Archive for the ‘Mathematics’ Category

This is the first in a series of articles I’ll be posting about the transit of Venus on June 6th.  In this one I’ll outline what happens during a transit of Venus and why they are such rare events.

On June 5th and 6th astronomers around the world will be training binoculars, telescopes and cameras on the Sun.  They’ll be hoping to witness an event that won’t be repeated in their lifetimes.  Venus, which circles the Sun within the Earth’s orbit, will move directly between us and the Sun.  For a period of up to nearly seven hours Venus will be seen by many around the world to be silhouetted against the brilliant solar disk.  Astronomers call this kind of event a transit.

Here is a picture of the transit of Venus that I took on June 8th 2004.

It takes Venus 225 days to complete one orbit compared to the 365 (and a bit) days for the Earth.  Like the hands of a clock, it’s reasonable to think that at regular intervals Earth and Venus will be aligned with the Sun.  In fact the alignment happens every 584 days – astronomers call it an inferior conjunction.

This scenario is complicated by the fact that the orbit of Venus is tilted with respect to the Earth’s orbit by a small angle.  Most of the time the Sun-Venus-Earth alignment is not exact – Venus is seen from Earth to pass above or below the Sun rather than in front of it.

The slight tilt of Venus’s orbit to ours means that transits only occur if the planets are lined up in early June or December; at one of the places in its orbit where it is ‘level’ with the Earth’s orbit (or near a node, as astronomers call them).

Pairs of transits

How often do transits occur?  The hands of a clock align every 65 minutes and 27 seconds.  For Venus and Earth the period between alignments is about 584 days; astronomers call this the synodic period of Venus.  And like the hands of a clock, the alignment between Earth and Venus will happen in different directions on their orbits.  So if they start lined up at a transit, in June say, then the next time they line up will be January – where Venus is above the Earth’s orbit.  No transit will be seen.  Roll on another 584 days and the planets are lined up again but in the wrong place for a transit.  Fast forward again.  And again…and again.  At the fifth alignment Venus has gone round the Sun 13 times and almost exactly 8 years have passed on Earth.  Venus and Earth are just about in the same positions they were at during the previous transit.  It’s this periodicity of 13 Venus Years = 8 Earth Years that ensures that if a transit happens then another will usually follow 8 years later.

The long wait between pairs

But transits of Venus don’t happen every 8 years.  The transits of 2004 and 2012 will not be followed by another in 2020.  Although the Venus and Earth are close to being in the same position after 8 years they’re not in exactly the same place.  The transit of 2004 happened on June 8th.  The transit of 2012 will be on June 6th.  The date is slipping back.  The alignment in 2020 will occur on June 3rd by which time the planets will be too far from the node of the orbit and Venus misses the Sun.   The eight-year slippage will continue and eventually, after more than a century, the alignments will occur near the December node where a transit can occur.  Eight years later, another December transit is also likely.  Eight years later Venus misses the Sun and no transits will be seen until the alignment next occurs in early June – more than a century later.

The next picture shows the path taken by Venus as it crosses the Sun during each transit since the 14th century.  In each case Venus moves from left to right.

There are some interesting patterns going on here so let’s discuss them!  Firstly, the transit periods in June and December slip back into the previous month (May and November) because the Julian Calendar was used prior to 1582.

Starting with the 1518 transit we see the following pattern:

1518 <– 8 years –>1526 <——105.5 years ——> 1631 <– 8 years –> 1639 <——–121.5 years ——–> 1761

…and then repeat.  Add these intervals together and we see that transits follow a pattern which repeats every 243 years!  This is because Venus completes almost exactly 395 orbits of the Sun in the time it takes Earth to do 243.  If the correspondence was exact then Venus would follow exactly the same path across the Sun every 243 years.  The transits of 1518, 1761 and 2004 followed very similar paths across the Sun.  Similarly, going back in time in leaps of 243 years: the transits of 1874 and 1631 have tracks close to the northern limb of the Sun.

But 243:395 correspondence isn’t quite exact and Venus follows a slightly different path every 243 years and eventually a transit is missed as in 1388.  The cycle of double transits is broken.

We currently live in an age where Venus transits occur in pairs.  This will change in the future; from the 40th century until the 53rd century, only single transits will take place.

Transits of Venus are incredibly rare events and only the previous six have definitely been observed by astronomers.  In the next part of this series I’ll discuss what astronomers have learned from them.