason for there being more than 12 hours of daylight at the equinox is that when the Sun is just below the horizon the Earth’s atmosphere bends the Sun’s rays, causing it to appear just above the horizon. This bending of light is known as refraction and has the effect of slightly extending the hours of daylight.

Taken together, these two effects mean that there are slightly more than 12 hours of daylight at the equinox. The table below shows the  amount of daylight for dates around the equinox in London and Wellington.  It shows that the date on which there are exactly 12 hours of daylight and 12 hours of darkness in London is 17 March, three days earlier but in Wellington it is 3 days later on 23 March.

 

(TimeandDate.com 2016b)

References

TimeandDate.com (2016) Solstices & Equinoxes for London (Surrounding 10 Years).  Available at: http://www.timeanddate.com/calendar/seasons.html?n=136 (Accessed: 5 March 2016).

TimeandDate.com (2016) London, ENG, United Kingdom — Sunrise, Sunset, and Daylength, March 2016, Available at: http://www.timeanddate.com/sun/uk/london(Accessed: 1 March 2016).

 

The equinox March 20 2017

Now that we are in the month of March, for most of us in the northern hemisphere the worst of the winter is over, and it is only a few days until 21 March, the first day of spring.

March 21

 

There is a commonly held view that March 21 is the spring equinox and that the equinoxes are the two days in the year when all places on the Earth have exactly 12 hours of daylight and 12 hours of darkness. In fact, as I’ll explain later, this is only approximately correct. March 21 can sometimes be the date on which the spring equinox falls but the precise date varies from year to year and also depends upon where you are located.  In fact, at the equinoxes there is actually nowhere on the Earth where there are exactly 12 hours of daylight and 12 hours of darkness.

What is an equinox?

The origin of the word equinox comes from two Latin words aequus (equal) and nox (night), suggesting that at an equinox the length of the day and night are equal. However the precise astronomical definition of an equinox is slightly different.

Earths Orbit

Because the axis of the Earth is tilted rather than perpendicular to its orbit around the Sun, different parts of the Earth are closer to the Sun at different times of the year.

  • At the winter solstice in December (point A in the diagram) the North Pole is tilted furthest away from the Sun than at any other time of the year, and the South Pole is tilted nearest the Sun.  In the northern hemisphere the period of darkness are longest compared with the period of daylight, and in the southern hemisphere the reverse applies.
  • At the summer solstice in June (point C in the diagram) it is exactly the opposite of the winter solstice – it is the North Pole which is now tilted nearest to the Sun so  the northern hemisphere experiences the longest period of daylight.
  • There are two times a year (B and D in the diagram) when the neither the North Pole nor the South Pole are tilted towards the Sun and these times are the equinoxes. At any given latitude, whether north or south of the equator, there will be the same amount of daylight.

On what date do the equinoxes occur?

The diagram also shows that the Earth moves in an oval, or elliptical, orbit around the Sun. This means that it has further to travel in its orbit between the March equinox and the September equinox than in the return leg of its journey from September to March. The two equinoxes are therefore not exactly half a year apart: from the March equinox to the September equinox is around 186 days, whereas from the September equinox to the March equinox is only 179 days.

The tables below give the times of the two equinoxes from 2016 to 2021  for three Locations: London (Greenwich Mean Time or GMT), Honolulu (GMT -10 hours) and Tokyo (GMT +9 hours).  As you can see, the northern hemisphere spring equinox can occur on March 19, 20 or 21 and the autumn equinox on Sept 22 or 23. Over a longer time span there is an even greater range of dates (see notes).

spring equinox times

autumn equinox times

(Data TimeandDate.com 2016a)

What date of the year are there are exactly 12 hours of daylight?

The first point to consider is what to we mean by daylight? Do we consider twilight, the time just after sunrise or just before sunset when it is not completely dark, to be daylight? If we use the common definition of “hours of daylight”as being the interval between sunrise and sunset then there are actually slightly more than 12 hours of daylight at the equinox everywhere in the world. There are two reasons for this. First the definition of sunrise is actually the point at which the first light from the Sun’s rays reaches above the horizon,not when the centre of the Sun is above the horizon. The diagram below shows the path of the Sun’s disk at sunrise at the equinox in London.

