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Some of you may be aware that there is an annular eclipse of the Sun on Sunday 26 February, which is why I am posting this blog a few days before it. Annular eclipses occur when the Moon is a little too far away to block the Sun out entirely, so instead we see a ring of light around the Moon, as this picture below shows. This particular picture was taken during the May 20 2012 annular eclipse

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An annular eclipse happens when the Moon is slightly too far away to block out the Sun entirely. This is a picture of the May 20 2012 annular eclipse.

The Moon’s elliptical orbit about the Earth

The diagram below shows an exaggerated cartoon of the Moon’s orbit about the Earth. The Moon’s orbit is an ellipse, it has an eccentricity of 0.0549 (a perfect circle has an eccentricity of 0). The average distance of the Moon from the Earth (actually, the distance between their centres) is 384,400 kilometres. The point at which it is furthest from the Earth is called the apogee, and is at a distance of 405,400 km. The point at which it is closest is called the perigee, and it is at a distance of 362,600 km.

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The Moon orbits the Earth in an ellipse, not a circle. The furthest it is from the Earth in its orbit (the apogee) is at a distance of 405,400 km, the nearest (the perigee) is at a distance of 362,600 km.

The angular size of the Moon

It is pure coincidence that the Moon is the correct angular size to block out the Sun. The Moon is slightly oblate, but has a mean radius of 1,737 km. With its average distance of 384,400, this means that from the Earth’s surface (the Earth’s mean radius is 6,371 km) the Moon has an angular size on the sky of

2 \times \tan^{-1} \left( \frac{ (1.737 \times 10^{6}) }{ (3.84 \times 10^{8} - 6.371 \times 10^{6}) } \right) = 2 \times \tan^{-1} (4.59975 \times 10^{-3} )

= 2 \times 0.2635 = \boxed{ 0.527 ^{\circ} \text{ or } 31.62 \text{ arc minutes} }
So, just over half a degree on the sky. But, this of course will vary depending on its distance. When it is at apogee (furthest away), its angular size will be

\boxed{ \text{ at apogee } 29.93 \text{ arc minutes } }

and when it is at perigee (closest) it will be

\boxed{ \text{ at perigee } 33.53 \text{ arc minutes } }

The angular size of the Sun

The Sun has an equatorial radius of 695,700 km, and its average distance from us is 149.6 million km (the Astronomical Unit – AU). So, at this average distance the Sun has an angular size of

2 \times \tan^{-1} \left( \frac{ (6.957 \times 10^{8}) }{ (1.496 \times 10^{11} - 6.371 \times 10^{6} ) } \right) = 2 \times 0.266 = \boxed {0.533^{\circ} }

Converting this to arc minutes, we get that the angular size of the Sun at its average distance is

\boxed{ 31.97 \text{ arc minutes} }

Compare this to the angular size of the Moon at its average distance, which we found to be 31.62 \text{ arc minutes}.

The angular size of the Sun varies much less than the variation in the angular size of the Moon, at aphelion (when we are furthest) from the Sun, we are at a distance of 152.1 million km, so this gives an angular size of

\boxed{ \text{ at aphelion } 31.44 \text{ arc minutes } }

and, at perielion, when the distance to the Sun is 147.095 million km, the angular size of the Sun is

\boxed{ \text{ at perihelion } 32.52 \text{ arc minutes } }

Annular Eclipses

So, from the calculations above one can see that, if the Moon is at or near perigee, its angular size of 33.53 \text{ arc minutes } is more than enough to block out the Sun. When the Moon is at its average distance, its angular size is 31.62 \text { arc minutes }, which is enough to block out the Sun unless we are near perihelion. But, when the Moon is near apogee, its angular size drops to 29.93 \text{ arc minutes }, and this is not enough to block out the Sun, even if we are at aphelion.

