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## Serena Slam stutters at first hurdle

Yesterday (Saturday 30 January), Serena Williams played in her seventh Australian Open final. She had not only won all six of her previous final appearances, but she had the opportunity to win more Australian Open titles than anyone in history. Having failed to win the US Open last year, and hence just miss out on the Grand Slam, Serena had looked very impressive in her previous rounds. But, she was denied her 22nd Major title (which would have equalled Steffi Graf’s record) by a relatively unknown German by the name of Angelique Kerber.

Serena Williams failed to win her first Major of 2016 and her 22nd of her career, to equal Steffi Graf’s record

It could not have started worse for Kerber, she lost the first seven points in the opening two games, but quickly turned things around and went on to win the first set 6-4. Serena won the second set 6-3, and in a tight third set it went all the way to a tense tenth game, which Kerber won to win the match and the championship.

With this year being an Olympic year, people were even talking of Serena winning a Grand Slam plus the Olympics, a “super Slam” maybe? But, with the Australian Open now lost, Serena clearly cannot now do that. However, it was nice to see her smiling in defeat. I suspect that the pressure she put on herself last year as the possibility of a Grand Slam progressed has now been replaced with a feeling of “if I stay fit, I will surpass Steffi, so why sweat it?”. Which is my feeling. She looks as fit as ever at 34, and if she does not injure herself there is no reason why she cannot play this year, next year and, who knows, maybe even into 2018. Surely, with 4 Majors every year, it is just a matter of time before she wins her 22nd, 23rd, 24th and…… who knows?

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## The 100 greatest songwriters – number 16 – Leonard Cohen

At number 16 in Rolling Stone Magazine’s list of the 100 greatest songwriters is Leonard Cohen. Cohen was born in Montreal, Canada, in 1934. He was raised in a middle-class religious Jewish family; his maternal grandfather was a Rabi, his father Nathan Cohen died when Cohen was 9 years old.

The part of Montreal in which he grew up was an English speaking part of this predominantly French-speaking city, and so one can say that Cohen grew up as a minority within a minority; an English-speaking Jewish boy in a predominantly French-speaking Catholic city. I have always held that this perception of himself as an “outsider” has influenced much of Cohen’s work.

Before becoming a songwriter, Cohen was a published poet. His first album of songs was Songs of Leonard Cohen, which was released in 1967. By this time, he had already published four books of poems; this poetic style is clearly visible in many of his song lyrics. I am a huge fan of Cohen, personally I would place him in my top five of the greatest songwriters. In terms of his lyrics, he is, in my opinion, up there with the likes of Bob Dylan and Paul Simon. Like Dylan and Simon, he has elevated “pop songs” to sheer poetry.

At number 16 in Rolling Stone Magazine’s list of the 100 greatest songwriters of all time is Leonard Cohen.

There are so many Cohen songs that I could have shared in this blogpost. I have already posted several Cohen songs, “Famous Blue Raincoat” here, “So Long Marianne” here and “The Partisan” here. The song I have decided to share today is possibly less well known; it is “The Guests”, a song which appears as the opening track on his 1979 album Recent Songs. This song illustrates many aspects typical of Cohen’s songs, including the evocative and complex lyrics, as well as another hallmark of Cohen’s songs which is his deep voice being accompanied by female voices, something I find quite enchanting.

One by one, the guests arrive
The guests are coming through
The open-hearted many
The broken-hearted few

And no one knows where the night is going
And no one knows why the wine is flowing
Oh love I need you
I need you
I need you
I need you
Oh I need you now

And those who dance, begin to dance
Those who weep begin
And “Welcome, welcome” cries a voice
“Let all my guests come in.”

And no one knows where the night is going
And no one knows why the wine is flowing
Oh love I need you
I need you
I need you
I need you
Oh I need you now

And all go stumbling through that house
in lonely secrecy
Saying “Do reveal yourself”
or “Why has thou forsaken me?”

And no one knows where the night is going
And no one knows why the wine is flowing
Oh love I need you
I need you
I need you
I need you
Oh I need you now

All at once the torches flare
The inner door flies open
One by one they enter there
In every style of passion

And no one knows where the night is going
And no one knows why the wine is flowing
Oh love I need you
I need you
I need you
I need you
Oh I need you now

And here they take their sweet repast
While house and grounds dissolve
And one by one the guests are cast
Beyond the garden wall

And no one knows where the night is going
And no one knows why the wine is flowing
Oh love I need you
I need you
I need you
I need you
Oh I need you now

Those who dance, begin to dance
Those who weep begin
Those who earnestly are lost
Are lost and lost again

And no one knows where the night is going
And no one knows why the wine is flowing
Oh love I need you
I need you
I need you
I need you
Oh I need you now

One by the guests arrive
The guests are coming through
The broken-hearted many
The open-hearted few

And no one knows where the night is going
And no one knows why the wine is flowing
Oh love I need you
I need you
I need you
I need you
Oh I need you now

Here is a video of this mesmerising song. Enjoy!