Sun path sunrise

Similarly, at sunset the time when the half of the Sun is above the horizon and half below the horizon is 6:13 pm, shown as B in the diagram, but sunset is defined when the very last light from the Sun’s rays are above the horizon and is about a minute after this time.

Sun path sunset

In addition, when the Sun is just below the horizon, the Earth’s atmosphere bends the Sun’s rays, causing it to appear just above the horizon. This bending of light is known as refraction and has the effect of slightly extending the hours of daylight.

Taken together, these two effects mean that there are slightly more than 12 hours of daylight at the equinox. The table below shows the dates around the equinox in London and Wellington (in the northern and southern hemispheres respectively) and it is clear to see that date on which there are exactly 12 hours of daylight and 12 hours of darkness is not 20 March. In London it is 3 days earlier on March 17 but in Wellington it is 3 days later on March 23.

Length of day march

(TimeandDate.com 2016b)

 

Notes

(1) The table shows that there is a pattern in that the times of the two equinoxes in a given year are just under six hours later than the previous year, unless the year is a leap year, in which case they are just under 18 hours earlier than the previous year.  Thus, the equinoxes will occur at roughly the same date and time every four years. For example the March equinox will occur at:

  • around 4 am (GMT) on March 20 in the years  2020, 2024 and 2028
  • around 10 am (GMT) on March 20 in the years 2017 , 2021 and 2025
  • around 4 pm (GMT) on March 20 in the years 2018 , 2022 and 2026
  • around 10 pm (GMT) on March 20 in the years 2019 , 2023 and 2027

However this four-year pattern doesn’t always hold because leap years don’t always occur every four years. Century years which are not divisible by 400 e.g. 1800, 1900, 2100 are not leap years. So for example in the year 1903, where there had not been a leap year for 7 years, the equinoxes occurred relatively late. On this year the equinoxes occurred at 7:15 pm (GMT) on 21 March and 5:45 am (GMT) on 24 September. So in Tokyo Japan, which is 9 hours ahead of GMT, in 1903 they occurred at 4:15 am on 22 March and 2:45 pm on 24 September

(2) The exact day on which there is 12 hours of daylight will vary with latitude.

References

TimeandDate.com (2016) Solstices & Equinoxes for London (Surrounding 10 Years).  Available at: http://www.timeanddate.com/calendar/seasons.html?n=136 (Accessed: 5 March 2016).

TimeandDate.com (2016) London, ENG, United Kingdom — Sunrise, Sunset, and Daylength, March 2016, Available at: http://www.timeanddate.com/sun/uk/london(Accessed: 1 March 2016).

 

The long summer evenings

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

 

 

 

June 20- The Solstice

The June solstice will fall on June 20 or June 21 this year, depending on where you are in the world.  It is the longest day in the northern hemisphere and the day when the Sun is at its highest in the midday sky (see note). The origin of the word solstice is from the Latin words sol, which means Sun, and sistere, to stand still, because around the time of the solstice the Sun stops getting higher, appears to stand still at the same height for a few days, and then gets lower in the midday sky.

The graph below show the maximum height, or elevation, of the Sun, measured in degrees above the horizon, during the month of June. The graph is for a place 50 degrees in latitude North, roughly the same latitude as the southern tip of the British Isles.  It shows how the elevation of the Sun changes around the solstice.

Sun height June

The fact that the Sun’s elevation changes only gradually means that the length of the days only changes very slowly around the time of the solstice. This is shown in the table below, which gives the sunrise and sunset times and the length of day in hours, minutes and seconds for June in London.  The amount of daylight on June 20 is only a fraction of a second more than on June 21.

June 16 sunrise and sunset

Table of sunrise and sunset times for London (Time and Date 2015). Although June 20 is the day with the most daylight, the earliest sunrise occurs on June 16 and the latest sunset on June 24.

Precise definition of the solstice

The diagram above shows the Earth’s orbit around the Sun. For clarity the sizes of the Earth and Sun have been greatly exaggerated.

Seasons

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  • During June, marked as A in the diagram, the Earth’s North pole is tilted towards the Sun and the days are longer in the northern hemisphere.
  • During December, marked as C in the diagram, the Earth’s South pole is tilted towards the Sun and days are longer in the southern hemisphere.
  • At points B and D known as the equinoxes, neither pole is tilted towards the Sun and the amounts of daylight in the northern and southern hemisphere are equal.

