Moon – The Science Geek

Lunar eclipse 27 July 2018

On 27 July 2018 there will be a total eclipse of the Moon, which will be viewable from many areas of the world. This will be the first total lunar eclipse able to be observed in the UK for nearly three years and it will be worth making the effort to see, especially since, for viewers in Europe, Africa and eastern Asia, it will occur at a sociable hour in the evening.

The Moon during a recent total lunar eclipse – image from NASA

What happens during a lunar eclipse?

A lunar eclipse occurs when the Earth prevents some or all of the Sun’s light from hitting the Moon’s surface. This is shown in the diagram below:

Image from Wikimedia Commons

In this diagram in the region marked Umbra the Earth completely blocks the Sun. In the region marked Penumbra the Earth partially blocks the Sun.

The stages of the July 27 lunar eclipse

The next diagram below shows how, to someone on Earth, the Moon will move through the Earth’s shadow on 27 July. The six points labelled P1, U1, U2, U3, U4 and P4 are known as the eclipse contacts and are the times when the eclipse moves from one stage to the next.

Diagram from NASA

At point P1 the Earth will start to block some of the Sun’s light from reaching the Moon. This will start at 5:15 pm GMT and is the start of the penumbral phase. The Moon’s brightness will dim a little, but this will be quite difficult to notice with the naked eye.

As the Moon continues in its orbit, more and more of the Sun’s light is obscured, until after about an hour some of the Moon will get no direct sunlight. This is known as the partial phase. It will start at point U1 which will occur at 6:24 GMT. The part of the Moon which receives no direct sunlight will appear dark, as shown in the picture below.

The partial phase of a lunar eclipse – Image from Wikimedia Commons

After a further hour the Earth will block all direct sunlight from reaching the entire Moon. This is shown as U2 is the diagram and this total phase will start at 7:30 PM. In the total phase, rather than disappearing completely, the Moon goes a dull red colour as shown in the picture at the top of this post. This is because, even though no direct sunlight can reach the Moon, some light from the Sun is bent round the Earth’s atmosphere towards the Moon. This light appears red because visible light from the Sun is a mixture of different wavelengths – red light has the longest wavelength and violet the shortest. Most of the light of the shorter wavelengths (orange, yellow, green, blue, indigo and violet) is removed from this light bent by the Earth’s atmosphere by a process called scattering, which I discussed in an earlier post https://thesciencegeek.org/2015/09/30/why-is-the-sky-blue/ . The same effect causes the western sky to be red after sunset on a clear day.

Interestingly, if we could stand on the surface of the Moon and view the eclipse we would see a red ring around the Earth.

The Moon will emerge from the total phase (point U3) at 9:13 GMT, the partial phase (point U4) will end at 10:19 PM and the eclipse will finish (P4) at 11:29 PM.

Which areas of the world can see the eclipse?

The eclipse timings are summarised below

Data from NASA (2009)

Not all areas of the world will be able to see the eclipse. This is because the Moon will have already set after the eclipse starts or will not have risen before it finishes. Other places will only be able to see part of the eclipse.

In Manchester where Mrs Geek and I live, the Moon will rise at 9:06 PM local times which is 8:06 PM GMT, so when the Moon rises the total eclipse will already be underway.
In Manila, the Moon will set at 5:44 am on July 28, Philippine Standard Time (PST) which is 9:44 PM GMT, so viewers will miss part of the final partial phase because this will occur after the Moon has set.

I have adapted the diagram below from NASA (2009) and this shows where in the world the eclipse can be seen.

The regions labelled A to L are as follows

How often do lunar eclipses occur?

Even though the Moon takes roughly a month to orbit the Earth, lunar eclipses do not occur every month. The Moon’s orbit around the Earth is tilted at about five degrees with respect to the Earth’s orbit around the Sun, as shown below.

This means that during most lunar months, as seen from the Moon, the Earth passes just below or just above the Sun rather than obscuring it. There are only two time windows in a year when a lunar eclipse can occur. These two points are known as the nodes (See note 2). Even then most lunar eclipses are partial eclipses where the Earth only partially covers the Moon.

Notes

GMT versus UTC

Although the term Greenwich Mean Time (GMT) is often used in popular writing it is no longer used by astronomers. Instead, they use two different times which agree with each other to within 1 second.

Universal Time, often abbreviated to UT1, is the mean solar time, the time determined by the rising and setting of the Sun at the Greenwich Meridian, zero degrees longitude.
Co-ordinated Universal Time, usually abbreviated to UTC, is the time measured by atomic clocks and is kept to within 1 second of UT1 by the addition of leap seconds.

In common use, GMT is often taken to be the same as UTC, which is the approach I have taken for this post. However, it can also be taken to mean UT1. Owing to the ambiguity of whether UTC or UT1 is meant, and because timekeeping laws usually refer to UTC, the term GMT is normally avoided in precise writing.

Nodes when eclipses can occur

The two nodes when a lunar eclipse can occur aren’t the same dates every year but change from year to year due to an astronomical effect called precession of the line of nodes.

References

NASA (2009) Total lunar eclipse of 2018 July 2017, Available at: https://eclipse.gsfc.nasa.gov/LEplot/LEplot2001/LE2018Jul27T.pdf (Accessed: 8 July 2018).

