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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.

## The Prediction of the Cosmic Microwave Background – the original paper

Last week I reposted my blog about the prediction of the cosmic microwave background (CMB), which I had originally written in April 2013. This month, July, marks the 50th anniversary of the first detection of the CMB, and I will blog about that historic discovery next week. But, in this blog, I wanted to show the original 1948 paper by Alpher and Hermann that predicted the CMB’s existence.

I learnt far more about the history of the CMB’s prediction whilst researching for my book on the CMB, which was published at the end of 2014 (follow this link to order a copy). In doing my research, I found out that many of the things I had been been told or had read about the prediction were wrong, so here I wanted to say a little bit more about what led up to the prediction.

My book “The Cosmic Microwave Background – how it changed our understanding of the Universe” is published by Springer and can be found by following this link.

## Gamow did not predict the CMB

Many people either do not know of the 1940s prediction of the CMB, or they attribute its prediction to George Gamow. In fact, it was his research assistants Ralph Alpher and Robert Hermann who made the prediction, but as head of the group it is often Gamow who gets the credit.

Ralph Alpher had just finished his PhD on the origin of the elements, and after the publication of the famous Alpher, Bethe, Gamow paper (see my blog here about that), Gamow started writing a series of papers on the nature of the early Universe. One of these papers was entitled “The Evolution of the Universe”, and it appeared in Nature magazine on the 30th of October 1948 (Nature 1948, volume 162, pages 680-682) – here is a link to the paper.

Gamow’s October 1948 paper in Nature was entitled “The Evolution of the Elements”.

Although a man of huge intellect and inventiveness, Gamow was often sloppy on mathematical detail. Alpher and Hermann spotted an error in some of Gamow’s calculations on the matter-density, and so wrote a short letter to Nature magazine to correct these mistakes. The letter is entitled “Evolution of the Universe”, nearly the same title as Gamow’s paper, but with no “The” at the start. The letter is dated 25 October 1948. It appeared in Nature magazine on the 13th of November 1948 (Nature 1948, volume 162, pages 774-775) – here is a link to the paper.

Here is the paper in its entirety (it is short!), and I have highlighted the part which refers to a relic radiation from the early Universe, what would become known as the cosmic microwave background.

The original paper (letter) by Alpher and Hermann which makes the first prediction of the cosmic microwave background (CMB). It was published in Nature magazine on the 13th of November 1948.

As you can see, the prediction is not the main part of the paper, it just forms two sentences!

Next week, I will blog about the accidental discovery of the CMB by Penzias and Wilson, which was published 50 years ago to this month (July).

## The sky from Buenos Aires

One of the lectures I will be giving on my cruise from Buenos Aires to Santiago is how the sky as seen from the southern parts of South America will look considerably different to the skies that Europeans and people from North America are used to seeing.﻿ Let me explain some of the obvious differences. First of all, although the Sun rises in the East and sets in the West in both the northern and southern hemisphere, if you are as far south as the southern parts of South America you need to look north to see the Sun. This means that you are facing north, and the Sun will appear to move from right to left across the sky, not from left to right as we northerners are used to seeing it. This can be quite disorientating.

Jupiter, and all the other planets, are visible from the Southern Hemisphere but again, one needs to look north to see them, not south. Just as in the Northern Hemisphere, Jupiter will dominate the evening sky for the next several months, and is in the constellation Cancer, slowly moving eastwards into Leo over the next 6-12 months.

The evening sky (7:15pm) from Buenos Aires on the 5th of March 2014. Jupiter is clearly visible, and will dominate the evening sky for the next several months. Just as with the Sun, from this location you need to look north to see Jupiter, not south as in the Northern Hemisphere.

This next diagram below shows Orion and Sirius, two very well known things in the winter sky, but as you can see from the Southern Hemisphere everything looks upside down! We are used to seeing Orion with Betelgeuse in the top left and Rigel in the bottom right, but from Buenos Aires this is flipped; Betelgeuse is in the bottom right, and Rigel in the top left (just imagine looking at Orion from the Northern Hemisphere but standing on your head to do so!). Just as confusingly, we are used to seeing Sirius (the brightest star in the sky) below Orion, closer to the horizon, because it is to the south of Orion. But, from Buenos Aires, it is above it, further away from the horizon. Very confusing!

