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 darker mornings

As I complete this post from my home in Manchester, England, it is 4:30 pm and already fairly dark outside. Many people think that it will continue to get dark earlier each day in the afternoon until we reach 21 December, the winter solstice. This, however, is not the case. The evenings in fact start to draw out a week or so before December 21, so it is already getting lighter in the evenings, although it does not start to get lighter in the mornings until early in the new year.

This post aims to explain this interesting phenomenon. (Those of you who have been following my blog for while and have a good memory may recall that I posted on this topic a couple of years ago 🙂 )

Sunrise and sunset in December

The table below shows the sunrise and sunset times for London for December at three day intervals.

 

In the table above, the daylight column shows the number of hours, minutes and seconds between sunrise and sunset. This clearly shows that 21 December has the shortest period of daylight, but while the time of sunrise continues to get later and later throughout the whole of December, the time of sunset stops getting earlier around 12 December.

The final column shows the solar noon, the time of day that the Sun is at its highest in the sky or, to put it another way, the mid-point between sunrise and sunset. The table shows that during December the solar noon drifts later by about 30 seconds each day.

Why does the solar noon shift ?

A solar day is the period of time between solar noon on one day and solar noon on the next day. The length of a solar day varies throughout the year. It is at its shortest, around 23 hours 59 minutes 38 seconds, in mid September and at its longest, around 24 hours 30 seconds around Christmas Day.

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Day length

The graph shows the difference between the length of a solar day and its average value of 24 hours throughout the year.  For example, a value of 10 means a solar day is 24 hours 10 seconds long , 20 means a solar day is 24 hours 20 seconds long, and -10 means  a solar day is only 23 hours 59 minutes 50 seconds long.

As you can imagine, it would be complete chaos if our clocks and watches had to cope with days of different lengths, so we use 24 hours, the average over the whole year, for all timekeeping purposes.

So, in December solar days are on average 24 hours and 30 seconds in length, while our clocks and watches are still assuming that each day is exactly 24 hours.  This causes the day to shift about 30 seconds later each day,  as shown in the diagram below.  This explains why the evenings start drawing out before the shortest day, but it continues to get darker in the mornings until the new year.

 

Sunrise and sunset for London in December.

Why does the length of a solar day vary ?

The reason why the length of the solar day varies is due to two different factors.

  1. The fact that the Earth moves in an elliptical orbit around the Sun and its speed varies, being faster in earlier January, when it is closer to the Sun and slower in early July, when it is further away.
  2. The fact that the axis of the Earth’s rotation is tilted.

If you want to know more about how these  factors work together to vary the length of the solar day, see my post September 18 the Shortest Day.

What about the southern hemisphere ?

In the southern hemisphere 21 December is the summer solstice, the day with the most daylight. What happens is that the Sun starts rising later before December 21, but it doesn’t start getting dark earlier in the evening until well after December 21. This is illustrated in the table below, which shows the sunrise and sunset times for December for Wellington in New Zealand, which lies at a latitude of roughly 41 degrees South.

 

Final note

It is not strictly true to say that a solar day is on average exactly 24 hours long.  As readers of a previous post,  “The Days are Getting Longer’, will be aware the Moon is gradually getting further away from the Earth. In fact, equipment left on the Moon by the Apollo astronauts has confirmed that the average distance from the Earth to the Moon is increasing by about 4 cm a year.

Aldrin_Apollo_11

-Image from NASA

As the Moon gradually saps energy from the Earth, the Earth’s rotation slows down, causing the length of a day to get gradually longer. In the year 1900 a mean solar day was 24 hours long. Now, in the early 21st century, a mean solar day is actually 24 hours 0.002 seconds long. To prevent the time we measure using accurate clocks from drifting away from the solar time we need to add an second called a leap second roughly every 18 months.

 

 

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).

 

Christmas Day – December 25th or January 7th?

Merry Christmas to all my readers and followers and I wish you all a happy New Year.

The majority of people who celebrate Christmas Day, whether for religious or cultural reasons or both, do so on 25 December.  However, followers of the Orthodox churches generally celebrate Christmas Day thirteen days later, on January 7. The reasons for this difference are interesting and, as I’ll discuss further in this post, are to do with both astronomical measurement and also disagreements between different branches of the Christian church.

Orthodox Christmas

The solar year

One of the most fundamental units of time is a the year.  A solar year is the term used by astronomers to describe the amount of time that the Sun takes to return to exactly the same position in the cycle of the seasons.  This has been accurately measured as 365.2421897 days, to the nearest 7 decimal places.

Earths Orbit

A solar year is the amount of time from a particular point in the cycle of the seasons to exactly the same point in the following year (e.g from one summer solstice to next or from one spring equinox to the next)

Because a solar year is slightly longer than 365 days, if we were to use a calendar where every year always had exactly 365 days, then the calendar year would slowly run ahead of the solar year at the rate of slightly less than a quarter of a day per year. In about 400 years the calendar would have drifted away from the seasons by about 97 days.  So, in the northern hemisphere, the start of spring would be at the end of June, the summer solstice (the day of the year with the most daylight) would be at the end of September and the autumn (or fall) equinox would be at the end of December. To prevent this happening we add an extra day (February 29) every four years. When this happens it is a leap year.

