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Re: Retrograde Motion - Virtual Particles

This guy David is phenomenal: Posts last night at 12m and then again at 6am
-- Reminds me of a guy who wears both a belt and suspenders (:-)

Yes, Dave, I remembered the Copernican plots (your presentation below) last
night after I posted to the list -- Though yesterday I started to doubt
myself, there *now* is no question in my mind re regression of the outer
planets (I don't know if I really want to call the motion of the inner
planets regression). But my main problem all along is *visualizing* what
happens as opposed to an academic belief. I think I should just chalk this
up to senility and old age forgetfulness and let it go for a while -- until
it comes back -- maybe.

Thanks all for trying to help this aging professor.

Jim Green

Instead of using a
straight road try having both cars on a circular, or better still, an oval
racetrack with the fast car on the far inside of the track and the slow car on
the far outside. Imagine how the direction of the line connecting the two
cars changes direction as the two cars go around the track. Alternatively,
(if you don't have access to a racetrack) draw two concentric circles on a
sheet of paper and place a series of equally spaced dots around the circum-
ference of each of the circles making sure that the dot spacing around the
inner circle is greater than the dot spacing around the outer circle. Now
draw a line through one dot on the inner circle which also goes through a dot
on the outer circle. Next draw another line connecting the two dots each
adjacent to the two previously connected dots of the previous line. Keep this
up connecting the sequential series' of dots on both circles until you run
out of dots on the inner circle. (If you go around the circles connecting the
dots in a CCW direction, this is like looking at the planets orbiting the Sun
from the Northern side of the ecliptic. If you went around the circles in a
CW direction, this is like watching the planets go around the Sun from the
Southern side of the ecliptic.) After the lines are drawn look at the
direction of each of the sequence of lines drawn in sequence. The overall
pattern is that the line directions tend to rotate in the direction that you
traversed the circles, but the directions of the lines where the inner circle
dots are on the same side of the circle as the outer circle dots (where the
lines point mostly radially outward away from the circle's center) tend to
rotate the opposite way of the overall line rotation sequence.

I hope this helps you visualize the situation.

David Bowman
Georgetown College