Archive for October, 2012

A few weeks ago I showed a photograph an an Analemma. As the Analemma in the photograph was vertical, I explained that it must have been taken at midday. Here is the photograph again, just to remind you.

A Solar analemma. Because it is vertical, this analemma was taken at midday.

In part 1 of my series on the Analemma, I also explained how the North-South motion of the Sun in the photograph was due to the changing elevation of the Sun at midday. This is, of course, due to the tilt of the Earth’s axis, as explained in this video below.

But, what about the East-West (left-right) motion? What is this due to?

It turns out that the East-West motion is due to two effects. One is the same inclination of the Earth’s axis in its orbit around the Sun which produces the North-South variation in the Sun’s elevation at different times of the year. I will explain how this affects the East-West position of the Sun at midday in part 3 of this blog.

But, the second effect is unrelated to this, it has to do with the details of the Earth’s path around the Sun.

The Heliocentric Universe

When Copernicus suggesed in 1547 that the Earth and the other planets went around the Sun, he argued that they would do so in perfect circles. He was, in fact, not the first to suggest that the Sun and not the Earth was at the centre of things. Aristarchus had suggested the same thing in the 3rd Century B.C., but his work had been largely ignored in preference to the teachings of Plato and Aristotle, who firmly held that the Earth was the natural centre of all things.

Building on Aristotle’s Geocentric Universe model, the Greek-Roman astronomer Ptolemy developed a sophisticated model of the Sun, Moon, planets and stars orbiting the Earth. This model was incredibly successful, and able to predict the positions of the celestial objects to a good degree of accuracy for some 1500 years.

In Copernicus’ 16th Century model, the planets orbited the Sun in circles. In the latter part of the 16th Century, the greatest observational astronomer was a Danish man, Tycho Brahe. Brahe had his own Observatory and research institute, Uraniborg, on the Danish (now Swedish) island of Hven, with a Royal patronage to fund his observing programme.

Tycho Brahe (1546-1601)

Brahe produced the most accurate observations of the planetary positions, and he found he got better agreement with Ptolemy’s geocentric model than he did with Copernicus’ heliocentric one. Towards the end of his career, a young mathematician by the name of Johannes Kepler came to work with him.

A very particular kind of curve

After Brahe’s death, Kepler set about seeing whether he could get a heliocentric model to agree with the observations. After over a decade of trial and error, he eventually found that, if he allowed the planets to move in ellipses rather than perfect circles, that very good agreement could be obtained. As Richard Feynman once said, “an ellipse is a very particular kind of curve”. To be more precise, it is the curve obtained when one passes a string about two drawing pins (“thumb tacks” as Americans call them) and draws the ensuing locus of points.

How to draw an ellipse

Kepler’s 2nd law states that a planet will “sweep out equal areas in equal times” in its orbit. What this means is that it will speed up when near the Sun (perihelion) and slow down when further from the Sun (aphelion).

Part of the East-West motion of the Sun in the Analemma is due to Kepler’s 2nd law, the fact that the Earth changes its speed of orbit as it goes around the Sun. The Earth moves quicker when it is closer to the Sun (perihelion), and slower when it is further from the Sun (aphelion). Kepler did not know why this happens, but it is a natural consequence of Newton’s law of gravity.

A mean Solar day

How do we measure the length of the day? It seems like a simple question. Surely, the answer is that it is the time it takes for the Earth to turn once on its axis. This is, in fact, the wrong answer. The time it takes for the Earth turn once on its axis is the sidereal day, and this is not how we measure our day. Why? The diagram below explains it.

The Earth has to turn a little bit extra for the Sun to cross the local meridian. We call this the Solar day. The sidereal day is the time for the Earth to rotate 360 degrees.

Because the Earth moves about the Sun in its orbit, the Earth has to rotate a little bit extra for the Sun to cross the local meridian on two successive occasions. This is how we define 24 hours, the solar day. But, there is an additional complication; because the Earth’s speed of orbit changes, the extra angle the Earth needs to turn to bring the Sun back over the meridian also changes. As the Earth approaches perihelion (closer to the Sun), it speeds up and so moves through a larger angle each 24 hours than when it is further from the Sun.