February29jpg

Having a leap year every four years is a key feature of the Julian calendar, named after Julius Caesar, who introduced it in the year 45 BCE, which was used by all Christian countries until 1582. However, if we always have a leap year every four years, this will result in a year which is on average 365.25 days long, which  is 0.078 days longer than the actual length of a solar year. This slight over correction causes the Julian calendar to drift backwards gradually from the natural calendar by 7.8 days per 1000 years .

Between 325, when the Julian calendar was first used by the church to define the date of Easter, and 1582, it had drifted back by 10 days. So in that year the spring equinox, the first day of spring, when the day and night are roughly 12 hours long, was on March 11 (whereas in 325 it had been on March 21), the day which had the most daylight was Jun 11 and the shortest day was December 11. The spring equinox is used to calculate Easter (see note 1) so the date range on which Easter could fall had drifted back by 10 days.

The Gregorian Calendar

In 1582 Pope Gregory XIII introduced a refinement  to prevent the calendar used by the church from drifting any further away from the natural calendar. The change he made was that a century year (e.g. 1600, 1700, 1900, 2000, 2100)  could only be a leap year if it was divisible by 400. So 1700, 1800, 1900 would not be not leap years, but 1600 and 2000 would be. He also proposed that the calendar be brought back in line with the seasons so the spring equinox would once again fall on March 21.  This required that 10 days be omitted when moving from the old to the new calendar. Pope Gregory’s calendar, which is the one that nearly every country in the world uses today, is called the Gregorian calendar. On average each year is 365.2425 days, which is very close to the length of the solar year.

The Gregorian calendar was quickly adopted by the Catholic countries in Europe. Spain, which at the time included Portugal and much of Italy, adopted it on 4 October 1582. In Spain the day after 4 October 1582 was 15 October 1582, with the days from 5 October to 14 October being simply missed out.

. Gregorian Calendar

Initially, the Protestant and Orthodox countries in Europe refused to adopt the Gregorian calendar, feeling that it was a plot by the Catholic church to impose its power over non-Catholic countries. This caused confusion over dates when some countries had converted to the Gregorian Calendar and other countries still used the Julian Calendar.  Conventions such as 10/20 February 1667 were used to indicate that an event took place on 10 February 1667 in the Julian Calendar, which was the same day as 20 February 1667 in the Gregorian Calendar.

The whole of Europe adopts the Gregorian calendar

Eventually, all the Protestant countries switched over to the Gregorian Calendar. In particular, Great Britain and its colonies, which at the time included America, adopted the Gregorian calendar on Wednesday 2 September 1752, which was followed by Thursday 14 September 1752. The eleven days from 3 September to 13 September were missed out.

Sept 1753

According to some accounts rioters took to the streets, demanding that the government “give us back our 11 days.”   In America, meanwhile, Benjamin Franklin (1705-1790) took a more positive view of the phenomenon and wrote that “it is pleasant for an old man to be able to go to bed on September 2, and not have to get up until September 14”.

The Orthodox countries of Eastern Europe were even slower to adopt the Gregorian calendar. The Soviet Union didn’t adopt it until in 1918 and Greece didn’t adopt until 1923.

Interestingly, even though all the Orthodox countries have adopted the Gregorian calendar for civil purposes, most Orthodox churches still use the Julian calendar and will not accept a calendar which they see as being imposed by the Catholic church. So, allthough Orthodox Christians do celebrate their Christmas on the day marked December 25 on their calendars, they are celebrating on a completely different day to the rest of the Christian world, as it is actually January 7 in the Gregorian calendar.

Calendars in other Countries in the World

Nearly all countries of the world use the Gregorian calendar for administrative purposes, sometimes alongside a more traditional calendar. For example, China uses the Gregorian calendar for public or business affairs such as most national holidays, but uses the traditional Chinese calendar, in which years have names rather than numbers, as well. In the Chinese calendar there can be 353, 354, 355 383, 384, or 385 days in a year and the first day of the new year occurs  in late January or February. The current year runs from 8 February 2016 to 27 January 2017 and is the year of the monkey. The Chinese New Year on 28 January 2017 will be start of the year of the rooster.

rooster

 

What will happen in the future ?

The Julian Calendar is slowly drifting away from the natural calendar at the rate of 7.8 days per thousand years, so if the Orthodox church doesn’t adopt the Gregorian calendar then the date of Orthodox Christmas will get later and later. In 2,000 years time Orthodox Christians would be celebrating Christmas on around January 23 (in the Gregorian calendar) and in 10,000 years time they would be celebrating Christmas at the end of March.

As mentioned previously, the average length of a year in the Gregorian calendar is 365.2425 days and the length of a solar year is 365.2421897. So even the Gregorian calendar is only an approximation to the “real year” and gives a very slight over-correction.   To bring the Gregorian calendar into line with the natural calendar it will be necessary to omit a day every 3,200 years.

On that final note I’ll sign off  and wish you all a healthy and happy 2017!!