The precise astronomical definition of the June solstice (also called the summer solstice in the northern hemisphere) is the exact point in time when the North pole is tilted furthest towards the Sun. The times when this will occur from now until 2020 are given in the table below – in Greenwich Mean Time, in Tokyo time (which is 9 hours ahead of GMT) and in Hawaiian time (which is 10 hours behind GMT).

June Solstice Times

 

As you can see, the time of the solstice varies from year to year. It can fall on 20, 21 or 22 June, depending on your longitude (and thus your time zone).

Importance of the solstice to early man

The solstice was of great importance to early man, and many prehistoric sites appear to have been built to celebrate it. The most famous of these is Stonehenge, which is located in Wiltshire, England. It is a set of concentric stone stone circles built between 4000 and 5000 years ago. It was an amazing feat of construction for stone age man. The stone circle is over 30 metres in diameter. The largest stones are more than 9 metres tall, weigh over 25 tonnes and were hauled over 30 km to the site. It is reckoned that the smaller stones were moved from western Wales, a distance of 225 km (Jarus 2014).

Stonehenge

Image from Wikimedia commons 

At the centre of Stonehenge is a horseshoe arrangement of five sets of arches called triliths, each containing three stones.  The open side of the horseshoe points North East towards a large stone 80 metres away called the Heel Stone, shown below.

Stonehenge_Heelstone

Image from Wikimedia-commons

The monument is arranged in such a way that, for a few days either side of the the June solstice and only at those dates, someone standing in the centre of the horse shoe and facing North East will see the Sun rise over the Heel stone.

Heel Stone Sunrise

How sunrise at the summer solstice at Stonehenge would have looked after the monument’s construction.

It is amazing that prehistoric man built such a large monument to line up with the June solstice. It clearly must have been a major event for a people living outdoors with only natural daylight, but in fact the solstice is still celebrated at Stonehenge today. Modern groups with ancient origins, such as Druids and Pagans, who revere the natural world more than many modern humans, join approximately 30,000 people who flock to Stonehenge to watch the Sun rise at the solstice each year.

For the BBC report on last year’s solstice celebrations click on the link below.

http://www.bbc.co.uk/news/uk-england-wiltshire-33211353

The southern hemisphere

To those of you who live in the southern hemisphere the June solstice is, of course, the winter solstice, when the midday Sun is at its lowest in the sky. After the solstice the days start getting gradually longer and the nights gradually shorter, although the change doesn’t really become noticeable until July.

Note

Strictly speaking it isn’t true that for the whole northern hemisphere the midday Sun is at its highest in the sky on the solstice. At the Tropic of Cancer, which is 23.5 degrees north, and is shown as the upper red line in diagram below, the Sun is directly overhead at midday on the June solstice. At low latitudes between the equator and the Tropic of Cancer the Sun is directly overhead at midday on two dates either side of the solstice. For example in San Juan, Puerto Rico, which lies only 18.5 degrees North of the equator, the Sun is overhead at midday on May 13 and July 30.

Tropic of cancer

References

Jarus, O (2014) Stonehenge: Facts & Theories About Mysterious Monument, Available at: http://www.livescience.com/22427-stonehenge-facts.html (Accessed: 10 June 2016).

Time and Date (2015) London, ENG, United Kingdom — sunrise, sunset, and daylength, June 2016, Available at: http://www.timeanddate.com/sun/uk/london(Accessed: 10 June 2016).

The first day of spring

Now that we are in the month of March, for most of us in the northern hemisphere the worst of the winter is over, and it is only a couple of weeks until 21 March, the first day of spring.

March 21

21 March is an important date for other reasons, too. For one thing, it is used as the basis for the calculation of Easter. Early Christian decision makers in the fourth century established that Easter would be held on the first Sunday after the first full moon occurring on or after March 21, and this definition is still used today.

Processed by: Helicon Filter;Traditional German Easter postcard – Image from Wikimedia Commons

March 21 is also the first day of the astrological calendar, although as a scientist I am unconvinced of astrology’s usefulness for anything other than entertainment.  In addition, in 2001 the United Nations declared 21 March as the International Day for the Elimination of Racial Discrimination (United Nations 2016).