The darker mornings

As I complete this post from my home in Manchester, England, it is 4:30 pm and already fairly dark outside. Many people think that it will continue to get dark earlier each day in the afternoon until we reach 21 December, the winter solstice. This, however, is not the case. The evenings in fact start to draw out a week or so before December 21, so it is already getting lighter in the evenings, although it does not start to get lighter in the mornings until early in the new year.

This post aims to explain this interesting phenomenon. (Those of you who have been following my blog for while and have a good memory may recall that I posted on this topic a couple of years ago 🙂 )

Sunrise and sunset in December

The table below shows the sunrise and sunset times for London for December at three day intervals.

In the table above, the daylight column shows the number of hours, minutes and seconds between sunrise and sunset. This clearly shows that 21 December has the shortest period of daylight, but while the time of sunrise continues to get later and later throughout the whole of December, the time of sunset stops getting earlier around 12 December.

The final column shows the solar noon, the time of day that the Sun is at its highest in the sky or, to put it another way, the mid-point between sunrise and sunset. The table shows that during December the solar noon drifts later by about 30 seconds each day.

Why does the solar noon shift ?

A solar day is the period of time between solar noon on one day and solar noon on the next day. The length of a solar day varies throughout the year. It is at its shortest, around 23 hours 59 minutes 38 seconds, in mid September and at its longest, around 24 hours 30 seconds around Christmas Day.

The graph shows the difference between the length of a solar day and its average value of 24 hours throughout the year. For example, a value of 10 means a solar day is 24 hours 10 seconds long , 20 means a solar day is 24 hours 20 seconds long, and -10 means a solar day is only 23 hours 59 minutes 50 seconds long.

As you can imagine, it would be complete chaos if our clocks and watches had to cope with days of different lengths, so we use 24 hours, the average over the whole year, for all timekeeping purposes.

So, in December solar days are on average 24 hours and 30 seconds in length, while our clocks and watches are still assuming that each day is exactly 24 hours. This causes the day to shift about 30 seconds later each day, as shown in the diagram below. This explains why the evenings start drawing out before the shortest day, but it continues to get darker in the mornings until the new year.

Sunrise and sunset for London in December.

Why does the length of a solar day vary ?

The reason why the length of the solar day varies is due to two different factors.

The fact that the Earth moves in an elliptical orbit around the Sun and its speed varies, being faster in earlier January, when it is closer to the Sun and slower in early July, when it is further away.
The fact that the axis of the Earth’s rotation is tilted.

If you want to know more about how these factors work together to vary the length of the solar day, see my post September 18 the Shortest Day.

What about the southern hemisphere ?

In the southern hemisphere 21 December is the summer solstice, the day with the most daylight. What happens is that the Sun starts rising later before December 21, but it doesn’t start getting dark earlier in the evening until well after December 21. This is illustrated in the table below, which shows the sunrise and sunset times for December for Wellington in New Zealand, which lies at a latitude of roughly 41 degrees South.

Final note

It is not strictly true to say that a solar day is on average exactly 24 hours long. As readers of a previous post, “The Days are Getting Longer’, will be aware the Moon is gradually getting further away from the Earth. In fact, equipment left on the Moon by the Apollo astronauts has confirmed that the average distance from the Earth to the Moon is increasing by about 4 cm a year.

-Image from NASA

As the Moon gradually saps energy from the Earth, the Earth’s rotation slows down, causing the length of a day to get gradually longer. In the year 1900 a mean solar day was 24 hours long. Now, in the early 21st century, a mean solar day is actually 24 hours 0.002 seconds long. To prevent the time we measure using accurate clocks from drifting away from the solar time we need to add an second called a leap second roughly every 18 months.

Geocentric Cosmology

Today it is generally accepted as a scientific fact that the Earth is one of eight planets which revolve around the Sun, that the Sun is one of 400 billion or so stars in our Milky Way galaxy and that the Milky Way is one of hundreds of billions of galaxies in the observable Universe.

Location of our solar system in the Milky Way galaxy

However, for most of human history a geocentric model was the standard explanation of the cosmos. In this model the Earth is the the centre of the Universe and all the planets and stars revolve around it. Although it has been long superseded, this model could actually still be used to predict the motion of the Sun, Moon and the planets to a reasonable accuracy.

The basis of the geocentric model

Anyone watching the sky over a period of time will notice that the Sun rises in the east, is at its highest in the sky at midday and the sets in the west. Like the Sun, the Moon and the stars also rise in the east, get higher in the sky and set in the west. It was perfectly natural for ancient astronomers to assume a geocentric model in which the Earth doesn’t itself rotate but that the Sun, Moon and stars all rotate around it. After all, people on the Earth do not actually feel that it is rotating.