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## Is Tim Peake getting younger or older?

As anyone who hasn’t been living under a rock knows, the International Space Station (ISS) orbits the Earth with (typically? always?) six astronauts on board. It has been doing this for something like the last fifteen years. One of the astronauts currently on board is the Disunited Kingdom’s first Government-funded astronaut, Tim Peake.

The first British person to go into space was Helen Sharman, but she went into space in a privately funded arrangement with the Russian Space Programme in 1991. Other British-born astronauts have gone into space through having become naturalised Americans, and going into space with NASA. But, Tim Peake has gone to the ISS as part of ESA’s space programme, and his place is due to Britain’s contribution to ESA’s astronaut programme. So, he is the first UK Government-funded astronaut, which is why there has been so much fuss about it in these lands.

Official NASA portrait of British astronaut Timothy Peake. Photo Date: August 28, 2013.

Anyway, I digress. This blog is not about Tim Peake per se, or about the ISS really. I wanted this blog to be about whether Tim Peake is getting older or younger whilst in orbit. Of course everyone is getting older, including Tim Peake, as ‘time waits for no man’ as the saying goes. What I really mean is whether time is passing more or less quickly for Tim Peake (and the other astronauts) in the ISS compared to those of us on Earth.

As some of you might now, when an astronaut is in orbit he is in a weaker gravitational field, as the Earth’s gravitational field drops off with distance (actually as the square of the distance) from the centre of the Earth. Time will therefore pass more quickly for Tim Peake than for someone on the Earth’s surface due to this effect. This is time dilation due to gravity, a general relativity (GR) effect.

But, there is also another time dilation, the time dilation due to one’s motion relative to another observer, the time dilation in special relativity (SR). Because Tim Peake is in orbit, and hence moving relative to someone on the surface of the Earth, this means that time will appear to move more slowly for him as observed by someone on Earth. Interestingly (at least for me!), the SR effect works in the opposite sense to the GR effect.

Which effect is greater? And, how big is the effect?

## Time dilation due to SR – slowing it down for Tim Peake

As I showed in this blog, the time dilation due to SR can be calculated using the equation

$t^{\prime} = \gamma t \text{ where } \gamma = \frac{ 1 }{ \sqrt{ ( 1 -v^{2}/c^{2} )} }$

If he is in orbit at an altitude of 500km (I guessed at this amount, according to Wikipedia it is 400km, but it does not alter the argument which ensues) then his distance from the centre of the Earth (assuming a spherical Earth) is $6.371 \times 10^{6} + 500 = 6.3715 \times 10^{6}$ metres. The centripetal force keeping him in orbit is provided by the force of gravity, and in this blog I showed that the centripetal force $F_{c}$ is given by

$F_{c} = \frac{mv^{2} }{r}$

where $m$ is the mass of the object in orbit, $v$ is its velocity and $r$ is the radius of its orbit.This centripetal force is being provided by gravity, which we know is

$F_{g} = \frac{ GMm }{ r^{2} }$

where $G$ is the universal gravitational constant, and $M$ is the mass of the Earth. Putting these two equal to each other

$\frac{ mv^{2} }{ r } = \frac{ GMm }{ r^{2} } \rightarrow v^{2} = \frac{GM}{r}$

Putting in the values we have for the ISS, where $r=6.3715 \times 10^{6}, G=6.67 \times 10^{-11}$ and $M= 5.97237 \times 10^{24}$, we find that

$v^{2} = 6.2522 \times 10^{7} \rightarrow v = 7.907(067129) \times 10^{3} \text { m/s} = \boxed{ 7.907(067129) \text{ km/s} }$

But, this is the motion relative to the centre of the Earth. People on the surface of the Earth are also moving about the centre, as the Earth is spinning on its axis. But, we cannot calculate this speed as we have done above; people on the surface are not in orbit, but on the Earth’s surface. For something to stay e.g. 1 metre above the Earth’s surface in orbit it would have to move considerably quicker than the rotation rate of the Earth.

The Earth turns once every 24 hours, so for someone on the equator they are moving at

$v_{se} = \frac{ 2 \pi \times 6.3715 \times 10^{6} }{ 24 \times 3600 } = 463.348(5554) \text { m/s}$

where $v_{se}$ refers to the speed of someone on the surface of the Earth. Someone at other latitudes is moving less quickly, at the poles they are not moving at all relative to the centre of the Earth. The speed of someone on the surface will go as $v_{se} \cos (\theta)$ where $\theta$ is the latitude. This is why we launch satellites as close to the Earth’s equator as is feasible; we maximise $v_{se}$ and thus get the benefit of the speed of rotation of the Earth at the launch site to boost the rocket’s speed in an easterly direction.