The Earth is currently at perihelion in early January (this year it was on January 4), so the Sun is slightly larger in the sky that it will be in August for the next solar eclipse. This, combined with the Moon being near its apogee, which occurred on February 18, (for a table of the dates of the Moon’s apogees and perigees in 2017 follow this link) means that the solar eclipse on Sunday February 26 is annular, and not total.

The February 26 2017 Annular Eclipse

Here is a map of the path of the eclipse, it is taken from the wonderful NASA Eclipse website. If you follow this link, you can find interactive maps of all the eclipses from -1999 BC to 3000 AD! If you have about 6 years to waste, this is an ideal place to do it!

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The February 26 2017 annular eclipse will start in the southern Pacific ocean, sweep across Chile and Argentina, then across the Atlantic Ocean, before reaching Angola, Zambia and the Democratic Republic of Congo (Congo-Kinshasa)

The eclipse finishes in Africa and, as luck would have it, I am going to be in Namibia on the day of the eclipse. In fact, if you are reading this anytime in the week before the eclipse, I am already there. I am in Namibia for a week as part of Cardiff University’s Phoenix Project, and I will be giving a public lecture at the University of Namibia about the eclipse on Wednesday 22 February. I also hope to give a public lecture to the Namibian Scientific Society on the Friday, and on the Sunday I will be helping University of Namibia astronomers with a public observing session in Windhoek.

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The February 20 2017 annular eclipse will finish in Africa, passing through Angola, Zambia and the Democratic Republic of Congo (Congo Kinshasa)

The interactive map to this eclipse, which you can find by following this link, allows you to click on any place and find out the eclipse details for that location. So, for Windhoek, the eclipse begins at 15:09 UT (which will be 17:09 local time), with the maximum of the partial eclipse being at 16:16 UT (18:16 local time), and the eclipse ending at 17:16 UT (19:16 local time). Because Windhoek is to the south of the path which will experience an annular eclipse, it will be a partial eclipse, with a coverage of 69%.

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As seen from Windhoek, where I will be for the annular eclipse, the obscuration will be 69%.

So, if you are anywhere Chile, Argentina, in western South Africa, in Namibia, in Angola, or the western parts of Congo-Kinshasa and Congo-Brazzaville, look out for this wonderful astronomical event this coming Sunday. And, remember to follow the safety advise when viewing an eclipse; never look directly at the Sun and only look through a viewing device that has correct filtration. Failure to follow these precautions can result in permanently damaging your eyesight.

Today I will continue with my series of blogposts of some Bob Dylan songs, in celebration of his winning the 2016 Nobel prize for literature. I am concentrating on songs which are on  his official Vevo channel, as other songs of his which are uploaded to YouTube are almost always swiftly removed.

The song I am sharing today is “Beyond Here Lies Nothin'”, which appears on his 2009 album Together Through Life. According to his website, he first performed this live in July 2009 and the most recent live performance was earlier this year, in July 2016. As of my writing this, he has performed it 398 times!

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“Beyond Here Lies Nothin'” appears on Dylan’s 2009 album Together Through Life.

 

Here are the lyrics to this song, which you can find here on Dylan’s official website.

I love you pretty baby
You’re the only love I’ve ever known
Just as long as you stay with me
The whole world is my throne
Beyond here lies nothin’
Nothin’ we can call our own

I’m movin’ after midnight
Down boulevards of broken cars
Don’t know what to do without it
Without this love that we call ours
Beyond here lies nothin’
Nothin’ but the moon and stars

Down every street there’s a window
And every window made of glass
We’ll keep on lovin’ pretty baby
For as long as love will last
Beyond here lies nothin’
But the mountains of the past

My ship is in the harbor
And the sails are spread
Listen to me pretty baby
Lay your hand upon my head
Beyond here lies nothin’
Nothin’ done and nothin’ said

Here is the official video of “Beyond Here Lies Nothin'” from Dylan’s Vevo channel. Enjoy!