Ancient astronomers noticed that the time at which a given star rises wasn’t the same but was roughly 4 minutes earlier each day and that virtually all of the thousands of stars in the sky didn’t move with respect to each other but were fixed. So, they put them together in structures which became known as constellations. However, five of the brightest stars weren’t fixed but moved around a narrow band of sky which became known as the zodiac. These five objects: Mercury, Venus, Mars, Jupiter and Saturn became known as the wandering stars or planets. (The outermost two planets Uranus and Neptune were only discovered in the last 250 years)

The geocentric model

The name most associated with the geocentric model is the ancient Greek astronomer Claudius Ptolemy. He lived in Alexandra, Egypt in the second century CE, although no one knows the exact dates of his birth and death. Ptolemy didn’t invent the geocentric model – no single astronomer did. Ptolemy’s contribution was to refine the model which had been built up by Greek astronomers over the previous centuries, so that it could accurately predict the positions of the stars and planets.

The geocentric model

An early version of the geocentric model is shown in the diagram above. At the centre of the Universe was the Earth. The Earth did not rotate and was surrounded by a set of eight invisible spheres to which the Sun, Moon, planets and stars were attached. The outermost of these spheres was a sphere of fixed stars. All the stars were attached to this sphere. Moving inward from the sphere of fixed stars were Saturn’s sphere, Jupiter’s sphere, Mars’s sphere, the Sun’s sphere, Venus’s sphere, Mercury’s sphere and finally, closest to the Earth, the Moon’s sphere. To simplify the diagram, only the sphere of fixed stars, the Sun’s and Mars’s spheres are shown.

To a viewer in the northern hemisphere, the sphere of fixed stars rotated anticlockwise around a point in the sky directly above the North pole, known as the North celestial pole, once every 23 hours 56 minutes (see note 1).

As viewed from Earth, the Sun’s, Moon’s and the planets’ spheres rotate more slowly than the sphere of fixed stars. For example, the Sun’s sphere takes 24 hours to complete a single rotation ,compared to the 23 hours 56 minutes for the sphere of fixed stars. So, compared to the sphere of fixed stars, the Sun’s sphere slipped back by around 4 minutes giving it a slow backwards rotation. The diagram above also shows that axes about which the Sun’s, Moon’s and planets’ spheres rotated didn’t go through the North pole but was inclined at an angle to it.

The diagram below shows a two dimensional slice through the model with the Sun, Moon and all the planets shown.

The uneven motions of the planets

If you observe how a planet moves over a period of time you will notice that it does not move at a steady rate. At times it will move more slowly against the background of stars, stop altogether, move in the opposite direction, stop again and then continue moving in the original direction. The reason for this is shown for one of the planets, Mars, in the diagram below.

As you can see from the diagram, the Earth is closer to the Sun than Mars, and moves faster in its orbit. At point 3, the Earth approaches Mars; to an observer on the Earth, between points 3 and 5 Mars will appear to change direction and move in a reverse direction against the background of stars. When it reaches point 5 the Earth is receding from Mars and so Mars will continue in its normal direction.

In the geocentric model the apparent uneven speed and change of direction of the planets’ motion was explained by introducing a concept known as an epicycle.

Epicycles and deferents – for simplicity only Mars is shown

Rather than than revolve directly round the Earth, a planet moves at constant speed in a small circle called an epicycle. The centre of the planet’s epicycle, marked with an ‘x in the diagram above, moves in a circular path around a larger circle called a deferent. For each planet the Earth lies at the centre of its deferent. At times the planet will be moving in the same direction as the orbital motion of the deferent and other times it will moving in the opposite direction. This will make the motion of the planet appear to be uneven – in keeping with the observations taken by the ancient astronomers.

The inferior planets Mercury and Venus

Mercury and Venus differ from the other planets in that, to an observer on the Earth, they never stray too far away from the Sun and, to viewers at low latitudes they can only be seen for a few hours after sunset or a few hours before sunrise. For this reason they were known by the Greek astronomers as the the inferior planets. The superior planets (Mars, Jupiter and Saturn) are not tied to the position of the Sun and at certain times were visible in the middle of the night.

The reason why Venus and Mercury always appear in the same part of the sky as the Sun is that their orbits lie inside the Earth’s orbit. This is shown in the diagram below.

Venus cannot appear more than 46 degrees away from the Sun. The green line shows the limits of Venus’s apparent position from the Sun.

In the geocentric model this was explained by locking the Mercury and Venus’s motion to that of the Sun. The centres of their epicycles took exactly 1 year to orbit the Earth and were always in a direct line between the Earth and the Sun. This is shown in the diagram below.

As Venus moves around the Earth the centre of its epicycle always lies on the red line between the Earth and the centre of the Sun’s epicycle. This ‘locks’ the position of Venus to the Sun so that, to an observer on Earth. it cannot appear too far from the Sun. Mercury is locked in a similar manner.

Fine tuning the geocentric model.

The geocentric model which I’ve described so far had been developed by astronomers in the centuries before Ptolemy, although very little of the early astronomers’ original writings survive. Ptolemy’s contribution was to make two further modifications to make it more accurately fit observations of stars and planets. The first one I’ll describe is to deal with a phenomenon known as the ‘precession of the equinoxes’. Even though the telescope hadn’t been invented, Greek astronomers had been taking precise observations of stars and measuring their positions for hundreds of years. Although the stars appeared fixed with respect to each other, over hundreds of years the alignment of the entire celestial sphere was slowly moving with respect to the Earth.