Of course, we cannot keep changing the length of the day, we fix it at 24 hours, which is what we call the mean solar day. This is the midday our watches will show. But, near perihelion, the Earth has to turn that little bit extra as I’ve explained, so when our watches say it is midday the Sun will still be to the East of the local meridian. So, if we were taking a photograph of where the Sun was at midday as shown by our watches, the Sun would have shifted eastwards of the mid-point.

The opposite effect happens near aphelion, when the Earth is moving more slowly in its orbit. This time, the Earth moves slightly less in 24 hours than it does in other parts of its orbit, and so the Earth does not have to turn through such a large angle to bring the Sun back over the local meridian. When our watch says midday, the Sun will have gone past the local meridian, and be to the West of it.

Hopefully, this now explains why there should be some East-West motion in the Solar Analemma. However, it turns out that there is a second effect which also causes an East-West motion, the tilt of the Earth’s axis in its orbit. I will explain this component and how it affects things in part 3 of this series.

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Towards the end of October last year, I blogged about the death of Sir Jimmy Savile, TV celebrity and disc jokey. He was someone who seemed to be universally loved and admired. In his life, he had raised over £40 million pounds for charity, and it is for this work that he received his knighthood. He was friends to Royalty, to the Prime Ministers over the last several decades. He moved in very high circle.

Fast forward a year. In a documentary aired on ITV in early October, it was alleged that Jimmy Savile had a darker side to his nature. It was alleged that he had molested a number of women and girls, many of them under the age of sexual consent (16). Since that documentary has aired, the number of fresh allegations coming to light has been hard to keep up with.

Disabled children, including boys, have come forward in adulthood to allege that they too were molested by Jimmy Savile many years ago, but they had never said anything. Or, more disturbingly, they had said something, but their complaints were not believed because Jimmy Savile was held by all to be such a good man.

Jimmy Savile has been labelled a “serial sex abuser of teenage girls” by the Police

The Police have been pursuing over 300 lines of enquiry, and have even gone so far as to state that “Jimmy Savile was was a serial sex abuser of teenage girls“.
Although the number of people who claim to have been abused by Savile in one way or another leaves one in little doubt that there must be truth to the allegations, they are still under investigation by the Police. In addition, two independent investigations initiated by the BBC will look into how his molestations at the BBC never came to light earlier, given that there were apparently numerous rumours of them.

As I am no legal expert, I will refrain from saying too much until more is officially known, in case I get into some legal trouble.

So, instead, I thought I would talk about something about which I know next to nothing, psychology. Talking about things about which I know next to nothing is not new to me, in fact some would say I make a habit of it.

Quite early on in this unfolding drama, it occurred to me that maybe Savile’s commitment to fundraising for charity was done as a means of balancing the wrong he felt he was doing in molesting young girls (and some boys). Maybe I think this because I cannot imagine someone doing that and not feeling they were doing wrong. But, maybe I am deluding myself; maybe for some people who commit such horrendous acts, they feel no guilt as they see nothing wrong in what they are doing.

I wonder how much research has been done on the psychological make-up of people like Savile, who clearly do a lot of good in their lives (raising over £40 million pounds for charity is admirable), but who have a much darker side. Was Savile a slave to his darker side, something he found he was not able to control? Did his charity work come about in a desire to make him feel better about himself as he felt ashamed of his compulsion to molest young girls?

This, to me, is fascinating.

**Breaking News**

An hour or so after posting this blog, it was reported on the news that the 1970s pop star Gary Glitter had been arrested for questioning by the Police on suspicion of sex offences as part of the ongoing investigations into Jimmy Savile. Gary Glitter has a history of sex offences, having being found guilty of having thousands of images of child pornography on his computer in 1999, and in 2006 he was imprisoned in Vietnam for having sex with under-age girls.

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I thought it about time I posted another song by Meic Stevens. I have, so far, only posted one of his songs, Tryweryn, in this blog here.

