Are there ever any simultaneous transits of both Mercury and Venus as seen from the Earth?

Question

Transits of Mercury happen fairly frequently due to its short period, but transits of Venus are less frequent. I've looked over the data available to me and found that there have been transits of both planets in the same calendar-year in 1631 (Nov & Dec) and in 1769 (Jun & Nov).

What would really be interesting is if the two planets transited the Sun at the same time! With the rule being, that the second transit begins before the first transit completes.

Can we figure out if they have ever so transited, or if they ever will so transit?

Answer 1

EDIT: As it turns out, I'm not the first or even the second person to run calculations like this:

• https://www.fourmilab.ch/documents/canon_transits/

• http://www.solexorb.it/SolexOld/Simtrans.pdf

Meeus' work (second link) mentions the 13425 CE event in "Table 1. Simultaneous and near-simultaneous transits of Mercury and Venus, years 1 to 300,000"

Within the limits of DE431 (7 May 13201 BCE to 7 May 17091 CE), there is no time at which both Mercury and Venus transit the Sun.

The closest we get to this:

• On 16 Sep 13425 CE at 11:57pm UTC, Venus starts transiting the Sun. This transit ends the next morning (17 Sep 13425 CE) at 7:30am.

• Less than 9 hours later, at 4:27pm, Mercury starts transiting the Sun. This transit ends at 10:26pm.

The program I used to compute this:

https://github.com/barrycarter/bcapps/blob/master/ASTRO/bc-solve-astro-13227.c

The list of transits I computed while solving this:

https://github.com/barrycarter/bcapps/blob/master/ASTRO/mercury-transits.txt.bz2 https://github.com/barrycarter/bcapps/blob/master/ASTRO/venus-transits.txt.bz2

Although I believe this answer is correct, Stellarium does not agree with me, and HORIZONS doesn't compute positions past 9999 CE, so don't put too much faith in this answer, since there's no good way to confirm it. I believe that I'm correct and Stellarium is wrong this far in the future, but it could be the other way around.

Even if my calculations are correct, the uncertainty in calculating the relevant positions (Sun, Merucry, Venus, Earth) this far in the future is high. On their own transit pages, NASA only computes Venus transits from 2000 BCE to 4000 CE, and Mercury transits from 1601 CE to 2300 CE, even though they could've made the same calculations I made from 13201 BCE to 17091 CE:

• http://eclipse.gsfc.nasa.gov/transit/catalog/MercuryCatalog.html
• http://eclipse.gsfc.nasa.gov/transit/catalog/VenusCatalog.html

This suggests NASA isn't confident enough of Mercury/Venus (and Earth/Sun) positions to predict that far in the past or future, so my results may be fairly inaccurate.

Answer 2

As others have calculated, there are no predicted double transits. Since Venus transits for about 12 hours each hundred years (roughly), Venus is in transit for about 1/100000 of the time.

Thus there is a (roughly) 1 in 100000 chance that a randomly chosen transit of mercury will coincide with a transit of Venus. Since Transits of Mercury occur every 10 years or so, one would expect a double transit to happen on average once every million years. This is clearly a very rough estimate, but we should not be surprised that such an event has not happened in the historical period.