An effect of the precession of the equinoxes is that the pole star gradually changes. Today the bright star Polaris in the constellation Ursa Minor (the Little Bear) lies near the celestial North pole and all the other stars appear to rotate around it. In Ptolemy’s time another star in Ursa Minor, β Ursae Minoris, was the pole star and in about 13,000 years time the bright star Vega will lie close to the celestial North pole.

Ptolemy explained procession of the equinoxes by giving the celestial sphere an additional very slow rotation once every 26,000 years about a different axis in addition to its daily rotation around the Earth’s North-South axis.

Ptolemy had to make one more adjustment to the model to allow it to fit historic observations of the stars and planets and thus be able to accurately predict their future positions. Even when epicycles were added, the position of the planets was not where the model predicted they would be. The motion of the planets was still uneven compared to the background stars. The reason for this is that the planets move around the Sun in elliptical (oval-shaped) orbits and the speed of a planet is fastest when it is closer to the Sun (see note 2). This is shown in an exaggerated form in the diagram below. In reality none of the planets’ orbits are actually this elliptical.

However Ptolemy, like all other Greek astronomers before him, believed that the all the planets’ deferents and epicycles must be perfect circles. This was for philosophical reasons, as the heavens were the epitome of perfection and the circle was seen as a perfect shape. So what he had to do was to modify the geocentric theory in a way summarised in the diagram below.

Firstly, the Earth didn’t lie at the centre of the deferent. He introduced a new point which he called the ‘eccentric’ for the centre of the deferent. The eccentric was some distance away from the Earth. Secondly, the centre of the epicycle didn’t move at a constant speed around the deferent but an uneven speed:

when it was closer to the Earth it moved faster – the dashed line
when it was further away it moved more slowly – the solid line.

The uneven speed was such that for each planet there was a point called the equant, at which the deferent would appear to move with a constant speed. A further complexity was that distance between the Earth, the equant and the eccentric varied for each planet.

So, strictly speaking, Ptolemy’s theory wasn’t truly geocentric, because the planets didn’t orbit the Earth, but each of their deferents orbited a hypothetical point called its eccentric which was offset from from Earth and was different for each planet. However, the theory fitted the observations in that it was possible to work out the past and the future position of the stars and planets using it. In around 150 CE Ptolemy published his theory in a book called ‘The Almagest’, which over the succeeding centuries was translated into many languages including Arabic and Latin and became the most influential astronomy textbooks for the next 1500 years.

A sixteenth century Latin translation of The Almagest -Image from Wikimedia Commons

Next post

I hope you enjoyed this rather long post. In my next post I’ll talk about how Ptolemy’s theory was swept away by the scientific revolution

Notes

(1) To a viewer In the southern hemisphere, the sphere of stars wold appear to to rotate clockwise around a point in the sky directly above the South pole.

(2) For the more technically-minded reader the motions of the planets around the Sun are governed by Kepler’s laws of planetary motion, which state:

The orbit of a planet is an ellipse with the Sun at one of the two foci.
A line segment joining a planet and the Sun sweeps out equal areas during equal intervals of time.
The square of the orbital period of a planet is proportional to the cube of the semi-major axis of its orbit.

The early days of the space race

In my previous post I talked about two significant successes for the Soviet Union in 1957: the first artificial satellite in orbit in October and the first living creature, a dog named Laika, in orbit in November. In December of that year the Americans had a humiliating failure when the Vanguard spacecraft exploded in a massive fireball on the launch pad.

Vanguard TV-3 a few seconds after launch

To boost American prestige and to show the American public that the US wasn’t falling further behind the Soviets, it was important that America get a satellite into orbit as soon as possible. They achieved this when Explorer 1 went into orbit on 1 February 1958.

Explorer 1- Image from NASA

Explorer 1 had a payload of numerous science instruments designed under the direction of James Van Allen (1914-2006), a space scientist at the University of Iowa. It made the discovery that the Earth is surrounded by a belt of electrically charged particles trapped in its magnetic field. The radiation in these belts is so intense that the readings from the Geiger counter on the spacecraft went off the scale when it passed through them. The belts are invisible to telescopes on Earth which is why they had not been detected previously. Today, in honour of Van Allen, they are known as the Van Allen radiation belts.

The Van Allen radiation belts

Explorer 1, like the Soviet Sputnik 1 and 2 spacecraft, had no solar cells to generate its own electricity. Electrical power came from a non-rechargeable battery. Three and a half months after launch, the battery ran out of charge so the spacecraft couldn’t transmit or receive signals and its instruments stopped working. However, Explorer 1 continued to orbit the Earth as a ‘dead’ satellite for much longer than Sputnik 1 or 2, for reasons which can be seen in the diagram below.

Only Sputnik 1 shown, Sputnik-2 had a similar orbit

As shown above, Explorer 1 was placed in a much higher orbit than Sputnik 1 and 2. At its closest approach it was 358 km above the surface of the Earth and its furthest 2,550 km. The higher a spacecraft’s orbit, the longer it remains in space because the traces of atmosphere which slow it down by friction are much less. Therefore, even though it couldn’t transmit any signals back to Earth, Explorer 1 remained in orbit until March 1970. This was over 12 years after its initial launch, whereas the Sputniks survived in space for around 4 months.