The difference in speeds between the ISS and someone at the equator on the surface of Earth is therefore

$7.907(067129) \times 10^{3} - 463.348(5554) = \boxed { 7.443(718574) \times 10^{3} \text { m/s} }$

Referring back to my blog on time dilation in special relativity that I mentioned at the start of this section, this means that the time dilation factor $\gamma$, using this value of $v$, is

$\gamma = \frac{ 1 }{ \sqrt{(1 - (v/c)^{2})} } = \frac{ 1 }{ 0.9999999997 }$
(where $c$ is, of course, the speed of light).
This value of $\gamma$ is equal to unity to 3 parts in $10^{10}$, so it would require Tim Peake to orbit for about $3 \times 10^{9}$ seconds for the time dilation factor to amount to 1 second. $3 \times 10^{9}$ seconds is just over 96 years, let us say 100 years.

## The time dilation due to GR – speeding it up for Tim Peake

For GR, the time dilation works in the other sense, it will run more slowly for those of us on the Earth’s surface; we experience gravitational time dilation which is greater than that experienced by Tim Peake. In this blog here, I derived from the principle of equivalence the time dilation due to GR, and found

$\Delta T_{B} = \Delta T_{A} \left( 1 - \frac{ gh }{ c^{2} } \right)$

where, in this case, $\Delta T_{B}$ would be the rate of time passing on the Earth’s surface, $\Delta T_{A}$ the rate of time passing on the ISS,  $g = 9.81$ (the acceleration due to gravity at the Earth’s surface) and $h$ is the height of the orbit, which we have assumed (see above) to be 500 km = $500 \times 10^{3}$.

Plugging in these values we get that

$\frac{ \Delta T_{B} }{ \Delta T_{A} } = 1 - 5.45 \times 10^{-11}$

So, the GR effect is about one part in $10^{11}$ (100 billion). In six months, the number of seconds that Tim Peake will be in orbit is about $1.6 \times 10^{7}$ seconds, so a factor of about 10,000 less than for the GR effect to amount to 1 second. Tim Peake would need to be in orbit for about 5,000 years for the GR effect to amount to 1 second of difference!

## Conclusions

In conclusion, the SR effect on how quickly time is passing for Tim Peake is about 3 parts in 10 billion, in the sense that it passes more slowly for Tim Peake. The GR effect is even smaller, about one part in 100 billion, but in the sense that time is passing more quickly for him. The SR ‘time slowing down’ effect is greater than the GR time ‘passing more quickly effect’, by roughly a factor of 300.

Tim Peake is therefore actually ageing more slowly by being in orbit than if he were on Earth. But, he would need to orbit for nearly 100 years for this difference to amount to just 1 second! And, none of this of course takes into account the detrimental biological effects of being in orbit, which are probably not good to anyone’s longevity!

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## The 100 best Beatles songs – number 31 – You’ve Got to Hide Your Love Away’

At number 31 in Rolling Stone Magazine’s list of the 100 greatest Beatles songs is “You’ve Got to Hide Your Love Away”. This John Lennon-composed song was recorded in February of 1965 and released in August of the same year as the third track on their album Help. It is one of my favourite Beatles songs from this period, with wonderful lyrics and melody; it is just perfect.

Ostensibly “You’ve Got to Hide Your Love Away” is a song aimed at a (presumably fictitious) girl who has left the singer; leaving him devastated. But, it is often thought that the song was, in fact, aimed at the Beatles manager Brian Epstein, who was gay at a time when it was illegal in England to be homosexual. Lennon and the other Beatles knew of Epstein’s homosexuality, and knew that he had to hide it or else he could be arrested and imprisoned.

At number 31 in Rolling Stone Magazine’s list of the 100 greatest Beatles songs is “You’ve Got to Hide Your Love Away”.

The song was written when Lennon was in his “Dylan period” (as he later called it). If you look at photographs of him at this time, he was often seen wearing a felt cap just like the one Dylan wears on the cover of his 1962 debut album Bob Dylan.

Here I stand head in hand
Turn my face to the wall
If she’s gone I can’t go on
Feeling two-foot small

Everywhere people stare
Each and every day
I can see them laugh at me
And I hear them say

Hey you’ve got to hide your love away
Hey you’ve got to hide your love away

How can I even try
I can never win
Hearing them, seeing them
In the state I’m in

How could she say to me
Love will find a way
Gather round all you clowns
Let me hear you say

Hey you’ve got to hide your love away
Hey you’ve got to hide your love away

Unfortunately, presumably for copyright reasons, I cannot find a video of “You’ve Got to Hide Your Love Away” on Youtube. However, I  have found it on DailyMotion, but I am not sure how long the link will work. This is the song as it appears in the movie Help!

