Arild Moland wrote:
> Hi folks,
>
> after the recent Venus transit, somebody in our astronomy club had speculated
> how often we should be able to observe a Venus and Mercury transit at the same
> time, ie. both planets on the Sun's disk simultaneously.
>
> He arrived at an interval of once every 745 thousand years, and even though I
> can't say if that makes sense, it's certainly a pretty rare event.
I think that figure is overly pessimistic.
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.
Now, this merely tells that concurrent Mercury/Venus transits are possible
at that time, but will one such event actually happen? I threw some
figures at this and concluded that on the averade about 0.9 double
transits ought to happen within each such 3400 year "window".
Mercury's node will overtake Venus's node every 63200 years. Which means
that on the average (over a very long time) there should be one double
transit every 63200/0.9 = 70200 years, but they should occur at intervals
of an even multiple of 63200 years. Of course there may occasionaly be
more than one double transit within one single 3400 year "window".
Note that this is only a rough estimate, based on current inclinations
and node rates of Mercury and Venus. Over time scales of hundreds of
thousands of years, these figures are likely to change significantly.
My arguments above may be reasonably valid for the next "window"
between 10300 and 13700 AD, but beyond that all bets are off.
So why not let your Guide search for Mercury and Venus transits
between the years 10000 and 14000 AD, and then manually inspect these
lists to see if any of them happen concurrently?
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The closest so far to a concurrent transit that has occurred since the
invention if the telescope was in 1631, when there was a Mercury transit
in November and a Venus transit in December. i.e. just one month apart.
These were also the first transits to ever be predicted, but they weren't
observed.
In 1769 there were also transits of both Venus and Mercury, but this time
they occured five months apart.
We have other possible "double transits" too: a transit concurrently
with a solar eclipse. I'm not aware of any such event either, but two
near-misses were on -476 May 22 and on 1769 June 3, when a total solar
eclipse occurred within some 10 hours of a Venus transit.
> Now, I wondered if Guide could give me a hint on when this would occur, but I
> then found that the Extras | Find conjunction menu option would only work with
> the two last selected celestial bodies.
>
> The question is, is there a way to make Guide find conjunctions of more than two
> planets?
>
> Best regards,
>
> Arild :)
>
> ---------------------------------
> http://www.astro.uio.no/~arildmi/Scopes/
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> http://www.astro.uio.no/nas/
> arildmi@...
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