After the success of Explorer 1, the Americans successfully launched 4 other spacecraft into orbit in 1958. However, there were also 18 launch failures, meaning that nearly 80% of American launches in 1958 failed to get into orbit.

Luna 1, 2 and 3

Despite the American successes in 1958, the next big advances in space exploration were all made in 1959 by the Soviet Union. In January 1959 the Soviets launched Luna 1. This was the first ever spacecraft to reach escape velocity, a speed high enough to enable it to escape from the Earth’s gravity altogether. It flew 6,000 km above the Moon’s surface and during its journey provided direct measurement of the solar wind, a stream of electrically charged particles coming from the Sun. Luna 1 didn’t have a camera, so was unable to send back any pictures of the Moon, but its instruments made the discovery that, unlike the Earth, the Moon has no magnetic field. Interestingly, Luna 1 was actually intended to hit the Moon’s surface but it missed its target due to a navigational error (Zak 2016) so, after passing the Moon, it went into orbit around the Sun, where it remains to this day.

Since 1959 Luna has been orbiting the Sun in an orbit which lies mainly between the Earth and Mars

Luna 2 was launched in September 1959 and this time succeeded in crash landing onto the Moon, becoming the first ever spacecraft to land on another celestial body. This again was a massive propaganda coup for the Soviets. It even boosted the reputation of the Communist system as a whole, according to some writers of the day: only a successful and thriving country could achieve such great scientific feats. Although their system couldn’t deliver the same level of material wealth for its citizens as free market capitalism, in 1959 the Soviets were ahead of America in space technology. It would not be until 1964 that America would successfully crash land a spacecraft on the Moon (see notes).

Even more exciting, however, was Luna 3. In October of the same year it became the first ever spacecraft to take pictures of the far side of the Moon, which had never before been seen from Earth and had remained an enigma throughout history.

Luna 3’s images caused immense excitement around the world. These and subsequent pictures showed that the far side looks very different from the near side. It has a battered, heavily cratered appearance with a relatively small portion of its surface covered by the smooth dark areas (known as seas, or the Latin word maria).

The near and far sides of the Moon (image from NASA)

The greatest leap of all in the early days of space exploration came 18 months later. On 21 April 1961, a Vostok spacecraft containing cosmonaut Yuri Gagarin (1934-1968) launched successfully, performed a single orbit of the Earth, and safely landed 108 minutes later. This was a massive propaganda triumph for the Soviet Union and Gagarin, an air force pilot, became instantly famous throughout the world.

Yuri Gagarin – image from Wikimedia Commons

The American reaction to Gagarin’s flight was swift. A month later President John F Kennedy made the following address to the United States Congress:

“I believe that this nation should commit itself to achieving the goal, before this decade is out, of landing a man on the Moon and returning him safely to the Earth. No single space project in this period will be more impressive to mankind, or more important in the long-range exploration of space; and none will be so difficult or expensive to accomplish.”

President J F Kennedy giving his address on 25 May 1961 – Image from NASA

This was an incredibly ambitious goal, given that in May 1961 America had not yet even placed a man in orbit. Nevertheless, Kennedy was advised that, given sufficient investment by the richest country in the world, a manned landing could be achieved before 1970. There was a good chance that the Soviets simply would not have the money to develop the new spacecraft and technologies required for this incredible leap forward.

So, the American government funded the largest commitment every undertaken by a nation in peacetime. At its peak the programme employed nearly half a million people and its total cost in today’s money was around $180 billion.

All this effort came to successful fruition on July 20 1969, when Neil Armstrong and Buzz Aldrin became the first human beings to land on the Moon. When Armstrong stepped out of the spacecraft he said the immortal words:

That’s one small step for man, one giant leap for mankind.

The Americans had won the space race.

Apollo 11 Astronaut Buzz Aldrin on the Moon – image from NASA

Notes

Actually, this is not strictly true. Ranger 4 crashed on the far side of the Moon in April 1962, thus becoming the first American spacecraft to land on another celestial body. However, due a computer malfunction, it returned no scientific data. The first American probe to land successfully at its planned landing site and send data was Ranger 7 in July 1964.

References

Zak, A (2016) USSR launches the first artificial planet. Available at: http://www.russianspaceweb.com/luna1.html (Accessed: 30 September 2017).

Solar eclipse 21 August 2017 – America on the move

Around 200 million Americans live within a day’s drive of the total eclipse path, the narrow band of territory from Oregon to South Carolina. According to an article in The Atlantic, up to 7 million people, perhaps even people reading this, will travel to see Monday’s total eclipse. They will join the 12 million who are lucky enough to see the total eclipse without needing to travel. If 7 million people do travel then it will be the biggest movement of people in human history to see a natural phenomenon. Even if the fear of being stuck in a traffic jam for many hours puts people off and a lower number of people actually make the journey, the growth of social media means that the number of people following the eclipse on-line in real time will be unprecedented.

Headline from the Atlantic

To mark this event I’ve decided to publish an updated version of my eclipse post from July 9.

Update of the original post below———-

As nearly all of my readers, particular those who live in the US, will know, there will be a solar eclipse on 21 August. For lucky viewers in a narrow band of territory running West to East across the US, it will be visible as a total eclipse – when the Moon completely obscures the Sun and it suddenly goes dark for a short period of time.

