Simultaneous Planetary Transits
Jeliazko Jeliazkov
When an unusual astronomical event occurs, people inevitably ask questions such as When will it happen again?
.
On 2006 November 8 there was a transit of Mercury across the disk of the Sun, and on 2004 June 8 there was a transit of
Venus. Some asked whether it is possible that Mercury and Venus - the two interior planets - can pass simultaneously over
the solar disk, and when this will happen.
A simultaneous transit of Mercury and Venus is an extremely rare phenomenon. Presently, such simultaneous transits cannot take place, but they are possible in the far future as they were possible in the far past. There are probably only several per million of years.
For a simultaneous transit to occur both planets must be close to inferior conjunction and close to one of their nodes. The nodes are the only two points of a planet's orbit where it crosses the ecliptic. The line trough these points is called line of nodes. As the Sun has an appreciable apparent diameter a planet does not need to be exactly at one of the nodes at inferior conjunction in order a transit to occur. Presently, a transit of Mercury is possible when the planet is withing 2.7° from descending node or within 4.8° from ascending node. For Venus limits are 1.8° and 1.7°, respectively. However, presently lines of nodes of Mercury and Venus form an angle of 28.3°, thus both planets cannot be in transit at the same time. Due to perurbations of other bodies lines of nodes changes its orientation with time, with a different rate for all planets. So the angle of 28.3° is not constant and is currently descreasing by some 0.285° per century.
Prediction of any phenomena, simultaneous transit in our case, however becomes less and less reliable as one goes further and further away in the past or future, no matter how accurate equations are used and how precise starting conditions are. This is because, like any dynamic system, Solar System is chaotic. Inner solar system (Mercury to Mars) has an estimated Lyapunov time of around 5 million years. From major planets Mercury has the shortest Lyapunov time of about 1.3 million years. However, due to accuracy of ephemerides (and probably to a lesser extent due to incomplete modelling, missing asteroids, etc.) timespan for reliable prediction becomes significantly shorter - 100-200 millennia both in future and past.
During the time interval BC 250 000 - AD 250 000 only two simultaneous transits of Mercury and Venus were found, both in future - AD 69 163 July 26 and AD 224 508 March 29. These times are in Terrestrial Time. On several occasions during the first 100 millennia of the Common Era simultaneous transits of Mercury and Venus on Mars occur - 18713 Oct 08, 19536 Aug 09, 20029 May 21, 87892 Jan 07. Going significantly farther doesnt make any sense since Martian orbit experiences greater perturbations from asteroids, thus timespan of reliable prediction is even shorter.
A list of all kind of simultaneous planetary transits from BC 5 000 to AD 10 000 can be found here.