Meic Stevens, often referred to as “the Welsh Bob Dylan”

Whereas Trywyen is a protest song, Môr o gariad is a love song. The title means “Sea of Love”. It is a very tender song. Here is a YouTube video of Meic Stevens singing the song.

Eistedd yma’n unig
‘ Ben fy hun
Heno ‘sdim amynedd
I helbul byd.
Ond mae’r nos yn ffoi,
Fel mae’r byd yn troi.
Fel y môr o gariad.
A roddais iti.

‘Sdim byd yma heno
Ond adlais cariad mawr.
Ac i’m gwydrau gweigion
Ar y llawr.
Ac i gwpla’r llun
Yn y botel, gwaddod gwin
Gwaddod y môr o gariad
A roddais iti.

O, hwn oedd cariad glân
Hwn oedd cariad ffôl
O roeddwn i ar dân
Ie, ‘sdim ar ôl.

Strydoedd oer y ddinas
Strydoedd mor llawn.
Atgofion fydd amdani
Ei serch a’i dawn.

Serch hynny mae’n rhaid byw
Ymuno efo hwyl y criw
Sych yw’r môr o gariad
A roddais iti.
Ie, sych yw’r môr o gariad
A roddais iti.

As usual with my translations, I will go for a literal translation, without trying to retain rhythm or rhyme. My rather poor attempt to translate these beautiful lyrics are

Sitting here, lonely
All on my own
This evening I have no patience
For the turmoils of the World.
But the night is escaping
As the World turns.
Like the sea of love
That I gave to you.

There is nothing here this evening
But the echo of a great love.
And my empty drink glasses
On the floor.
And to finish the picture
In the bottle, dregs of wine.
The sea was the dregs of love
That I gave to you.

Oh, this was a great love.
This was a stupid love.
Oh, I was on fire.
Yes, there is nothing left.

The cold streets of the city
Streets that are so busy.
It will be memories of her,
Her lust and her skill.

Despite this, one must live
Join in with the fun of the group
The sea is dry of love
That I gave to you.
Yes, the sea is dry of love
That I gave to you.

I needed a little help with the translation from Gwen Rice, of Cardiff University‘s Welsh Language Services. Meic Stevens does not have the most correct grammar, and often does not mutate properly. Also, sometimes his enunciation is not the clearest.So, many thanks Gwen for helping me out.


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With November approaching, it is almost time for the annual tradition of the Wales rugby team playing 4 autumn test matches. This year, Wales have the following fixtures:

Wales’ autumn tests, 2012
Date Country Record (Played/Win/Loss/Draw)
Saturday 10th November Argentina 13/7/5/1
Friday 16th November Samoa 7/4/3/0
Saturday 24th November New Zealand 27/3/24/0
Saturday st December Australia 29/10/18/1

Of course, Wales are reigning Grand Slam champions, and have been playing some superb rugby since August 2011. They were very unlucky not to get to the 2011 rugby World Cup final, narrowly losing to France 8-7 in the semi-final after having their captain Sam Warburton sent off early in the match.

Wales winning the 2012 Grand Slam.

Realistically, I think anything less than a 3-1 win ratio in the 2012 Autumn series will be disappointing. We have to beat Argentina and Samoa, but also we need to win one of the two last games, either against New Zealand or Australia. Of these two, I think we are more likely to beat Australia. This prediction is partly based on coming so close to beating them in 2 of the 3 test matches Wales played in Australia this last June, but also because we have not beaten the All Blacks since 1953!!

In all, Wales have played the All Blacks on 27 occasions. Amazingly, when Wales last beat NZ, in 1953, it was only the 4th test match between the two countries, and in winning that test Wales were 3-1 up in the series, with wins in 1905, 1935 and 1953 and only one loss in 1924. Since then, it has been all one-way traffic, with Wales losing 23 matches in succession!

