Jubilee

The 4th of June 2012 will see the celebration of the Queen’s Official Birthday in the United Kingdom and the commemoration of the Diamond Jubilee marking the 60th anniversary of the accession of Queen Elizabeth II to the throne. A unique and special event you might say. But barely a couple of days later, as the 5th of June rolls into the 6th, another special event is to take place. Not on our planet, let alone the United Kingdom, but in the sky. From our privileged place in the Solar System, we will be lucky enough to witness an event truly astronomical in proportion and of such rarity. On that day, or night, depending on where you are on Earth, you will be able to observe the transit of Venus. Venus, the queen of the night sky, for she is the second brightest celestial body in the night sky after the majestic Moon, will gracefully move across the face of the Sun as she positions herself between the Earth and the Sun. This alignment of position, Earth-Venus-Sun, will not occur again for another 105 years. The Queen’s Diamond Jubilee might also be an equally rare event.

Even though we have to wait at least another century for Venus to transit again between us and the Sun, the last time this event occurred was just 8 years ago. And before that, it was in 1882. Almost like clockwork, the recurrence of the event follows a regular pattern. We can expect Venus to transit at every 8, 105, 8, 122, 8, 105, 8, 122, 8,… etc. years interval. The reason we can be so confident about the regularity and recurrence of the transit is down to the principles of motion and gravitational force. Venus, being closer to the Sun than the Earth is, takes less time to go round the Sun than the Earth does. The Earth, not surprisingly, takes a year to go round the Sun. This is about 365.25 days. Venus takes only about 224.70 days to orbit the Sun. The fact that they travel at different speed round the Sun would mean that one of them will overtake the other at some point round their journey. This is analogous to the minute and hour hands on an analogue clock. The minute hand takes 1 hour to round the clock. The hour hand takes 12. If they start of together at noon, or midnight, their paths will cross again at around 01:05 and again at around 02:11 and so on for 22 times every day. This is easy to work out using mathematics.

In a similar way, we can use mathematics to figure that Venus’s and Earth’s paths round the Sun will cross each other at certain regular points. Now, unlike the clock hands which cross each other at regular intervals every time, that is, they cross each other every 65.45 minutes or so, Venus’s and Earth’s paths will cross at every 8, 105, 8, 122, 8, 105, 8,… years interval. There is another reason why their paths cross at such a peculiar interval. We can use the analogue clock again as example. The minute hand is usually slightly above the hour hand. They do not rotate on the same plane because, if they did, they would not go past each other. Just as we have this different level or plane on which the hands go round the clock, in the Solar System we have different planes of rotation for Venus and Earth. However, the planes of rotation for the clock hands are still horizontal even though one is above the other. For Venus, its plane is inclined by about 3.4 degrees relative to the Earth’s. This additional difference in the way to go round the Sun also contributes to this particular pattern of 8, 105, 8, 122 interval.

This phenomenon can allow us to figure out the distance between the Earth and the Sun. With some clever yet simple use of mathematics, it is possible to figure out how far the Earth is from the Sun based on how long Venus takes to transit. And once you have the Earth-Sun distance, you can use that to map out the scale of the whole system. The Earth-Sun distance does not remain the same as the Earth goes around the Sun. This is because the path is not circular. By definition, a circle would have a constant radius. The orbit of the Earth around the Sun is elliptic. This is in fact the shape of all the orbits of the planets around the Sun. By being elliptic, the orbits of the planets have a varying radius. Sometimes the planets are closer to the Sun, sometimes further away than on average. The Earth-Sun distance changes as the Earth goes round the Sun in its elliptic path but it doesn’t change by too much. This distance, called the Astronomical Unit (AU) is used as a ruler, albeit a gigantic one, to measure other big distances in space. For example, the furthest planet from the Sun is Neptune and it is about 30 AU away. That is, it is about 30 times further away from the Sun as compared to the Earth. This might not seem a lot but when you convert that unit into the more familiar kilometre then you realise that Neptune orbits about 4.5 billion km away from the Sun. The Earth orbits about 150 million km. 1 AU, thus, is about 150 million km.

Of all the elliptic orbits, that of Venus is the least elliptic. In other words, Venus is the one whose orbit is most circular. There is a way to quantify how circular an orbit is and it is called the ‘eccentricity‘ of the orbit. A circle has an eccentricity of 0. That means it is not eccentric at all. The more it is like an ellipse, the more eccentric it is. As mentioned earlier, a circle has a constant radius. An ellipse, on the other hand, has a varying radius. An ellipse’s radius varies from small to big. The eccentricity is simply a measure of the smallest radius compared to the biggest radius. For an ellipse, this measure or quantity varies from anywhere between 0 and 1 but it can never be 0 or 1. If it is 0, then we call it a circle. If it is 1, then we call that shape a ‘parabola’. And for anything greater than 1, we call it a ‘hyperbola’. So, for all the planets in the Solar System, the eccentricity lies somewhere between 0 and 1. That for the Earth is about 0.0167. The planet with the most eccentric orbit is Mercury. Its eccentricity is about 0.2056. How comparable are these eccentricities? 0.2056 is about 12 times 0.0167. How significant really is it that Mercury’s orbit is 12 times more eccentric than Earth’s? A quick look at the following diagram of ellipses with different eccentricities shows us  that it is difficult to tell the first 2 ellipses apart from each other. Their eccentricity is shown inside them. Mars’s orbit has an eccentricity of almost 0.1. So the first 2 ellipses are approximately how the orbits of Mars and Mercury would look like. Almost indistinguishable. These 2 planets have the most eccentric orbits in the Solar System. As such, it is easy to see why we tend to consider most planetary orbits to be circular. All the other planets have an eccentricity much less than 0.02. Only Mercury and Mars stand out in their eccentricity. Even then, it is not very significant. If we consider Pluto, for instance, then even its eccentricity is not that big at about 0.25. However, if we look at Sedna, which is a dwarf-planet, just like Pluto is, then its orbit is the most eccentric one in the outermost reaches of the Solar System. At 0.86, it definitely wins hand down in terms of eccentricity.

Ellipses with different eccentricity.

So, in short, most objects in the Solar System orbit the Sun in an almost circular path. Very few objects have eccentric orbits that are close to what we typically recognise as ellipses. To recapitulate, therefore, why the transit occurs at such peculiar intervals, then we have to consider 2 things: first, that Venus takes less time than Earth does to go round the Sun, and second, that Venus orbits the Sun on a slightly slanted plane compared to the plane of orbit of the Earth. It is therefore quite rare that their paths will cross each other. And if they do, it so happens to be at such paired intervals of 105 and 122 years separated by this 8 year gap.

It is in some way humbling to realise that the chances anyone of us living on the planet has to witness a second transit of Venus is very small. Unless, of course, anyone who has seen the transit on the 5th of June 2012, lives to the ripe old age of at least 105 years. With that in mind, let us contemplate the magnitude and, why not even, the majesty of the wonderful Solar System.

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  1. Pingback: Lady in Red | electrolights

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