On Tuesday, I blogged about the theoretical work done in the early 1970s by Martin Rees, and others, which proposed that there may be a supermassive black hole at the centre of our Galaxy and most spiral galaxies.

What about the observational evidence?

In the early 1980s two teams set about observing the orbits of stars near Sgr A*. The two teams, working separately, were at UCLA and The Max Planck Institute For Extra-terrestrial Physics (MPE). The team at UCLA is known as the UCLA Galactic Center Group, the team at the MPE doesn’t have a snazzy name, but their website can be found here. Gradually, over many years, each of the two teams has determined the orbits of several dozens of stars, and hence have been able to use the laws of gravity to determine the mass of the enclosed mass which the stars are orbiting.

Below is an image of Sgr A* taken by the MPE team using the NACO near-infrared camera on the VLT with adaptive optics. The entire image is only 30 arc seconds across.

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A combined H, K and L-band near infrared image of the Galactic Centre obtained by the NACO camera on the VLT using adaptive optics. This image is from the MPE website.

Here is a paper, published in 2009, entitled “Monitoring Stellar Orbits Around the Massive Black Hole in the Galactic Center”, published by the MPE group in The Astrophysical Journal. Here is a link to the paper.

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This paper, published in The Astrophysical Journal in 2009, is one of several showing overwhelming evidence for a supermassive blackhole at the centre of the Milky Way galaxy.

In this paper, entitled “The Galactic Center massive black hole and nuclear star cluster”, Reinhard Genzel (the director of the MPE) and colleagues summarise the evidence from their studies of their being a supermassive blackhole at the centre of the Milky Way, with a calculated mass of about 4.4 million solar masses. Here is a link to the paper.

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In a paper entitled “The Galactic Center massive black hole and nuclear star cluster”, Genzel etal. summarise their finding that the Galaxy harbours a massive black hole with a mass of about 4.4 million solar masses.

The UCLA group published this paper “Measuring Distance and Properties of the Milky Way’s Central Supermassive Black Hole With Stellar Orbits”, in 2008 in The Astrophysical Journal (here is a link to the paper). In it,they calculate the mass of the supermassive black hole to be 4.5 million solar masses, with an error of plus or minus 0.4 million solar masses.

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Ghez etal. (2008) find the  mass of the supermassive black hole to be 4.5 million solar masses, slightly higher than the MPE group, but well within the errors of the two groups’ measurements.

The mass of this black hole is about 4.45 million times the mass of the Sun (the two groups calculate different masses, with the UCLA group calculating about 4.5 million solar masses, the MPE group about 4.4 million solar masses). Let us assume it is 4.5 million solar masses, just to round up to the nearest half a million solar masses.

As some of you may know, blackholes are observable in certain ways. They clearly affect the orbit of nearby objects (this is how the UCLA and MPE teams have garnered the evidence for the supermassive blackhole), but also the accretion disk which usually surrounds a blackhole has very hot gas spiralling into the blackhole. This very hot gas emits radiation as a blackbody, so most of it comes out in the X-ray part of the spectrum due to the very high temperature of several millions of Kelvin.

But, a blackbody will also radiate at other wavelengths (see my blog here to remind yourself of the shape of a blackbody curve), so such accretion disks will also radiate visible light, infrared light, and even radio emission. The question then arises, is it possible to observe the accretion disk way in towards the event horizon of the Galaxy’s supermassive blackhole?

I will answer that question next week.

There is now overwhelming evidence that our Galaxy harbours a supermassive black hole at its centre. Not only that, but the Hubble Space Telescope has discovered that all spiral galaxies harbour supermassive black holes at their centres, and the mass of that black hole is directly proportional to the mass of the galaxy in which it resides. The reasons for this are still unclear.

The idea of supermassive black holes driving the prodigious energy output at the centre of some galaxies was first proposed by Edwin Salpeter in a 1964 paper. Salpeter is probably better known for his work on the initial mass function of star formation, but in this paper (follow this link to read it), Salpeter proposed that supermassive black holes may be the energy source behind the then newly discovered quasars.

