A transit of Venus is like a solar eclipse but instead of the Moon being in line between the Earth and Sun it is the planet Venus that is directly in line. You can hardly fail to notice a solar eclipse because the Moon, being about the same apparent size as the Sun, blocks it out. Venus, on the other hand looks very much smaller from Earth and so you would have to be especially observing the Sun to see the small disc of Venus passing across it. You would also have to wait a long time. Whereas a solar eclipse occurs every year or so somewhere on Earth you could have been observing the Sun for the last century and still not have seen a transit of Venus.
In fact there is a rather curious pattern to transits of Venus and the purpose of this article is to explore why.
Here is a list of the transit dates from the 17th to the 21st century.
There is a curious 243 year repeating pattern with two transits in December (around the 8th), eight years apart, then a wait of 121 and a half years, then two June transits (around the 7th), again eight years apart, then a wait of 105 and a half years and then the pattern repeats again.
To start to understand what is going imagine a circular race track and two runners, Eartha and Vera. Eartha can do a lap of the track in one minute. Vera is quite a bit faster, and also has the advantage of the inside track, and she can do a lap in just under 37 seconds. The question is, if they start off together how long is it before Vera catches up with Eartha so they are together again?
To work out the answer it is convenient if the runners' speeds are in a whole number ratio, so let us assume Vera can lap the track in 8/13 minutes (36.92 seconds). That means Vera is going 13/8 times faster than Eartha so Vera is catching Eartha up at 5/8 laps per minute (13/8 minus 1). Vera will therefore catch up Eartha after 8/5 minutes, ie 1.6 minutes or 1 minute 36 seconds. Check it out and you will see that in 1.6 minutes Eartha has gone round the track once plus 3/5 of the track while Vera has gone round the track twice and 3/5 of the track, so they meet up.
Translate runners into planets and minutes into years and the picture is close to that for Earth and Venus. It is not quite as simple as that because the tracks are a bit elliptical rather than circular and the runners do not go at quite a constant speed. Also Venus orbits the Sun just a bit faster than 8 thirteenths of a year, more like 7.997. As we shall see this is a small but crucial difference.
The time of 1.6 years between Sun, Venus and Earth lining up is called the synodic period (synod = meeting). Fig 1 shows the lined-up positions from 1996 to 2002. You can see that there is a five spoke pattern. (Ignore for the moment the dotted line). The planets travel anti-clockwise and each lined-up position is 3/5 of the circle on from the previous one.
If we continue the pattern we can see that the next lining-up after 2002 will be in June 2004 in the same place as June 1996, 8 years previously. Almost but not quite. Since Venus travels a little bit faster than one orbit in 8/13 of a year it catches up with the Earth a little bit before the meeting place 8 years previous. Consequently, if you draw the five spoke pattern 8 years on from Fig 1 it will look like Fig 1 but with the spokes rotated slightly clockwise.
We can start to see that 8 years might be a significant interval but it is still not clear how it relates to transits. For a start we have said that Earth, Venus and the Sun are lined up every 1.6 years so why is there not a transit of Venus every 1.6 years? The answer is there would be if the orbit planes were exactly aligned. However, the orbit of Venus is at a small angle (3.4 degrees) to that of Earth. The result is that, although the planets appear lined up when looking down on the orbit planes, most of the time Venus viewed from the Earth will be either above or below the Sun. For a transit to occur the planets not only have to line up as in Fig 1 but they have to do it just in the place where the orbit planes cross, which makes it a much rarer event.
The same thing happens with a solar eclipse. Every month the Earth, Moon and Sun are lined up at New Moon. However the Moon/Earth orbit plane is at an angle to the Sun/Earth orbit plane and it is only when New Moon occurs at the orbit plane crossing that there is a solar eclipse. Otherwise, seen from Earth, the New Moon is either above or below the Sun.
Referring back to Fig 1 the dotted line shows where the orbit planes of
Earth and Venus cross. The crossing line corresponds to about 7 June and 8
December. We can see that the lining-up in 1996 was very close to the
orbit-crossing line but was not quite there. Venus was near to the Sun but
passed just south of it. On
After that there is a long wait until the January 1998 "spoke" in Fig 1 slowly makes its way round clockwise in eight year ticks until it gets close to the December orbit-crossing line in 2117. Eight years later in 2125 there will be another transit when the "spoke" ticks through to the other side of the orbit-crossing line. This time the orbit path rises from south to north so the first transit will be north of the ecliptic and the second transit south. There is then a long wait while the "spokes" tick round until the lower one arrives close to the June orbit-crossing line again. And so the process continues.
On a final note we saw that because the orbit time of Venus (measured in units of Earth-orbit time, ie one year) was close to 8/13 it led to 8 year cycles. A closer approximation to the orbit time of Venus is 243/395 years, which by similar logic leads to a longer run 243 year cycle.
Copyright Peter M Langford, September 1998
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