On Monday, March 5, 2018 at 1:19:07 PM UTC-7, Gerald Kelleher wrote:
If you can distinguish between the open-ended illusory loop of Mars from the
closed actual loop of Venus you have already come to understand what Galileo and
the original Sun centered astronomers did not and that does nothing to diminish
those astronomers. I do not even ask observers to know why their perspectives
were incomplete but it does help to know why Venus ad Mercury do not trace out
open-ended loops as previous views held -

You are expressing a genuine astronomical fact here, but you have also made an
error.

With the superior planets like Mars and Jupiter, the general apparent motion is
due to their actual orbits, while the loops, that give rise to retrograde
motion, are due to the Earth's motion.

With the inferior planets like Mercury and Venus, the general apparent motion is
due to the Earth's motion around the Sun, while loops, that give rise to
retrograde motion, are due to their own actual orbits.

That is true. And their orbits around the Sun are closed ellipses (neglecting
details like perturbation). But the loops due to those closed orbits in their
*apparent* paths, which also include the results of the Earth's orbit, are still
open-ended - not closed.

John Savard