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In a 1964 paper, Edwin Salpeter (possibly more famous for his work on the initial mass function of star-formation) was the first to propose supermassive black holes as the energy source of the newly-discovered quasars (or QSOs).

In 1971, Donald Lynden-Bell and Martin Rees wrote an important paper entitled “On quasars, dust and the galactic centre”, (follow this link to the paper). It was the first paper to suggest that our own Galaxy, the Milky Way, may harbour a supermassive black hole at its centre.

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The possibility that our Milky Way harboured a supermassive blackhole at its centre was first proposed by Donald Lynden-Bell and Martin Rees in 1971.

Another important paper entitled “Accretion onto Massive Black Holes” was written in 1973 by Pringle, Rees and Pacholczyk (follow this link), who considered the observable effects that matter accreting onto a (super)massive black hole would have.

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In a 1973 paper, Pringle, Rees and Packolczyk considered the observable effects of the accretion of matter onto a supermassive black hole.

Pringle etal. draw two main conclusions, the second of which is possibly the more important; that material falling onto a (super)massive black hole will emit a huge amount of radiation.

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The two main conclusions of the Pringle etal. (1973) paper.

In a 1974 review article in The Observatory entitled “Black Holes”, Martin Rees further stated the arguments for supermassive black holes at the centres of galaxies.

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In a 1974 review article in The Observatory, Martin Rees wrote that “a black hole might lurk in the centres of most galaxies.”. 35-40 years later, he was shown to be correct.

He stated (my highlight)

If we regard quasars as hyperactive galactic nuclei, then a black hole might lurk in the centres of most normal galaxies.

How prescient were these words!

Later in the same year, radio astronomers Bruce Balick and Robert Brown discovered a compact radio source in the constellation Sagittarius. They announced their result in a paper entitled “Intense Sub-Arcsecond Structure in the Galactic Center” (here is a link to the paper).

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In 1974, Bruce Balick and Robert Brown used the Very Large Array of radio telescopes in New Mexico to discover a compact radio source at the centre of the Milky Way. We now call this source Sagittarius A*

Using the Very Large Array of radio telescopes in New Mexico, Balick and Brown found a sub-arcsecond radio source at both 2695 MHz (11cm) and 8085 MHz (3.7cm). We now call this source Sagittarius A*, and it is believed to be where the Galaxy’s supermassive black hole resides. Here is their image obtained at 2695 MHz (at right, the image at left is the base-line coverage in the u-v plane, the interferometry plane of the array).

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Bruce Balick and Robert Brown discovered a sub-arcsecond radio source in the constellation Sagittarius. We now call this source Sagittarius A*. Their discovery was made at 2695 MHz (which corresponds to a wavelength of 11 centimetres)

Since these discovery observations, Sagittarius A* (or Sgr A* as it is often known) has been observed at many other wavelengths (but not in visible light, the dust extinction is too great). For example, here is a combined infrared and X-ray image.

The supermassive black hole located 26,000 light years from Earth in the center of the Milky Way.

A composite infrared and X-ray image of Sagittarius A*

And, here are some images taken by the SPIRE camera on the Herschel Space Observatory at 250, 350 and 500 microns.

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Images of Sagittarius A* taken by the SPIRE camera on the Herschel Space Telescope. The observations are at (from left to right) 250, 350 and 500 microns.

Later this week I will blog about the observational evidence for this compact object being a supermassive black hole.

The second weekend of the 2017 6 Nations is over, and I think it is fair to say that this year is on course to be one of the most exciting 6 Nations in history. After Ireland running rampant in Italy, England narrowly beat Wales in Cardiff by scoring a converted try in the last 4 minutes, and France narrowly beat Scotland in Paris. It seems that 5 of the 6 nations are pretty evenly matched, so most of the games look like they could be very close.