This shows how confusing the southern skies can be to someone from the Northern Hemisphere. Orion is upside down, and Sirius is above (further south) Orion, not below as we see it in the Northern Hemisphere.

During the cruise, the other very bright object that people cannot miss is Venus, which is dominating the early evening sky. Venus will be at greatest eastern elongation on﻿ the 6th of June, which means that between now and then it will be moving further and further to the east of the Sun as seen from Earth (remember both we and Venus are moving in orbit about the Sun as this is going on), and as it moves further and further east the time between sunset and Venus setting gets bigger and bigger. On the 5th of March the Sun sets at 7:25pm from Buenos Aires, and Venus will set at 8:46pm. This gives a good hour to see Venus after sunset.
By early June, from the same location, the Sun sets at 5:50pm and Venus will set at 9:04pm, giving about three hours.

Venus is the evening sky as seen from Buenos Aires on the 5th of March at 7:14pm. At the moment Venus and Mars are close, and Uranus is near them too.

## Upcoming solar eclipses

I have had a few people ask me about the Solar eclipse on the 20th of March, and whether it is worth seeing; or are people better off waiting for another one in the next few years? So, here is my attempt to answer those questions.

This upcoming eclipse on the 20th of March will be the last total eclipse visible from anywhere in Europe until 2026, but as you can see from the figure below, the path of totality is way north where no one lives! From mainland Europe and the British Isles it will be partial, and depending on how far south you are that will determine how partial it appears.

If you look closely at the diagram below you will see that everyone in the British Isles will see the eclipse as more than 80%, which is not too bad. Although the figure does not have the curve, I suspect in Scotland it is more than 90%. Ditto main-land Europe, if you can get up as far north as Scandinavia you will see a more than 80% eclipse. But, if you are in France or Germany or central Europe, it is going to be between 60% and 80%. Places like London or Cardiff (where I live) look like they will see an 84-85% eclipse, which I am pretty pleased about as I thought it was going to be less.

The eclipse on the 20th of March is total if you are far enough north, but to most of us in Europe it will be a partial eclipse. From the Disunited Kingdom it will be better if you are in Scotland than if you are in southern England or south Wales.

The next total eclipse after this one is on March the 9th next year (2016). But, for those of us in Europe or North America, it involves a bit of a trek to Asia. The eclipse starts near Indonesia, and sweeps out across the Pacific ocean. It doesn’t really cross any largely populated land-masses, apart from Borneo I guess.

This eclipse, on the 9th of March 2016, passes just to the north of Indonesia and sweeps out across the Pacific ocean.

After the 2016 total eclipse, the next eclipse is the big one. On the 21st of August 2017 there will be a total eclipse which will sweep across the continental United States! I am guessing that this will probably be the most observed solar eclipse in history so far; the only one to possibly rival it would be the eclipse which swept across mainland Europe in 1999, which is to date the only total eclipse I have seen.

Details of the total eclipse on the 21st of August 2017. As you can see, this one passes right across the continental United States, and will probably be the most observed total eclipse in history.

So, in answer to the question “which is the best solar eclipse to try and see over the next few years?”, I would have to say it is the 21st of August 2017 one. I also suspect that there will be tens of millions of people, if not hundreds of millions, all trying to view this eclipse, so the path of totality may get quite crowded! But the eclipse next month is well worth seeing, even if most of us in Europe will only see it as a partial eclipse. I well remember seeing a partial eclipse as a teenager, and I also saw a partial one in 1994. Whilst not as spectacular as being in the path of totality, it is still a memorable sight to see the Moon move across the Sun.

