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<*munch*>

In article <1240@ncr-sd.UUCP> randall@ncr-sd.UUCP (0000-Randall Rathbun) writes:

>                                                   Does somebody know if all 3
> planets (Mercury, Venus, Earth) transit the Sun from Mars, all 4 from Jupiter,
> all 5 from Saturn, etc,etc. Are there some, from which transits are never seen
> of all the inferior planets (Pluto?) How often do the above transits occur?
> Would appreciate this information. Thanks.

    Each planet should see transits of all planets inferior to itself.  Proof:
The orbital planes of every pair of planets necessarily intersect in at least a
line.  By happenstance, sooner or later both planets will both be on the same
side of the Sun, "on" that line.  At that time, the superior planet will see
a transit of the inferior.

    The "on" is in quotes because what I really mean is "sufficiently close to
the line that the angle Sun-superior-inferior is less than the angular radius of
the Sun's disc as seen from the superior planet."

    Actually, if the angle between the two orbital planes is sufficiently small,
the two planets can both be quite far from the actual intersecting line, in the
same direction around the orbits, and still have a transit.  If both planets
orbited in the same plane or sufficiently close to it, there would be a transit
every time the inferior one caught up to the superior and passed it.

    Stroboscopic effects might lead to long intervals in which no transits
were seen.

    A way to think about the probabilities is:  At the distance from the Sun of
the superior planet's orbit, how wide is the cone of space within which an
observer would see the inferior planet in transit?  What are the odds that the
orbit of the superior planet lies within that cone?  What are the odds that the
superior planet is in the right place in its orbit at that time?

Jay Freeman -- Schlumberger Palo Alto Research -- Canonical Disclaimer