Note

This is described in more detail in my post Easter – 27 March 2016.

December 31 2016 Leap Second

On New Year’s Eve an extra second will be added to the end of the day. This extra second is called a leap second. As I’ll explain later, leap seconds need to be added periodically to bring the time we measure with accurate atomic clocks in line with the natural time which results from the rotation of the Earth.

Leap Second

 

Why do we need leap seconds?

Although we take the average length of a day to be 24 hours, the mean solar day, or average “natural” day measured by the Earth’s rotation, is now slightly longer than this. As discussed in a previous post, this is due to the slowing down of the Earth’s rotation (see note 1).  In the year 1900 a day was almost exactly 24 hours, but it is now around 24 hours 0.001 seconds. So, to bring the time measured by accurate atomic clocks to within a second of the natural time, a leap second needs to be added approximately every 1,000 days. The extra second is always added at the end of the day on 30 June or 31 December. The previous two were added on 30 June 2012 and on 30 June 2015.

Problems with leap seconds

It has been possible for around two hundred years to accurately measure the rotation of the Earth, and it is now clear that it is slowing down, which means that the length of the mean solar day is increasing. However, over shorter time-scales things aren’t quite as simple as this. The actual speed of the Earth’s rotation is variable and events such as

  • large earthquakes
  • movements in the Earth’s crust
  • melting of glaciers and
  • changes in the mantle (the region of the Earth below the crust)

may temporarily speed it up. So although the trend over decades and centuries is that the days are getting longer, over shorter time-scales the average length of a natural day may actually decrease. This is illustrated in the diagram below which shows, in milliseconds, the amount by which the average length of a day was longer than 24 hours for the years 2000 to 2014. (1 millisecond equals one thousandth of a second.)

 

Day lengths 2000s

This variation means that, unlike leap years, where there are precise rules for determining whether or not a given year will be a leap year, it is not possible to say years in advance when there will be a leap second. A body called the International Earth Rotation and Reference Systems Service (www.iers.org) decides from accurate measurements of the Earth’s rotation when the next leap second will occur.

This announcement is made around six months in advance. For example, the official announcement of the December 31 leap second was made on 6 July 2016 by the following bulletin.

leap-second-2016

In the past when leap seconds have been applied, a number of data centres and websites around the world experienced system problems and crashed. This was because they could not cope with a minute which contains 61 seconds and interpreted this unforeseen event as a system failure.

The Google approach – smearing time 

For the next leap second Google are using an interesting solution to the problem. (Google 2016) For the 20 hour period from 2 pm on 31 December to 10 am on 1 January Google will abolish the normal rules of timekeeping.  Instead of normal seconds, they will be using a “Google Second” which is fractionally longer than the usual second. Instead of adding an extra second just before midnight, they are spreading out that extra second throughout this 20 hour period which means that no extra second will be need to be inserted.  This is shown in the diagram below:

 

googletime

What will happen in the longer term?

As the length of the day gradually increases, leap seconds will need to added more often. In 100 years time we will have, on average, a leap second once a year and in 1,000 years time we will have 7 leap seconds per year, which is equivalent to one leap second every 52 days.

leap-second-future2016

 

When will the leap second be added?

The extra second is inserted at 23:59:60 at 31 December 2016, Greenwich Mean Time (GMT) (see note 2).  So in the UK which uses GMT in the winter months, it will occur just before midnight. In different parts of the world the leap second will be added at different local times. New York is 5 hours behind GMT, so the extra second will be added at 18:59:60 on 31 December local time.  Beijing is 8 hours ahead of GMT and the extra second will be added at 07:59:60 on 1 January.  Use it wisely ;-).

 

Notes

1)The average length of day when calculated over a entire year is just over 24 hours. However, over the course of a year the the actual length of a solar day varies. This variation throughout the year is due to entirely different effects than the slowing of the Earth’s rotation. It is at its longest – 24 hours and 30 seconds – around Christmas day and it is shortest at around 23 hours 59 minutes and 38 seconds in mid September. This is variation is described in more detail in my post  September 18 the shortest day.

2) The term Greenwich Mean Time is no longer used by astronomers.    Instead, they use two different times which agree with each other to within 1 second.

  • Universal Time, often abbreviated to UT1, is the mean solar time, the time determined by the rising and setting of the Sun at the Greenwich Meridian, zero degrees longitude.
  • Co-ordinated Universal Time, usually abbreviated to UTC, is the time measured by atomic clocks and is kept to within 1 second of UT1 by the addition of leap seconds.

In common use, Greenwich Mean Time (GMT) is often taken to be the  same as UTC, which is the approach I have taken for this post. However, it can also be taken to mean UT1. Owing to the ambiguity of whether UTC or UT1 is meant, and because timekeeping laws usually refer to UTC, GMT is normally avoided in precise writing.

Greenwich Meridian

The Greenwich Meridian- Image from Wikimedia Commons 

References

Google. Making every (leap) second count with our new public NTP servers. https://cloudplatform.googleblog.com/2016/11/making-every-leap-second-count-with-our-new-public-NTP-servers.html (accessed 7 December 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