Enjoy!

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## The 100 greatest songwriters – number 17 – Neil Young

At number 17 in Rolling Stone Magazine’s list of the 100 greatest songwriters is Neil Young. Young was born in 1945 in Toronto, Canada. I first came across him on the 1970 album Déjà Vu as one of Crosby, Stills, Nash and Young. This was before I knew that he had previously been in Buffalo Springfield with Stephen Stills, or that Crosby, Stills and Nash had released an album before being briefly joined by Young.

I have blogged about Buffalo Springfield’s 1967 song “For What It’s Worth” here, and there are several songs on Déjà Vu which I like a great deal, but my favourite Neil Young work are his two solo albums After the Gold Rush and Harvest. I adore these two albums, I think both are masterpieces.

At number 17 in Rolling Stone Magazine’s list of the 100 greatest songwriters of all time is Neil Young.

The song I have decided to share in this blogpost is “Heart of Gold”, which is one of my favourite Neil Young songs. It is from his 1972 album Harvest.

I want to live,
I want to give
I’ve been a miner for a heart of gold.
It’s these expressions
I never give
That keep me searching for a heart of gold.And I’m getting old.
Keep me searching for a heart of gold
And I’m getting old.I’ve been to Hollywood
I’ve been to Redwood
I crossed the ocean for a heart of gold.
I’ve been in my mind,
It’s such a fine line
That keeps me searching for a heart of gold.

And I’m getting old.
Keeps me searching for a heart of gold
And I’m getting old.

Keep me searching for a heart of gold.
You keep me searching and I’m growing old.
Keep me searching for a heart of gold
I’ve been a miner for a heart of gold.

Here is a video of this wonderful song. Enjoy!

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## Have we found a new planet in the Solar System?

Yesterday (Thursday 21 January) I was on BBC Radio talking about the possibility of their being a 9th planet in the Solar System (remember, in 2006 Pluto was demoted to being a minor-planet, leaving us with 8). If this suggestion is true, this would lead to our once again having to revise the list of planets that many of us know knew by heart. It would not be the first time we have had to revise it, nor I suspect will it be the last.

The team’s argument is based on anomalies in the orbits of Kuiper belt objects. The Kuiper belt is a region beyond the orbit of Pluto which is the reservoir of short-period comets. I have blogged about the Kuiper belt before here. The authors of this new paper argue that some Kuiper belt objects are having their orbits disturbed by an unseen object, and they suggest that it is an object about ten times larger than Earth.

The Caltech team claim that anomalies in the orbits of Kuiper belt objects suggest that there is a large planet disturbing them

It may come as a surprise to some of you that this is precisely the way that Neptune was discovered. After Uranus’ discovery by William Herschel in 1781, astronomers noticed that it was not orbiting exactly as it should. The simplest explanation was that its orbit was being affected by an unseen planet. Two mathematicians (Frenchman Urbain le Verrier and Englishman John Couch Adams) separately worked out where the disturbing object should be.  There was a race on for astronomers to find the object, and the race was won by astronomer Johann Galle in 1846 working at the Berlin Observatory.

The existence of this new 9th planet is a long way from being proven. The anomalies in the orbits of the Kuiper belt objects is an example of something called a ‘many-body problem’. The gravitational influence of many objects, including the Sun, Jupiter, the other gas giants, as well as other Kuiper belt objects, all have to be calculated to see if there are any unaccounted for effects. This is a horrendously complicated problem, and I am sure this prediction by this team from Caltech will be challenged by others working in this area of research.

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## Ospreys win to top the table

On Saturday (16 January) the Ospreys fought back from a half-time deficit to win against Clermont Auvergne and go top of their group in the European Champions Cup (the replacement to the Heineken Cup). In the revamped European club competition, only two Welsh regions are competing this season, and the Scarlets are languishing at the  bottom of their group.

The second half saw the Ospreys shut out Clermont Auvergne, scoring 15 unanswered points. They had gone into half time 13-6 down, but in a remarkable second half turnaround they managed to stop Clermont Auvergne in their tracks and score 15 points to make them comfortable winners.

What is even more remarkable is that those 15 unanswered points did not come from Dan Biggar, who has grown in the last 2 seasons to become one of the most accomplished outside halves in world rugby. Rather, after he hobbled off with a dead leg, the points were made by replacement Sam Davies.

In the European Champions Cup, the Ospreys fought back from a 6-13 half-time deficit to win 21-13

There now remains one game in the group stages, on the 24th of January the Ospreys will take on Exeter away. If they win that game they will qualify for the knockout stages of the European rugby competition for the first time in 6 seasons. With the 6 Nations on the horizon, this will be a welcome boost to the confidence of the numerous players who are also in the Wales national squad.

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