Image from NASA

Although there is, on average, a total eclipse somewhere on Earth every 18 months, for each eclipse the region of on the world where a total eclipse can be seen is relatively small. Unless you are a so-called eclipse chaser – people who travel long distance to see solar eclipses, you will probably only get a change to see a total eclipse within 1000 km of where you live once or twice in your lifetime. The last time that one has been visible anywhere in the contiguous US was back in February 1979, when most people currently alive weren’t even born (see note 1).

Image from NASA

The path of totality, where a total eclipse can be seen is shown as the blue band in the map below. Places either side of the blue band will only see a partial eclipse, when the Sun is only partially obscured and the further away from it you are, the smaller the fraction of the Sun that will be covered. Unfortunately for people like me who live in the UK the eclipse will be barely noticeable, only a small fraction of the Sun will be obscured, just before sunset.

Image from timeanddate.com

The path of the eclipse as it moves across the US is shown below. If you click on the diagram it will show the map in greater detail. The total eclipse will begin over the Pacific Ocean and will reach the Pacific coast of America in Oregon just West of the state capital Salem (shown below) at 10:16 am local time.

Salem Oregon, the first major city to see the total eclipse

The table below shows the eclipse times from some selected cities in its path.

Data from timeanddate.com

Why do we have eclipses?

It is common knowledge that solar eclipses occur when the Moon passes in front of the Sun, obscuring some or all of its light. This is shown in the diagram below, although the distances and sizes of the Earth, Moon and Sun aren’t to scale.

In the diagram above, the regions labelled A see a partial eclipse. Only in the small region labelled B does the Moon fully obscure the Sun and a total eclipse is seen.

From the diagram above you would expect the Moon to pass in front of the Sun every month and there to be an eclipse every month. This is clearly not the case.

The Moon’s obit around the Earth is actually tilted at about five degrees with respect to the Earth’s orbit around the Sun, as shown in the diagram below.

This means that during most lunar months the Moon will pass just below or just above the Sun rather than obscuring it. There are only two time windows in a year when it is possible for a solar eclipse to occur (see note 2). It also only possible for a lunar eclipse, when the Earth blocks sunlight hitting the Moon, to occur in the same time window.

The other reason why we can have eclipses is that, although the Moon is much smaller than the Sun – roughly 400 times less in diameter, by a strange coincidence it is also roughly 400 times closer to the Earth than the Sun. This means that, when viewed from the Earth, the Sun and the Moon appear to be almost exactly the same size. If the Moon were closer to the Earth, or larger in size, then solar eclipses would be more frequent and would last longer. If the Moon were further away, or smaller, then we would only have what is called an annular eclipse where the disc of the Moon is too small to fully cover the Sun.

Variation in the apparent size of the Sun and Moon throughout the year

The Moon, rather than moving in a circular orbit, moves in an elliptical (oval-shaped) orbit around the Earth. This means that its apparent size as seen from Earth varies. It appears largest when it is closest to the Earth and smallest when it is furthest away. The apparent sizes of large objects in the sky are measured in degrees. 1 degree is roughly how big a British 1 pence or US 1 cent coin would appear to be if you held it up at a distance of approximately 1.2 metres (4 feet) away from your eye. When it is at its closest, the Moon is 0.558 degrees in diameter and at its furthest away it is 0.491 degrees in diameter.

The Earth also moves in a elliptical orbit around the Sun. So the apparent size of the Sun varies as seen from the Earth, but the variation is not as a great as the apparent variation in the size of the Moon. When the Earth is at its closest to the Sun, the Sun is 0.545 degrees in diameter and when the Earth is at its furthest away the Sun is 0.526 degrees in diameter.

This variation means that there are times when the Moon lies directly in front of Sun, but, because it appears to be slightly smaller, we only see an annular eclipse.

An annular eclipse- image from NASA

How long can a total eclipse last?

The maximum time that anyone will see a total eclipse on 21 August 2017 is just over 2 and half minutes. The are a number of factors leading to a longer eclipse. The main ones are

the Moon should be as close to the Earth as possible making its apparent size as large as possible
the Earth should be as far as possible from the Sun making the Sun’s apparent size as small as possible.

Another less important factor is that the eclipse should occur at a point on the Earth when the Sun and the Moon are directly overhead. This gives an additional but very small boost to the apparent size of the Moon relative to the Sun.

This diagram, which is greatly exaggerated, shows that when the Moon is directly overhead (A) it is very slightly closer to the Earth then when it is at the horizon (B). This causes the moon to appear to be slightly (1.8%) larger in diameter.

All of these conditions will be achieved for an eclipse which is predicted in South America near the equator on 16 July 2186 and will be 7 and half minutes at its greatest duration (Espinak and Meeus 2011). I will not be around to see it, and neither will you!

Notes

(1) This is because, according to the CIA world fact book, for the United States the median age (the age at which 50% of the population is under this age and 50% of the population is over this age ) is 37.9 years. So half the American population were born less than 37.9 years ago, i.e on on after Sept 1979.

