Hi Fraser,
Thanks for the comments on this. I knew Jean Meeus had done some
work on the simultaneous transit issue a while back, but couldn't
remember what he'd come up with for conclusions.
You are correct in thinking that Guide isn't up to such truly
distant-future (or distant-past) computations. VSOP is intended to
cover the years -2000 to +6000 with arcsecond or better accuracy,
degrading a bit outside that range. DE-406 covers the years -3000
to +3000. It sounds as if Meeus and Vitagliano just took the DE-406
initial conditions and integrated them out a heck of a lot farther.
I've contemplated doing this, making a sort of "DE-406a" file. It
need not be tremendously huge; at such distant dates, there is no
point in attempting to store ephemerides at great precision.
It would be an interesting project, but I've got a few too many
of those going on, so this one has been of low priority.
"...Incidentally, transits of the inner planets seen from the
outer planets are surprisingly common."
A while back, I ran some tables of such events. If you download
this file to your Guide directory (about 2 KBytes):
http://www.projectpluto.com/ear_tran.etb
...under Tables, Miscellaneous Tables, you'll see a "Transits
of Earth from Mars, -1000 to +3000" listed. It also lists a few
transits of Jupiter as seen from Saturn (not many; it's a rare event)
and the only transit of Saturn as seen from Uranus that I could find.
You will have to set your "home planet" to Mars, Saturn, or Uranus
to get these events to show up properly in Guide.
"...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."
An understandable level of caution. You _can_, however, simulate
this in Guide. Hit Ctrl-B (or use Go To... Object Name) and enter
"Cassini". Guide will recenter on that probe (though you won't see an
indicator for it on-screen).
Next, hit the '<' (less-than) key. Guide will switch to Cassini as
its "home planet", so you're now viewing the universe as seen from
Cassini. Saturn will be (right now, at least) a ringed, gibbous
object a bit larger than the moon.
Set your date/time to 14 January 2005, 0:00 UT, and "go to" the
earth. You'll see it transiting in front of the sun.
-- Bill