End racial descrimination

Is March 21 the spring equinox?

There is a commonly held view that March 21 is the spring equinox and that the equinoxes are the two days in the year when all places on the Earth have exactly 12 hours of daylight and 12 hours of darkness. In fact, as I’ll explain later, this is only approximately correct. March 21 can sometimes be the date on which the spring equinox falls but its precise date varies from year to year and also depends upon where you are located.  In fact, at the equinoxes there is actually nowhere on the Earth where there are exactly 12 hours of daylight and 12 hours of darkness.

What is an equinox?

The origin of the word equinox comes from two Latin words aequus (equal) and nox (night), suggesting that at an equinox the length of the day and night are equal. However the precise astronomical definition of an equinox is slightly different.

Earths Orbit

Because the axis of the Earth is tilted rather than perpendicular to its orbit around the Sun, different parts of the Earth are closer to the Sun at different times of the year.

  • At the winter solstice in December (point A in the diagram) the North Pole is tilted furthest away from the Sun than at any other time of the year, and the South Pole is tilted nearest the Sun.  In the northern hemisphere the period of darkness are longest compared with the period of daylight, and in the southern hemisphere the reverse applies.
  • At the summer solstice in June (point C in the diagram) it is exactly the opposite of the winter solstice – it is the North Pole which is now tilted nearest to the Sun so  the northern hemisphere experiences the longest period of daylight.
  • There are two times a year (B and D in the diagram) when the neither the North Pole nor the South Pole are tilted towards the Sun and these times are the equinoxes. At any given latitude, whether north or south of the equator, there will be the same amount of daylight.

When do the equinoxes occur?

The diagram also shows that the Earth moves in an oval, or elliptical, orbit around the Sun. This means that it has further to travel in its orbit between the March equinox and the September equinox than in the return leg of its journey from September to March. The two equinoxes are therefore not exactly half a year apart: from the March equinox to the September equinox is around 186 days, whereas from the September equinox to the March equinox is only 179 days.

The tables below give the times of the two equinoxes over the next six years for three Locations: London (Greenwich Mean Time or GMT), Honolulu (GMT -10 hours) and Tokyo (GMT +9 hours).  As you can see, the northern hemisphere spring equinox can occur on March 19, 20 or 21 and the autumn equinox on Sept 22 or 23 (see note 1 below).

spring equinox times

autumn equinox times

(TimeandDate.com 2016a)

What date of the year are there are exactly 12 hours of daylight?

If we use the normal definition of hours of daylight as being the interval between sunrise and sunset then there are actually slightly more than 12 hours of daylight at the equinox. There are two reasons for this. If sunrise were defined as when half of the Sun is above the horizon and half below, then there would be exactly 12 hours of daylight.  However, the definition of sunrise is actually the point at which the first light from the Sun’s rays reaches above the horizon, so there is actually slightly more daylight.  The diagram below shows the path of the Sun’s disk at sunrise at the equinox in London.

Sun path sunrise

Similarly, at sunset the time when the half of the Sun is above the horizon and half below the horizon is 6:13 pm, shown as B in the diagram, but sunset is defined when the very last light from the Sun’s rays are above the horizon and is about a minute after this time.

Sun path sunset

In addition, when the Sun is just below the horizon, light bends, causing the Sun to appear just above the horizon. This bending of light is known as refraction and has the effect of slightly extending the hours of daylight.

Taken together, these two effects mean that there are slightly more than 12 hours of daylight at the equinox. The table below shows the dates around the equinox in London and Wellington (in the northern and southern hemispheres respectively) and it is clear to see that date on which there are exactly 12 hours of daylight and 12 hours of darkness is not 21 March.

Length of day march

(TimeandDate.com 2016b)

I hope you have enjoyed this post and, with apologies to my readers in the southern hemisphere, are enjoying the promise of the long summer evenings in the not too distant future.