(2) The two times in a year when a total eclipse can occur aren’t the same every year but change from year to year. This is due to an astronomical effect called precession of the line of nodes.

References

Espinak, F and Meeus J (2011) Five millennium canon of solar eclipses: -1999 to +3000, Available at: https://eclipse.gsfc.nasa.gov/SEpubs/5MCSE.html (Accessed: 9 July 2017).

Solar Eclipse 21 August 2017

Image from NASA

Although there is, on average, a total eclipse somewhere on Earth every 18 months, for each eclipse the region of on the world where a total eclipse can be seen is relatively small. Unless you are a so-called eclipse chaser – people who travel long distance to see solar eclipses, you will probably only get a change to see a total eclipse within 1000 km of where you live once or twice in your lifetime. The last time that one has been visible in the contiguous US was back in February 1979, when most people currently alive weren’t even born (see note 1).

Image from NASA

The path of totality, where a total eclipse can be seen is shown as the blue band in the map below. Places either side of the blue band will only see a partial eclipse, when the Sun is only partially obscured and the further away from it you are, the smaller the fraction of the Sun that will be covered. Unfortunately for those of us in the UK, only a small fraction of the Sun will be obscured here, just before sunset.

Image from timeanddate.com

Data from timeanddate.com

Because the chance to see a total solar eclipse is so rare, millions of people – perhaps some of you – are making journeys of hundreds and in many cases thousands of miles to view it. Hotels and campsites will be fully booked – and perhaps already are. Many states on the path of totality have used the sudden influx of millions of people to promote other tourist sites as well.

Why do we have eclipses?

In the diagram above, the regions labelled A see a partial eclipse. Only in the small region labelled B does the Moon fully obscure the Sun and a total eclipse is seen.

From the diagram above you would expect the Moon to pass in front of the Sun every month and there to be an eclipse every month. This is clearly not the case.

The Moon’s obit around the Earth is actually tilted at about five degrees with respect to the Earth’s orbit around the Sun, as shown in the diagram below.

Variation in the apparent size of the Sun and Moon throughout the year

This variation means that there are times when the Moon lies directly in front of Sun, but, because it appears to be slightly smaller, we only see an annular eclipse.

An annular eclipse- image from NASA

How long can a total eclipse last?

The maximum time that anyone will see a total eclipse on 21 August 2017 is just over 2 and half minutes. The are a number of factors leading to a longer eclipse. The main ones are

the Moon should be as close to the Earth as possible making its apparent size as large as possible
the Earth should be as far as possible from the Sun making the Sun’s apparent size as small as possible.

Notes

(2) The two times in a year when a total eclipse can occur aren’t the same every year but change from year to year. This is due to an astronomical effect called precession of the line of nodes.

References

Espinak, F and Meeus J (2011) Five millennium canon of solar eclipses: -1999 to +3000, Available at: https://eclipse.gsfc.nasa.gov/SEpubs/5MCSE.html (Accessed: 9 July 2017).

The Evening Star-Venus

Anybody who has looked up into the western sky after sunset in the past month will have noticed a brilliant white object – the planet Venus, sometimes called the Evening Star. It is brighter than any other planet and ten times brighter than the brightest star Sirius, also known as the Dog Star.

The “Evening Star” Venus next to the Moon just after sunset – image from NASA

There are three reasons why Venus is so bright. Firstly, it comes closer to the Earth than any other planet. Secondly, it is relatively large compared to other inner planets, roughly twice the diameter of Mars and three times that of Mercury. Although the giant planets – Jupiter, Saturn Uranus and Neptune – are larger than Venus, they are further away and so appear smaller. Thirdly, the thick clouds which completely cover Venus reflect most of the light back into space. In fact Venus reflects 65% of the sunlight hitting it, more than any other planet. Venus is so bright that it even possible to see it during daylight. If you know exactly where to look it appears as a faint white dot against the bright blue sky

Venus over the next two years

Venus is both closer to Sun and moves faster in its orbit than the Earth and, on average, it takes 584 days for Venus to be in the same place in its orbit as seen from the Earth. The reason for this 584 day cycle is given in the notes at the bottom of this post. Because the orbit of Venus is inside the Earth’s orbit, Venus can never appear too far away from the Sun in the sky. In general it is only clearly visible for at most a few hours before sunrise or a few hours after sunset (see note 2). The two points where Venus appears furthest away from the Sun are called the greatest elongation points and are marked as A and B in the diagram below.

Data from Espinak (2014)

Venus has just passed a greatest elongation point which it reached on 12 January 2017, and it is a brilliant object in the western sky, visible for at least 3 hours after sunset, depending on your latitude. Over the next few month as it gets closer to the Sun it will be visible for a shorter and shorter time after sunset. On 25 March Venus will pass between the Earth and the Sun. This is known as inferior conjunction, and for a few weeks or so either side of this date Venus will be very difficult to see because it will only be visible in daytime close to the Sun.

Looking the diagram above, you might think that Venus will pass directly in front of the Sun at inferior conjunction. However, this diagram only shows the picture in two dimensions. As shown below, because the orbit of Venus is tilted with respect to the Earth, at inferior conjunction it normally passes above or below the Sun.