We have come close to beating them on a couple of occassions. One of those is the match in 1978, when the dominant Welsh teacm of the 1970s should have beaten them, and would ahve beaten them if it had not been for some cheating by NZ. With just minutes on the clock, the score was 12-10 to Wales. NZ secured a line out about 30 metres from the Welsh tryline. In the ensuing line out, the NZ second-row forward Andy Haden came flying out of the line and onto the ground. The referee, without hesitation, awarded NZ with a penalty. Except TV footage showed that no-one had pushed Haden, he had dived out of his own accord to cheat get just that decision from the referee. Haden himself finally admitted that it was a professional dive in an interview. NZ converted the penatly, and won the game 12-13.

From an article in The Independent, about Andy Haden of New Zealand confessing to his deliberate dive in the 1978 match against Wales.

What are your predictions for this Autumn series?

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Last week it was announced that John Terry would start serving his 4 match ban, imposed on him by the Football Association for racially abusing Anton Ferdinand in October of last year. Chelsea Football Club announced that they would not be imposing a further ban on Terry, but claimed they had given him a “very very heavy fine“. I’m sorry, for a player who purportedly earns £140,000 a week, any fine is hardly going to affect his bank balance in any meaningful way, in my opinion.

To make Chelsea’s lack of punishment even worse, they have announced that Terry will retain the captaincy of the club during his 4 match ban! I am appalled by how Terry has, apparently, got away with very little punishment for saying something which would get ordinary people summarily dismissed from their jobs with no compensation. To call a colleague or client a “f***ing black c**t” would lead to our being marched out of the door so quickly our feet would not touch the ground. But, appallingly, John Terry has got away with it.

The incident when John Terry racially abused Anton Ferdinand in October of 2011.

As readers of this blog (all 2 of you!) will know, I have been a fan of Chelsea since 1970. I have blogged about my surprise at Terry’s acquittal of criminal charges here, and about the FA’s lenient punishment here.

I am ashamed to call myself a Chelsea supporter in light of this. If I had a season ticket, or went to their games, I would refuse to go. Although I am no fan of players being abused by opposing fans when they play matches away from home, for John Terry I will make an exception. I hope he gets all the abuse he deserves. The man is a disgrace. And, so are Chelsea Football Club for not dismissing him with no compensation, as they would be perfectly entitled to do.

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As the nights are now getting longer (for those of us in the Northern Hemisphere) and the clocks are about to go back making sunset earlier, I thought it was about time I blogged about the planets which will be visible this winter. Of the 5 naked eye planets, Mercury, Venus, Mars, Jupiter and Saturn, 4 of them are visible this winter. These are Mercury, Venus, Jupiter and Saturn. Mars, unfortunately, will not be visible at all this winter.

Here is a table showing the rise, transit and setting times of the Sun and the 5 naked eye planets (the transit time is the time at which the object crosses the local meridian, an imaginary line going from due North to due South across the sky).

The Planets in mid-October
Planet Rise Time Transit Time Set Time Constellation
The Sun 07:44 12:58 18:11 Virgo
Mercury 10:11 14:24 18:40 Libra
Venus 04:09 10:41 17:12 Leo
Mars 11:50 15:47 19:44 Ophiuchus
Jupiter 20:12 04:20 12:25 Taurus
Saturn 08:08 13:20 18:33 Virgo

The Planets in mid-January
Planet Rise Time Transit Time Set Time Constellation
The Sun 08:12 12:22 16:34 Sagittarius
Mercury 08:22 12:16 16:11 Sagittarius
Venus 07:12 11:07 15:02 Sagittarius
Mars 09:15 13:48 18:22 Capricorn
Jupiter 12:54 20:51 04:52 Taurus
Saturn 02:11 07:09 12:06 Libra

The Planets in mid-March
Planet Rise Time Transit Time Set Time Constellation
The Sun 06:27 12:22 18:18 Pisces
Mercury 05:45 11:08 16:31 Aquarius
Venus 06:32 12:12 17:53 Aquarius
Mars 06:46 12:50 18:56 Pisces
Jupiter 09:09 17:10 01:15 Taurus
Saturn 22:17 03:19 08:17 Libra


Mercury, the closest planet to the Sun, is the most difficult to see. Because it is close to the Sun it can never be seen in the middle of the night, it is only visible near sunset or sunrise. Over the next 5 months there are two opportunities to see Mercury, the first one being in early December. As the figure below shows, Mercury will be visible in the morning sky before Sunrise in December, with early December being the best time to see it, as its elevation above the eastern horizon will be greatest, about 10 degrees. The Earth turns 15 degrees each hour, so 10 degrees represents about 40 minutes before the Sun rises.