The Science Geek

Notes

(1) The table shows that there is a pattern in that the times of the two equinoxes in a given year are just under six hours later than the previous year, unless the year is a leap year, in which case they are just under 18 hours earlier than the previous year.  Thus, the equinoxes will occur at roughly the same date and time every four years. For example the spring equinox will occur at:

  • around 4 am (GMT) on March 20 in the years 2016, 2020 and 2024
  • around 10 am (GMT) on March 20 in the years 2017 , 2021 and 2025
  • around 4 pm (GMT) on March 20 in the years 2018 , 2022 and 2026
  • around 10 pm (GMT) on March 20 in the years 2019 , 2023 and 2027

However this four-year pattern doesn’t always hold because leap years don’t always occur every four years. Century years which are not divisible by 400 e.g. 1800, 1900, 2100 are not leap years. So for example in the year 1903, where there had not been a leap year for 7 years, the equinoxes occurred relatively late. On this year the equinoxes occurred at 7:15 pm (GMT) on 21 March and 5:45 am (GMT) on 24 September. So in Tokyo Japan, which is 9 hours ahead of GMT, in 1903 they occurred at 4:15 am on 22 March and 2:45 pm on 24 September

(2) The exact day on which there is 12 hours of daylight will vary with latitude.

References

TimeandDate.com (2016) Solstices & Equinoxes for London (Surrounding 10 Years).  Available at: http://www.timeanddate.com/calendar/seasons.html?n=136 (Accessed: 5 March 2016).

TimeandDate.com (2016) London, ENG, United Kingdom — Sunrise, Sunset, and Daylength, March 2016, Available at: http://www.timeanddate.com/sun/uk/london(Accessed: 1 March 2016).

United Nations (2016) International Day for the Elimination of Racial Discrimination. Available at: http://www.un.org/en/events/racialdiscriminationday/ (Accessed: 1 March 2016).

September 18 The Shortest Day

Revised 10 September 2018

Most people are probably unaware of this but the length of a solar day, which is the natural day measured by the rising and setting of the Sun isn’t  always 24 hours. It varies slightly throughout the course of the year and that September 18 is in fact the shortest solar day in the year. This post discusses this curiosity, which is not widely known.

Background- the variation in the length of the day.

Although a day for practical timekeeping purposes is always 24 hours, the actual length of a solar day, which is the time difference between two successive occasions when the Sun is at its highest in the sky, varies throughout the year. As shown in the graph below, it is at its longest, 24 hours 30 seconds, around Christmas Day and is at its shortest, 23 hours 59 minutes 38 seconds, in mid-September.

Day length

How the length of a solar day differs from the average value of 24 hours.

The y-axis shows the difference in seconds between the length of a solar day and 24 hours on a given date measured in seconds. So, for example:

  • 10 means 24 hours 10 seconds
  • 20 means 24 hours 20 seconds
  • -10 means 23 hours 59 minutes 50 seconds.

If we look in detail around the middle of September then we get the following

Sept 18 Shortest

 

September 18 is the shortest day of the year, although the difference in day length between September 18 and the days either side is extremely small!

Why does the length of the solar day vary?

The variation in the length of the solar day is not due to the change in the rotation speed of the Earth around its axis. Although the Earth’s rotation speed does vary and is gradually slowing down, as described in my previous post on leap seconds, the effects are very small and unpredictable. In fact the time for the Earth to turn once on its axis will vary by only 0.005 seconds during a year. Whereas, the variation in the length of a solar day is both predictable and is much larger.

There are actually two different causes of this variation. Firstly, the Earth moves in an elliptical (oval shaped) orbit around the Sun and secondly the Earth is tilted on its axis. I’ll now talk about each of these effects in turn.

Effects due to the elliptical orbit

The Earth takes roughly 23 hours and 56 minutes to make a complete rotation on its axis. However a day is clearly not 23 hours and 56 minutes long! This is because during the time it has performed one rotation the Earth has moved around the Sun a little. So if we take the point in time when the Sun is at its highest in the sky the Earth needs to make slightly more than one complete turn for the Sun to be at the highest point in the sky on the following day (0.00274 of a turn to be precise). It takes an extra 4 minutes to make this extra small fraction of a turn, which is why a day is, on average, 24 hours long. This is shown in the diagram below.

Earths Orbit around sun

 If we take a point on the Earth when the Sun is highest in the sky, then after 1 rotation the Sun won’t be at the highest in the sky again. The Earth has to make slightly more than one rotation for this to happen.

