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## The February 2017 annular solar eclipse

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

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.

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!

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.

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%.

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.

## 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.

## November 2013 Solar eclipse in Kenya

Later this year, on the 3rd of November, there will be a Solar eclipse which will pass across the Atlantic ocean, across Africa and end in Somalia. The eclipse is actually termed a hybrid eclipse, because it starts as annular (where the Moon is a little further from the Earth and so does not block out all of the Sun), but changes to a total eclipse during the event, as the distance between the Moon and the Earth gets less. The figure below shows the path of the eclipse.

I am part of a planned expedition to go and see the eclipse in Kenya. The expedition is run by the International Space Schools Education Trust (ISSET – a registered UK charity), and is part of their Astronaut Leadership Experience. I will go as the trip’s astronomy expert, and in addition to Chris Barber of ISSET, who will organise and lead the expedition, there will be two people from NASA, Ken Ham who has commanded Space Shuttle missions, and his wife Michelle who is an astronaut trainer.

The path of the eclipse in Kenya is shown in the figure below, it passes right across Lake Turkana which is in the northern part of Kenya near its borders with Uganda and Ethiopia and South Sudan.

This area is very beautiful and very interesting. It is part of the Great Rift Valley, and on its shores Lucy was found, the oldest humanoid ever discovered. Lake Turkana also boasts a volcanic island, which is shown in one of the slides below. The plan is to fly to Kenya on the 26th of October, and go up to the Lake Turkana region towards the end of the week for the eclipse, which is on the 3rd. Before going to the north, we will go to the Masai Mara National Park, Mount Kenya (which straddles the equator), and explore more areas of the Great Rift Valley.

The trip is open to anyone; to find out the costs and day-by-day itinerary you can visit the website here. The costs include return (round trip) flights to Kenya, and all accommodation, food and transport whilst in Kenya. If it is anything like the week we spent in the Gobi Desert in June for the Transit of Venus, it will be a truly memorable week full of activity, learning, exploration and fun.