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## Why do we have leap seconds?

At midnight on the night of Monday the 30th of June, an extra second was added to our clocks. A so-called leap second. Did you enjoy it? Me too 🙂 I got so much more done….. But, why do we have leap seconds?

In this blog here, I explained the difference between how long the Earth takes to rotate $360^{\circ}$ (the sidereal day) and how long it takes for the Sun to appear to go once around the Earth (the mean solar day). We set the length of our day, 24 hours, by the solar day. If there are 24 hours in a day, 60 minutes in an hour, and 60 seconds in a minute, then there should be $24 \times 60 \times 60 = 86,400 \text{ seconds}$ in a solar day. But, there aren’t! The Earth’s rotation is not consistent, that is if we measure the length of a mean solar day, it is not consistently 86,400 seconds. This difference is why we need leap seconds.

A leap second was added at midnight on the 30th of June. It was the first leap second to be added since 2012.

But, how do we accurately measure the mean solar day (the average time the Sun appears to take to go once around the sky) , and what is causing the length of the mean solar day to change?

## How do we define a second?

When the second was first defined, it was defined so that there were 86,400 seconds in a mean solar day. But, since the 1950s, we have a very accurate method qof measuring time, atomic clocks. Using these incredibly accurate time pieces (the most accurate atomic clocks will be correct to 1 second over some tens of thousands of years) we have been able to see that the mean solar day varies. It varies in two ways, there is a gradual lengthening, but there are also random changes which can be either the Earth speeding up or slowing down its rotation.

## How do we measure the Earth’s rotation so accurately

In order to measure the Earth’s rotation accurately we use the sidereal day, which is roughly four minutes shorter than the mean solar day. By definition, the sidereal day is the time it takes for a star to cross through a local meridian a second time. But, actually, stars in our Galaxy are not good for this as they are moving relative to our Sun. So, in fact, we use quasars, which are active galactic nuclei in the very distant Universe; and use radio telescopes to pinpoint their position.

## The gradual slowing down of the Earth’s rotation

There is a gradual and unrelenting slowing down of the Earth’s rotation, which may or may not be greater than the random changes I am going to discuss below. This gradual slowing down is due to the Moon, or more specifically to the Moon’s tidal effects on the Earth. As you know, the Moon produces two high tides a day, and this bulge rotates as the Earth rotates. But, the Moon moves around the Earth much more slowly (a month), so the Moon pulls back on the bulge of the Earth, slowing it down. To conserve angular momentum, the Earth slowing down means the Moon moves further away from the Earth, about 3cm further away each year.

## The random fluctuations in the Earth’s rotation

In addition to the unrelenting slowing down of the Earth’s rotation due to the Moon, there are also random changes in the Earth’s rotation. These can be due to all manner of things, including volcanoes and atmospheric pressure. These random fluctuations can either speed up or slow down the Earth’s rotation.

We have been having leap seconds since the 1970s when atomic clocks became accurate enough to measure the tiny changes in our planet’s rotation. Since them we have added a leap second when it is decided that we need it, typically but not quite once a year. However, having that extra second at the end of June can cause glitches with computers, and so there are discussions to remove the leap second and replace it with something larger on a less frequent basis.

## My photos of the March 20th 2015 Solar Eclipse

On Friday the 20th of March there was a Solar eclipse. In Cardiff it was partial, reaching a maximum of 87% at 09:28 GMT.

The details of the 20th March 2015 eclipse from the NASA eclipse website

This image is taken from the NASA eclipse website, which can be found here. On this amazing website, you can look up eclipses going back thousands of years and going thousands of years into the future.

An alternative graphic of the eclipse is this.

An alternative graphic of the 20th of March 2015 eclipse

These are some of the pictures I took. I started taking photographs as 08:33 using a 300mm lens on my Nikon DSLR, with Baader paper taped over a spare lens shield which I have. The pictures below are about every 10 minutes (I was taking them more frequently so these are just a sub-set). The last picture shown below was taken at 10:33.

The eclipse at its maximum from Cardiff, 87% at 09:28.