In fact it is a little more complicated than this because  the Earth’s orbit is oval shaped its distance from the Sun varies throughout the year. It is at its closest in early January and its furthest away in early July. When the Earth is closest to the Sun it moves more rapidly in its orbit and, when it furthest away, it moves more slowly. This is shown in the diagram below.

 

  • In January, when the Earth is moving faster in its orbit, if we take a point in time when the Sun is at its highest in the sky the Earth needs to make slightly more than 1.00274 of a turn for the Sun to be at the highest point in the sky on the following day. So a solar day is slightly longer than 24 hours.
  • In July, when the Earth is moving more slowly in its orbit, the Earth needs to make less than 1.00274 of a turn for the Sun to be at the highest point in the sky on the following day. This would make a day shorter than 24 hours.

If the ovalness of the Earth’s orbit were the only effect then the length of a solar day would be the longest on Jan 2 at 24 hours and 10 seconds and the shortest at 23 hours 50 seconds on July 4. However, this isn’t the only effect, the tilt of the Earth’s axis causes a larger variation in the length of a solar day than the ovalness of the Earth’s orbit and I’ll talk about that now.

Why should the tilt of the Earth’s axis cause the length of day to vary?

Most people will remember from high school that the tilt of the Earth’s axis causes the seasons. At first sight it is not clear why the tilt of the Earth’s axis should also cause the length of a solar day to vary and this cause is harder to understand than the variation due to the ovalness of the Earth’s orbit. I will explain this below. I hope my explanation is clear.

As seen from the Earth, the Sun appears to orbit the Earth once a year and the Earth spins on its axis every 23 hours 56 mins. This is shown in the diagram below. This is a perfectly valid thing to do even though of course, in reality, the Earth orbits the Sun. Interestingly, astronomers use a coordinate system to give the position of the Sun and the planets assuming that they are in orbit around the Earth.

 

Sun around Earth

As mentioned above, the Earth takes roughly 23 hours and 56 minutes to make a complete rotation on its axis.  During this time, the Sun appears to have moved around the Earth a little.  If we take a point in time when the Sun is at its highest in the sky, once again the Earth needs to make an extra 0.00274 of a turn for the Sun to be at the highest point in the sky on the following day.

 

However because of the tilt of the Earth’s axis, when we look at the picture in three dimension the sun appears to follow the path shown below. This path is called the ecliptic and is tilted compared to the Earth’s equator.

Ecliptic

The Sun appears to move at the same speed around the ecliptic throughout the year, taking 1 year to do a complete circuit. However, as you can see from the diagram:

  • At the equinoxes, in March and September, the Sun is moving steeply in latitude and thus changes more slowly in longitudeSee notes.
  • At the solstices, in June and December, the Sun’s latitude doesn’t change very much and the Sun moves more  rapidly in longitude.

Therefore, when we look at the picture in two dimensions. The Sun appears to move at an uneven speed in longitude in its imaginary orbit around the Earth.

 

It is this uneven speed at which the Sun moves in longitude which causes the variation in the length of a solar day.

If this were the only effect then the length of a solar day would be the longest at the June and December solstices, at around 24 hours and 20 seconds, and its shortest at 23 hours 40 seconds at the equinoxes.

Putting the two effects toghether

The combination of the two effect is shown in the graph below.

 

In the graph:

  • The horizontal axis gives the months of the year and the vertical axis gives the difference in the length of a solar day from 24 hours in seconds. So, for example, a value of 10 means 24 hours 10 seconds, 20 means 24 hours 20 seconds, -10 means 23 hours 59 minutes 50 seconds.
  • The blue line gives the difference due to the tilt of the Earth’s axis.
  • The red line gives the difference due to the ovalness of the Earth’s orbit.
  • The black line gives the overall effect which is the combination of the blue and red lines.

What effects does this have?

Because the length of a solar day varies throughout the year, the natural time measured by a sundial drifts up to 15 minutes ahead or behind the time measured by an accurate clock. Astronomers call this difference the “equation of time”.

equation

Notes

Strictly speaking the terms right ascension and declination should be used rather than latitude and longitude.