> First, for a Mercury transit and a Venus transit to occur concurrently,
> the nodes of Mercury's and Venus' orbits must be sufficiently close
> toghether. Today, Venus' node is "ahead" by some 28 degrees (that's why
> Venus transits happen about one month later in our calendar year than
> Mercury transits), but Mercury's node is catching up, and in almost
> precisely 10,000 years the two nodes will conicide. Then there'll
> be a "window" 3400 years wide and centered very nearly at 12000 AD
> when concurrent Mercury and Venus transits will happen.
Jean Meeus announced on the Solar Eclipses mailing list recently that he had
co-authored a paper on this very question (J Meeus & A Vitagliano, Journal of
the British Astronomical Association 114, 3, 2004). And he kindly sent me a
copy :-)
Quick summary:
- Yes the nodes of Mercury & Venus are slowly moving together and will
coincide in about 12,720 (ie: about 107 centuries from now). Incidentally
this movement will also shift the "transit months" for both planets to March
& September. Assuming there's no calender change by then.
- Simultaneous transits become -possible- when their line of nodes are less
than 6.6 degrees apart. This happens between the years 10,100 and 15,400
approximately.
- However, a rigorous numerical integration, using JPL ephemeris DE406 for
all planets + Ceres, Palls & Vesta, reveals NO simultaneous transits between
the years 5,000 and 20,000. A near-miss case will occur on 13,425 September
17 (Dynamical Time), with a Mercury transit beginning about 9 hours after the
end of a Venus transit. Venus then occults Mercury four days later.
- The search was extended far into the past and future, and eventually
simultaneous transits occur on 69,163 July 26 and 224,508 March 27 (Dynamical
Time), and another near-miss on -90,109 February 7 (Julian calendar).
- Martian observers will have to wait until 571,741 to see a simultaneous
transit. Of Venus, with the Earth and Moon.
I suspect Guide's planetary equations may not be good enough to simulate such
remote events accurately?
Meeus & Vitagliano also investigated transits occurring during a solar
eclipse, and found no case for an Earth observer before 6757 July 5. However,
they find a simultaneous Mercury transit and lunar eclipse on 2236 November
13, where Meeus comments
"...an observer on the Moon would see the Earth passing over the Sun during
the transit. This was confirmed by using the software Guide 7.0."
I think Bill can regard that as a compliment... :-)
But I have noticed one quirk with using Guide to find transits. It works fine
if you use the "show eclipse" method. But it fails to find any transits - or
the inevitably associated conjunction with the sun - if you use the "show
conjunction" method. Curiously, "show conjunction" does find the times when
the planet is occulted by the sun's disc.
Incidentally, transits of the inner planets seen from the outer planets are
surprisingly common. For example, an Earth transit occurs next January for
Saturnian observers. I'm told that Cassini's cameras -could- resolve the 1.8
arcsecond dot of the Earth, but they don't want to risk damage to them so
early in the mission.
cheers,
--
Fraser Farrell
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