Italy v Ireland

Ireland went to Rome seeking to make amends for their loss last week to Scotland. They won comfortably by 63 points to 10, running in 9 tries. Italy were woeful, not to take anything away from Ireland, and it has re-opened the debate as to whether Italy deserve to be in the 6 Nations at all. An idea which has been floating around for a while is that there should be relegation from the 6 Nations, with the second tier European countries like Romania and Georgia in a play-off against the bottom placed country in the 6 Nations table to see who should make up the sixth place the following year.

But, one needs to bear in mind that, when France joined the then 4 Nations to make the 5 Nations (back in 1910) they barely won any matches for well over a decade. Their initial record in the 5 Nations was worse that Italy’s current record in the 6 Nations, but they went on to be one of the best teams in the world. So, in my opinion we should give Italy more time to bring their rugby up to speed, not expel them yet.

Wales v England

This was, for most people, the big game of the weekend. Wales and England have been playing each other since 1881, and had played each other a total of 129 times prior to this weekend. With the record at 60 wins to England, 57 to Wales and 12 drawn matches, long-term they could not be more evenly matched.

It was a cracking match; at no point were the two sides more than 5 points apart, and the ferocity and competitiveness on display was something to behold. This was the best Welsh performance since beating England in the world cup in September 2014. And, it is a match that Wales could have won and should have won. At half time we were 13-8 up, and between 50 and 75 minutes we were, in my opinion, by far the better side. England looked rattled, and at 74 minutes the score was 16-14 to Wales.

With England threatening the Welsh try line, Dan Biggar made a superb interception and broke up field. Isolated, he kicked ahead and a desparate English defence kicked it into touch, giving Wales an attacking line-out in the English 22. But, we fluffed it, and this for me was the incident which lost us the match. With only 5 minutes on the clock, we could have won the line-out, and played out the remaining 5 minutes in England’s 22, or even gone for a drop goal.

But, instead, we found ourselves back under pressure near our own try line. The ball came back to centre Jonathan Davies, who kicked up-field. But, rather than kicking into touch, he kicked in-field, something the Welsh team had been doing all afternoon. It was a crazy decision; he should have belted it into the stands and given the Welsh forwards as much time as possible to slow the game down and regain their breath for the line-out. Instead, George Ford caught Davies’ in-field kick, passed it to Owen Farrell who spun a long pass to winger Elliot Daly. Daly outclassed a poor Alex Cuthbert to score in the corner, and Farrell slotted the conversion to rub salt into the wound.

We went from being in control and 16-14 ahead to losing 21-16.

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Wales lost to England 21-16 in Cardiff, with England snatching a try with only 4 minutes left on the clock to break Welsh hearts.

As I say, in my opinion not only were Wales the better team, but it is a match that we lost rather than England winning it. Poor decision making, particularly in the last 5 minutes, cost us what would have been a memorable win over a very good England team. On the plus side, it was the closest this England team under Eddie Jones has been pushed during his 14 months in charge. And, Wales are finally beginning to develop their game beyond the Warren-ball of the last too many years. I hope we can back it up by winning in Scotland in two weeks’ time.

France v Scotland

This was another close fought match, with France sneaking it 22-16. Scotland had their chances, and they are a much improved side. They have so many good back-line players that they look dangerous from anywhere on the field, and it is great to see them so competitive again. They are going to be a tough prospect for Wales in what is our next game.

Round 3 of the 6 Nations

The 6 Nations now takes a slight hiatus; the next round of matches are in a fortnight’s time rather than this coming weekend. On Saturday 25th February, Wales head up to Murrayfield to take on Scotland, with the KO at 14:25. The second match of the day is Ireland at home to France, KO is 16:50. On Sunday 26th, England host Italy at Twickenham, with the KO at 15:00. I will preview these matches closer to the time.