## Jupiter and the Moon last week

On Tuesday morning of last week (the 3rd) I woke up early, which is a habit I am trying to get back into so that I can recommence my running, which I try to do first thing in the morning before work. In a semi-awake state I was listening to BBC Radio 5’s breakfast show co-presenter Rachel Burden and someone else on the show between 6 and 7 (was it George Riley the sports person or someone else??) discussing how they had seen the Moon and Jupiter very bright in the sky on Monday evening.

The following morning during the same 6-7am period, the discussion was resumed with remarks being made about how much Jupiter had moved away from the Moon. I decided to tweet into the show and to Rachel saying that it was the Moon which has moved, not Jupiter. To cut a long story short, I ended up being on the show on the Thursday morning to explain what was moving and why. Here is a link to a recording of my 3-minute stint, where Rachel and Nicky Campbell (Rachel’s co-presenter) interview me.

The evening before my being on the show, one of the show’s researchers had asked me to send in a list of the five most interesting facts about Jupiter. They then put those out as a tweet during my interview. I chose the following five, would you have chosen the same ones?

The tweet from BBC Radio 5 with the five most interesting facts about Jupiter.

The list of the five facts

I will talk about each of these five facts separately in future blogs over the next several weeks. I will also blog in a little more detail about the NASA mission to Europa and the proposed ESA mission Juice; both of which intend to study this fascinating moon in more detail.

Being on the radio it is, of course, impossible to show diagrams about the motion of the Moon and Jupiter; and there really wasn’t enough time to explain it properly. So, I have decided to put together these slides to explain it in a little more detail.

## Jupiter and the Moon during the first week of February 2015

Getting software to show you what is in the sky is easy, and although for PCs and Macs you may end up paying several tens of pounds, for tablet devices the software is much cheaper, with many reasonable ones being free. I use “Skysafari”, which is not free but is not too expensive either. It is made by Carina Software, who made the wonderful Voyager Software on Macs that I used for many many years in my classes.

Below is a screen capture using this software of the sky as seen from London at 20:00 on Thursday the 5th of February 2015. As you can see, I have done the screen capture with Jupiter just to the left (East) of the middle of the window (in the software you can use your finger to move around and look in different directions such as north or north-east if you wish). The Moon is at about 7 o’clock from Jupiter in direction, if you imagine a clock face.

This is a screen capture from an app I use on my iPad called “Skysafari” which can show what is in the sky at any location and at any time and date. There are lots of other similar apps available, but I like this one the most of the ones I’ve tried. This is the screen capture looking south for 20:00 on Thursday the 5th of February 2015 as seen from London.

Below I show a sequence of screen captures of Jupiter and the Moon (I have zoomed in on just enough to show the two) from Monday evening (the 2nd) to Friday evening (the 6th), all at 20:00 to show the motion of the Moon compared to Jupiter’s position.

Jupiter and the Moon as seen on Monday the 2nd of February at 20:00 from London

Jupiter and the Moon as seen on Tuesday the 3rd of February at 20:00 from London

Jupiter and the Moon as seen on Wednesday the 4th of February at 20:00 from London

Jupiter and the Moon as seen on Thursday the 5th of February at 20:00 from London

Jupiter and the Moon as seen on Friday the 6th of February at 20:00 from London

I think these screen captures make it quite easy to see that Jupiter is staying fixed in the same place relative to the stars during this sequence (which spans 5 nights), and it is the Moon which is moving. Why is this?

## The Motion of the Moon in the sky

The reason it is the Moon which appears to move against the background of Jupiter and the stars is because the Moon is orbiting us; whereas Jupiter is orbiting the Sun and the stars are not orbiting the Sun but are, along with the Sun, in fact orbiting the centre of our Milky Way galaxy.

As the Moon takes roughly 30 days to orbit the Earth (see this blog for the more precise figure, and the difference between how long it takes to orbit the Earth – the “sidereal month” – and how long it is between two New Moons – the “synodic months”), then if we divide $360^{\circ}$ by 30 we get that the Moon moves $12^{\circ}$ in its orbit about the Earth each day/night. This figure is only approximate (but good enough for our purposes) because (a) a sidereal month is not exactly 30 days and (b) the Moon moves in an ellipse and not a circle about the Earth, and so changes its speed at different points in the orbit, so does not move the same amount each 24 hour period.