Rarely at inferior conjunction Venus will pass directly in front of the Sun. When this occurs it is known as a transit of Venus.

A transit of Venus. Venus is the dark dot crossing the Sun’s surface – image from Wikimedia Commons

After inferior conjunction, it will appear to move away from the Sun and will rise and set earlier in the day and will start to become visible in the eastern sky before sunrise. At this point in its orbit Venus is known as the Morning Star. It will reach the other greatest elongation point on 3 June 2017, when it will be visible for least 3 hours before sunrise.

After reaching the greatest elongation, Venus will start to move closer to the Sun again. It will be visible for a shorter and shorter time before sunrise. On 9 January 2018 Venus will be directly behind the Sun. This is called superior conjunction and, for a few weeks or so either side of this date, Venus will be very difficult to see because it will only be visible in daytime and will appear close to the Sun. After superior conjunction Venus will appear in the evening sky after sunset and as it gets further from the Sun it will be visible for longer and longer before the Sun sets

On 17 August 2018 Venus will reach the greatest elongation point it had previously reached on 12 January 2017 and once again it will be visible for at least 3 hours after sunset as a brilliant object in the western sky.

Venus’s phases during the 584 day cycle

As seen from the Earth over the 584 day cycle, Venus goes through a full set of phases in a similar way to the Moon. However, because Venus appears so small, these are only visible through a telescope.

At inferior conjunction, point A in the diagram above, when Venus is between the Earth and the Sun, the sunlit part of Venus faces away from us making the planet almost invisible. The amount of the sunlit part of Venus we can see gets larger or waxes through to a crescent phase (B), to a half Venus (C) at the greatest elongation and then to a full Venus at superior conjunction (D), when the whole sunlit side facing the Earth is illuminated. It then gets smaller or wanes back to a half Venus (E) at greatest elongation, then to a crescent (F) and then finally back to being almost invisible at inferior conjunction

Galileo’s discovery

The first person to discover the phases of Venus was the Italian astronomer Galileo Galilei (1564-1642).

Image from Wikimedia Commons

In 1543, just before his death, Nicolas Copernicus (1473-1543) had published the theory of heliocentrism which was completely revolutionary in its day – that the planets orbit the Sun. However, in Gallileo’s time, the teaching of the Catholic church favoured geocentrism, the widely held view that the Earth was the centre of the Universe and the stars, planets, the Sun and the Moon were in orbit around it. Indeed certain verses of the bible could be interpreted as supporting that viewpoint, such as Psalm 104:5 “the Lord set the earth on its foundations; it can never be moved.”

However, the phases of Venus and the way that it appears smaller when it is a full Venus can only be fully explained by Venus orbiting the Sun, not the Earth. Therefore, Galileo concluded that the geocentric theory was incorrect. Unfortunately for Galileo, in 1616 the Catholic church declared heliocentrism to be heresy. Heliocentric books were banned and Galileo was ordered to refrain from holding, teaching or defending heliocentric ideas.

Despite this ruling Galileo continued to defend heliocentrism, and in 1633 the Roman Inquisition found him “vehemently suspect of heresy”, sentencing him to indefinite imprisonment. Galileo was kept under house arrest until his death in 1642.

However the facts cannot be disputed. When viewed through a telescope Venus does show changes in size and shape, which can only be satisfactorily explained in a heliocentric model. Eventually, in 1758, the Catholic Church dropped the general prohibition of books advocating heliocentrism.

And finally….

I hope you have you have enjoyed this post. In 2015 and 2016 I published a series of posts on Venus. Some of them are listed below.

Venus a Mysterious world describes Venus in science fiction and compares it these depictions of the planet to reality.

Akatsuki – a second chance describes the mission of the Japanese spacecraft Akatsuki which is currently in orbit around Venus studying its weather. The spacecraft should have gone into orbit in 2010. This didn’t happen but mission control were able to successfully put the spacecraft in hibernation for 5 years before making another successful attempt.

Terraforming Venus describes how in the future we could alter Venus to make it more Earth-like so that we could live on the planet without needing any special protective equipment.

Notes

(1) The diagrams below illustrate why it takes 584 days for Venus to be in the same position in its orbit in relation to the Earth. Venus and the Earth in their orbits around the Sun are like two runners on a track. The Earth takes 365.256 to do one circuit, whereas Venus, whose orbit is inside the Earth and moves faster around the Sun, only takes 224.701 days to do one circuit.

The point in time when Venus is closest to the Earth and lies between the Earth and the Sun is called inferior conjunction. The time interval between one inferior conjunction and the next is the time it takes for Venus to ‘gain a lap’ in its orbit around the Sun. This is shown in the diagrams below.

After approximately 580 days Venus and the Earth line up again.

In fact, because the Earth’s and Venus’s speed in their individual orbits isn’t constant but varies slightly, the interval between one inferior conjunction also varies. On average it is 584 days but it actually varies between 580 and 588 days.

(2) Strictly speaking, this depends on the latitude of the observer. Venus is visible for much longer at higher latitudes.

References

Espenak, F (2014) 2017 calendar of astronomical events, Available at: http://www.astropixels.com/ephemeris/astrocal/astrocal2017gmt.html (Accessed: 6 January 2017).

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