Later today Wales take on England in the 2017 6 Nations. Unfortunately for Wales, this is only our second game of the championships, and I don’t think we are up to speed yet. Yes, we won convincingly in Italy last Sunday, but our first half display showed many of our weaknesses. England, on the other hand, battled to a win against France, and with only 10 minutes to go they looked like they would lose. So, which side will be better prepared for today’s clash?

Wales have two injury worries to deal with. Both Dan Biggar (outside-half) and George North (wing) suffered injuries against Italy. They have been named in the starting 15, but Rob Howley may find that they fail final fitness tests and do not play. Should Dan Biggar not start, then Sam Davies will start in his place. Davies is a more attacking outside-half than Biggar, and personally I think that he gets the backline moving better. But, if Biggar is fit I would prefer to see him start, with Davies coming on at about 60 minutes as the game opens up for the last quarter.

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Both Dan Biggar and George North are doubts for today’s clash with England. They have been named in the starting 15, but both suffered injuries against Italy last Sunday.

The other impact player which Wales will hope to bring on during the last quarter is our outstanding number 8 Taulupe Faletau. He has been injured, so has not played much rugby in the last few months. But, I am sure that he has kept himself fit enough to put in a barn-storming 20 minutes and I’m in no doubt that he will be brought on as impact replacement.

England have only won two of their last seven visits to Cardiff, so their coach Eddie Jones will be doing all he can to tell his players that they should not fear the Millennium Stadium. But, if you have ever been to this cathedral of rugby you will know that it is intimidating. England have opted to leave the roof open, which does reduce the noise in the stadium somewhat. But, with 74,500 supporters, most of them shouting for Wales, do not underestimate how intimidating that will be for England. And, with England unbeaten under Eddie Jones, there is nothing Wales would like more than to be the first country to break this winning streak. Beating England is not the be-all and end-all of Welsh rugby, but it is very sweet when we do beat our larger, noisier neighbour.

The head-to-head between Wales and England is almost tied. They have played each other 129 times. England have won 60, Wales 57, with 12 matches being drawn. Will it be 61 to 57, or 60 to 58 after today? We will know in a few hours……

DERE ‘MLAEN CYMRU!!!! / COME ON WALES!!!!

On Monday (6th February) the sad news was announced that the great South African scrum-half Joost van der Westhuizen (JVD) had died at the age of 45. In 2011 JVD was diagnosed with motor neurone disease. Over the next few years he did much to raise awareness of and money to conduct research into this cruel disease; showing the same fighting spirit which led to his being one of the true greats of rugby of any era.

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Joost van der Westhuizen was one of the greats of world rugby. In 2011 he was diagnosed with motor neurone disease. He died on Monday (6th February) at the age of 45.

 

I heard it said this week that JVD was the first muscular scrum  half and the first large scrum half (a position traditionally played by smaller men). I would disagree with both of these statements. I grew up watching Gareth Edwards, often considered the greatest Welsh rugby player, who was a strong, muscular and dynamic scrum half. The only thing he lacked was height, but in the early 1980s Terry Holmes played for Wales, and he was 1m87, the same height as JVD. So, I would not agree that JVD was the first muscular scrum half or the first scrum half who was as large as a back-row forward.

It is sometimes easy when someone has died far too early to overstate their greatness. But, JVD was a great scrum half, there is no denying that. He was an inspiration to his team, and someone that other teams feared. In the 1995 World Cup, he was the first player to successfully tackle Jona Lomu, who had run rampant through every team against which the All Blacks had played.

But, JVD showed his true greatness in the way with which he dealt with his motor neurone disease (MND). He took it as an another challenge, and spent the rest of his life raising awareness of MND and raising money for researching in to it. In the video below is an excerpt from an interview which JVD did with the BBC in late 2014 or early 2015. It was replayed on Monday evening, the day of his death. Listen to his final words, when he is asked whether his MND may be considered a “blessing”

In a way I am glad I had MND. I now know what life is about

RIP Joost van der Westhuizen.