## Monday, May 28, 2012

### Earth-Venus Conjunction Explanation

I've previously mentioned the upcoming transit of Venus, and said I'd write more about it, then completely forgot about it. So tonight I'd like to rectify that by writing a bit more about these amazing events. Looking back at my previous post I see two things that I specifically mentioned talking about: further details of how Earth's and Venus's orbits interact, and more about why transits of Venus are scientifically important.

As I wrote in my earlier post, transits of Venus happen at what appear to be – at first glance – rather strange intervals. Specifically, in the present era, transits happen in pairs 8 years apart, separated by intervals of either 105.5 or 121.5 years. The reason this happens has to do with the shape and orientation of the orbits of Earth and Venus. In the picture I put together below, the orbits of Earth and Venus are shown at the correct scale relative to the Sun and each other. Earth's orbit is green, and Venus's is blue. Venus and Earth themselves are too small to be seen at this scale. One point of terminology: the point when Venus passes Earth in its orbits is called its conjunction.

Although the angle between Earth and Venus's orbits is only 3.4°, you can see in the top half of the picture that most of the time Venus passes above or below the Sun at its conjunction (when it passes us in its orbit). The only time we can actually see it cross the face of the Sun is when both planets are close to what is called the line of nodes of their orbits. This is where their orbits cross as seen from edge on (as seen in the top half), and is denoted by the dashed red line in the lower half of the picture. The location of Venus's conjunction, however, is not fixed, but moves slowly backwards around the orbit over time. Whenever it happens within a narrow region around the line of nodes, a transit of Venus is seen.

Because of the arrangement of their orbits, 8 Earth years are almost exactly equal to 13 Venus years (with a difference of just 0.4 days). That is, each 8 years Earth and Venus are in almost exactly the same position relative to each other, just rotated slightly along their respective orbits. Thus, two transits of Venus can happen 8 years apart within the narrow region around the line of nodes, but the region is narrow enough that adjacent conjunctions result in Venus passing above or below the Sun as seen from Earth. Currently Earth reaches the line of nodes in June and December, so transits occur in pairs with one in December (such as the 2004 transit) and one in June (this one).

But why the 105.5 and 121.5 year intervals between transit pairs? That results from the fact that neither Earth's nor Venus's orbits are perfectly round (although Venus's orbit does have the lowest eccentricity of all the planets). Because of this fact, the rate that the Earth-Venus conjunction moves is not constant, and also has a different distance to move. This difference causes the difference in duration between pairs.

Hopefully the preceding explanation has helped you better understand what's going on. I'm going to defer the explanation of the scientific value of a transit for a later post as this one is getting pretty long and I need to get to bed. I also hope to show you the designs for the posters for the transit of Venus that I created, which have now been printed and are actually on sale for a limited time around the transit!