It didn’t actually get dark (anyone who has witnessed a total eclipse will know that even when the eclipse is 99.95% it is not dark, it requires totality for it to go dark). But, the light did take on a strange ethereal quality, a little like dusk but not quite the same either.

If you managed to get any photographs of this eclipse, feel free to share them below in the comments box.

## Cardiff Castle Astronomical (and Astrological) Statues

On the clock tower of Cardiff Castle is a wonderful collection of Astronomical (or astrological) figures. Here is a little photo gallery of the figures. I will do a separate blog about Cardiff Castle and its history in the near future. Although the castle dates back to Roman times, most of what one sees these days was built by the Third Marquess of Bute in the late 1800s, with the clock tower itself being built in 1868.

Mars and the Sun on the clock tower of Cardiff Castle.

The clock tower shows statues of figures representing the Sun, the Moon, and all 5 “naked eye” planets: Mercury, Venus, Mars, Jupiter and Saturn. In a separate blog I will show photographs of the sumptuous interior of the castle, including a room in the clock tower which has a star-painted ceiling and many astronomical motifs.

## Happy Diwali ( “Diwali ki Shubhkamnayein” दिवाली की शुभकामनाएं )

Today is the day of the Hindu festival Diwali, the festival of light. About 200m from my house is a Hindu temple, and it has been lit up for the last several days in celebration of this important Hindu festival. Here is a picture I took on Sunday evening.

The Hindu temple in Cardiff, lit up for Diwali

Like most religions, with the exception of Islam, the Hindu calendar is a luni-solar calendar, and so the date of Diwali changes. Last year (2011) it was on the 26th of October, and next year (2013) it is on the 3rd of November, but this year it is today, the 13th of November. How is the date of Diwali calculated?

Being a luni-solar calendar, this means it follows something both the Moon and the Sun are doing. Today is a new Moon. So, the question is, what is special about today’s new Moon? What recent important Solar event happened? The Autumn equinox of course, which was on the 22nd of September this year (2012). The firsrt new Moon after this year’s Autumn equinox was on the 15th of October, and today is the second new Moon after the Autumn equinox. So, Diwali always falls on the 2nd new Moon after the Autum equinox! It’s that simple……

I wish a very happy Diwali to all my Hindu friends and students (and readers) around the World.

## Happy Chinese New Year (农历新年)

Today (23rd of January 2012) is Chinese New Year, so happy Chinese New Year to all my Chinese friends and students. Today, over 1 billion Chinese will be celebrating the start of the year of the Dragon (龍). From what I heard yesterday on the radio, many Chinese couples await to have children in the year of the Dragon, as this year is thought to be the most lucky of the cycle of 12 animals.

Candles being lit for Chinese New Year

Last year (2011), Chinese New Year was on the 3rd of February, and next year (2013) it will be on the 10th of February. The table below shows the dates of Chinese New Year from 2009 to 2014.

 year date 2009 26th January 2010 14th February 2011 3rd February 2012 23rd January 2013 10th February 2014 31st January

Clearly, Chinese New Year does not fall each year on the same date in the civil calendar. So, how is it calculated?

The Chinese calendar is an example of a lunisolar calendar, which means it depends on both the Moon (Luna) and the Sun (Solar). The same is true of the traditional Jewish calendar, and the calendars of many other civilisations and religions including Hindu, Tibetan and Buddhist calendars.

The date of the Chinese New Year is determined by the following, very simple, formula.

 The date of the Chinese New Year is the day of the 2nd New Moon after the Winter Solstice (the shortest day of the year in the Northern Hemisphere).

This fixes it between the 21st of January (the earliest it can be, which would occur if there were a New Moon on the day after the Winter Solstice), and the 20th of February, which would occur if there were a New Moon on the day of the Winter Solstice.

So, it is that simple. Today (23rd of January) is a New Moon, and the previous New Moon (the first after the Winter Solstice) was on the 24th of December, with the Winter Solstice itself falling on 22nd of December in 2011. Next year, 2013, the first New Moon after the Winter Solstice will be on the 11th of January, the 2nd one will be on the 10th of February, so this will be the date of the Chinese New Year in 2013.

How will you be celebrating Chinese New Year?