As the Moon is $0.5^{\circ}$ in diameter, $12^{\circ}$ corresponds to 24 times the diameter of the Moon. This is quite a lot, and so the motion of the Moon from night to night against the background planets and stars is very easily seen, as the sequence of diagrams above show.

In fact, Jupiter is also moving against the background stars, but it does so much more slowly. Jupiter takes about 12 years to orbit the Sun, and so each year it moves roughly 1/12th of a full circle. Along with the Sun, the Moon and the other planets, Jupiter moves through the zodiacal constellations during its travels, and so moves roughly into a new zodiacal constellation each year. At the moment it is in Cancer, but by this time next year it will be in Leo, the next constellation along the zodiac to the East (to the left of Cancer in the diagram above). You may be able to notice that Jupiter has moved relative to the background stars in a month or two, but certainly by next February, if you remember where it is now, you will see a difference.

Finally, although we refer to the stars as “the fixed stars”, they are not fixed. They, along with our Sun, are orbiting the centre of our Milky Way galaxy. Our Sun will take 250 million years to do this, stars closer to the centre of the Milky Way will take less time and stars further out from the centre will take longer. This leads to the positions of the stars relative to each other changing, but the change is very very slow, taking tens of thousands of years to be noticeable.

## Over 1,000 exoplanets found!

This story got my attention a while ago, but for some reason I forgot about it until recently. It is astounding to think that it was only in 1995 that we discovered the first extra-solar planet (exoplanet), and less than 20 years later the tally is at over 1000!

The first few hundred exoplanets were discovered using the Doppler technique, where an orbiting planet causes its parent star to move back and forth in a rhythmic and regular manner which can be detected by shifts in the star’s spectral lines. However, in 2009 NASA launched its Kepler Space Telescope, and this led to more and more exoplanets being detected using the transit technique, and as of now most have been discovered by Kepler using this technique. You can read more about these two techniques in one my previous blogs here.

There is also a great episode of BBC Radio 4’s “In Our Time” which was broadcast last year (2013) which discusses exoplanets. The link is here, it is still available to listen to. Enjoy!

## The earliest stars

This story caught my attention recently, it pertains to the earliest stars in the Universe. These earliest stars have not yet been directly observed, this story is about observations of unusual stars in our own Galaxy which are believed to be formed from the first generation of stars.

In the early Universe, the only elements created were hydrogen and helium. All the elements heavier than hydrogen and helium have been formed in the interior of stars, and more recent generations of stars contain these heavier elements along with hydrogen and helium formed in the early Universe. As the earliest stars would have been formed from only hydrogen and helium, and because of the absence of an effect called “line blanketing”, this earliest generation of stars could form with masses much greater than subsequent generations. Theoreticians believe that masses beyond 100 solar masses were possible in the first generation of stars.

Theoretical models also suggest that such super-massive stars would have ended their lives in something called a pair-instabiliuty supernova, which is different from the supernova which signals the end of the high mass stars we see around us today. In a pair-instabiliuty supernova, the models suggest that no neutron star or black hole is left at the centre, instead all of the material in the exploding star is sent back into the interstellar medium.

Researchers using the Japanese Subaru telescope in Hawaii have been taking spectra of stars in our Galaxy which show a particularly low level of iron, a level which is about 1,000 times less than in our Sun. Such a low iron level suggests that the stars belong to an earlier generation than our Sun, which is believed to be a third-generation star. The stars they have been observing are not first generation stars, but probably second generation. They have found one star, named SDSS J0018-0939 (it was found to be low in iron by the Sloan Digital Sky Survey) to have a very unusual spectrum. The ratio of the abundance of various elements in the star’s spectrum suggests that it could have been formed from a pair-instabiliuty supernova, and thus be the direct descendent of a first generation star.

The original paper, entitled “A chemical signature of first-generation very massive stars” can be found here.