This figure shows the position of the planet Mercury in the morning sky between mid-November and the end of December. The y-axis is the elevation above the horizon, the x-axis is azimuth, where due East is 90 degrees, and due South is 180 degrees. The azimuth angles in this figure show the planet will be visible in the South-East. As this figure shows, Mercury’s maximum elevation is in early December, when it is about 10 degrees. This means it will be visible some 40 minutes before Sunrise.

The next opportunity to see Mercury is in mid-February, in the evening sky. As the figure below shows, on 17th/18th of February, Mercury will be about 10 degrees above the horizon in the Western sky after sunset.

This figure shows the visibility of Mercury in the morning sky between the dates of early February and the end of February. The y-axis shows elevation in degrees above the horizon. The x-axis is azimuth. Due West is 270 degrees, and due South is 180 degrees. The azimuth angles in this figure show the planet will be visible in the South-West.


Venus is currently (mid-October) easily visible in the Eastern sky before sunrise. The figure below shows where to find it. You cannot really fail to find Venus when it is visible, it is by far the brightest “star like” object in the sky, outshining any of the stars (and even Jupiter) by a factor of at least two. At the moment, with Venus and Sirius visible in the same part of the sky before sunrise, one can see quite clearly how much brighter Venus is than the brightest star in the sky. Over the next few months it will get lower and lower before Dawn, until by the end of December it will disapppear and will not be visible again this winter.

Where to find Venus in the pre-dawn sky. It is to the East of the constellation Orion and Sirius, the brightest star. Seeing Venus and Sirius at the same time shows clearly how much brighter Venus is than Sirius.

Venus in the morning sky from mid-October to mid-December. Over the next 2 months it will sink lower and lower, and by the end of December will not be observable for the rest of the winter. The y-axis shows elevation above the horizon in degrees. The x-axis shows azimuth, with due East being 90 degrees and due South being 180 degrees. Venus is visible in the South-East sky before sunrise at the moment.


Mars is not visible over the next 5 months. It will next be at opposition in April 2014, so will begin to become visible towards the end of 2013.


Jupiter is currently in the constellation Taurus. It is currently easily visible high in the early morning sky before sunrise. The figure below shows where to expect to see it at 1am in mid-October. It is currently near Aldebaran, but outshines this red giant star by a factor of over 30 (the visual magnitude of Jupiter at the moment is -2.7 and of Aldebaran is +1). It is the brightest object in that part of the sky, with only Venus in the pre-dawn sky outshining it. If you wait until January, Jupiter will be visible in the evening sky rather than after midnight. A small telescope will reveal Jupiter’s 4 Galilean satellites, Io, Europa, Ganymede and Callisto.

An image of Jupiter taken by the Cassini space probe.

A map showing Jupiter in the sky at 1am as seen in mid-October as seen from Cardiff.


Saturn is not currently visible, but will be as we move towards winter. By December it will be visible in the morning sky. It is currently in the constellation Libra, where it will remain for the next 2 years. By mid-January, Saturn will be quite visible in the early hours of the morning, but it will be even higher by mid-March. You might find it easier to wait until the Spring to see Saturn, as by April it will be quite high before midnight.

Saturn, the ringed planet. This image clearly shows the Cassini division in the rings.

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I thought it was about time I posted another Leonard Cohen song. Previously I have blogged about “So Long Marianne” and “The Partisan“. “Famous Blue Raincoat” is another of his early songs, released in 1971 from his 3rd album “Songs Of Love and Hate“.

The cover of Leonard Cohen’s 3rd album, Songs of Love and Hate.

The song is in the form of a letter, and speaks of a love triangle between the singer, a woman named Jane, and an unnamed man. Enjoy!

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