[geocentrism] Re: Sphere movement
- From: Paul Deema <paul_deema@xxxxxxxxxxx>
- To: Geocentrism@xxxxxxxxxxxxx
- Date: Sat, 17 Nov 2007 07:37:44 +0100 (CET)
Neville J
Concerning your post this thread - From Neville Jones Fri Nov 16 21:51:44 2007.
Here is my promised reply.
OK, here is my view of what I think your post is saying. I will try to make
simple statements (which will rely upon your willingness to understand) and to
avoid terminology which is precise in this specialised arena.
1. Take a disk of convenient size in free space with a rod passing orthogonally
through its centre and cause it to turn about the rod. At any distance greater
than zero from the rod, a point on its surface will describe a circle. Neither
the rate at which it turns nor the frequency at which we sample its position
will alter this fact.
2. Place a cylinder on another rod passing orthogonally through the disk and
located near the rim. Cause this cylinder to turn about this second rod at a
rate ten times greater than and in the same direction as the disk. A point on
the curved surface will now describe a circular path which when added to the
circular motion of the disk will describe a 'flower pattern' path having ten
petals.
3. Diametrically opposite the cylinder and also near the rim of the disk, embed
a small disk in the same plane as the large disk. Cause it to turn at the same
rate as the large disk and in the same plane -- but in the opposite direction.
Pass another rod orthogonally through the centre of this small disk and at a
suitable distance from this small disk, bend it through 45 deg. Place a second
cylinder on the bent rod and cause it to turn at a rate equal to the first
cylinder and in the same direction. A point on the curved surface will describe
a complex path which will be the vector sum of a point travelling in a large
circle and a point travelling in a small circle the plane of which is inclined
to the large disk at an angle of 45 deg and whose plane of rotation is constant.
Not a part of the main thrust of this mechanism but which may help to visualise
the motions involved is the following.
4. Instead of the mechanism of 3. above, place a cylinder on a rod held
parallel with the large disk and tangential to it. Cause the cylinder to turn
at a rate ten times greater than the large disk. A point on its curved surface
will describe a circular path about the large circle which is easy to visualise
-- like a stretched spring enclosing a donut.
5. As for 4. above but place the rod on a radius ie at right angles to the
tangent. A point on the curved surface will now trace a path which can be
visualised in two steps. First, stretch out a spring and squash it 'sideways'
so as to produce a flat linear 'flower pattern'. Second, take this flat linear
'flower pattern' and wrap it around a cylinder.
6. As for 4. and 5. above except that the rod is now fixed to the small turning
disk of 3. The resultant pattern will be a hybrid of those produced in 4. and
5. that is a stretched spring varying from squashed to not squashed and wrapped
around a cylinder at two points and a donut at two points, the latter at 90 deg
separation from the former.
7. If you are still with me, the pattern of 6. is nearly the pattern of 3. All
that is needed is to repeat the exercise with the rod bent over at 45 deg and
I'll leave you to do the visualising 'cos I don't think I can describe it.
Now it would be useful to observe this mechanism 1. to 3. from the point of
view of the reference points.
8. The first point (on the large disk) when looking out in the plane of the
disk will see objects in the distance moving past his line of sight in a
straight line. If he looks up he will see objects turning about a stationary
point P1 directly above the rod making circles whose diameter depends upon
their angular separation from a line to the stationary point P1.
9. The second point (on the vertical cylinder) when looking out in the plane of
the disk will see objects in the distance moving past his line of sight in a
straight line at a rate ten times greater than the first point sees. If he
looks up he will see distant objects turning about the same stationary point P1
making circles whose diameter depends upon their angular separation from a line
to the stationary point P1 at a rate ten times greater than the first point
sees.
10. The third point (on the inclined cylinder) when looking out in the plane of
the disk will see in the distance, objects moving past his line of sight rising
and falling sinusoidally above and below his horizon at a rate of ten cycles
per turn of the disk. If he looks up he will see distant objects turning about
a stationary point P2 making circles whose diameter depends upon their angular
separation from a line to the stationary point P2 at a rate ten times greater
than the first point sees. This stationary point P2 will be a fixed 45 deg from
the stationary point P1 seen in 8. which will simply be a point turning about
this stationary point P2 (and vice versa).
Paul D
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