6 Apr 2000 16:46

Re: Re: Modeling the Orbitsphere

```Luther, I tend to agree with you. I dont see why the summation should
necessarily extend to root 2 pi when it would make sense to rotate thru pi
to get to the other side - so to speak.

But then look at it this way:

In normal cartesian coordinates, if a point a is moved up the y axis by some
distance r, the distance traveled is then r. If another point b is moved
along the axis x by r, then the distance travelled is also r. But the
distance between a and b if both are moved simultaneously along their
respective axes is obviously going to to be sqrt(r^2+r^2) = sqrt(2)*r. In
other words, the length of the line ab along the plane of ab in units of r
is going to be sqrt(2) times r. Please forgive the apparently childlike
explanation, but this is partially me explaining to myself too.

Now, similarly with angles. If a plane (orbitsphere or whatever) is rotated
by angle a in the plane of axis y, while at the same time being rotated by
angle a in the plane of axis x, then the total angle of rotation to get back
to the starting point (albeit with the z axis now flipped 180 degrees) is
also going to be Sqrt(2) times the angle a, but, and this to me is the key,
ALONG THE PATH OF OF SOME SOME ARBITRARY POINT DESCRIBED - in this case on a
great circle, in agular increments as measured at the origin. In other
words, each time you move thru delta a in one direction and at the same time
delta a at 90 degrees to that direction, the effective angle moved is then
sqrt(2) times delta a, and thus the total angle moved must then be to a
maximum of sqrt(2)*pi. But this is in terms of the combined angle as moved
thru both axes.

Now this is where I start to get really confused. Because the incremetal
step chosen for n in going from n =1 to some maximum, then maximum would
```

6 Apr 2000 23:57

Re: Re: Modeling the Orbitsphere

```--- In hydrino@..., Dudley Baylis <dudleyb <at> g.yahoo.invalid> wrote:
> This brings me to another point. has anyone any ideas on why two
point
> charges on two current great circles are chosen for the modelling
excercise.
> I can see that it produces nice results and patterns that perhaps
correspond
> in different views to conventional distribution densities or
electron
> orbits. But why two. Why not one, or one for each axis?

One set of great circles corresponds to magnetic lines of force, the
other set corresponds to electric lines--these are perpendicular to
each other as in classical electromagnetism.

There are actually two sets of these two sets aligned symmetrically
at opposite sides of the orbitsphere--forming a kind of square if you
look at it head-on at some instant in time. So there are actually
four total great circle groups. This is necessary to provide
symmetry and represents a minimum energy configuration where the
opposing magnetic and electric "sides" of the square are as far apart
as possible. This entire structure rotates in 3 axes and thereby
creates the spherical distribution we all know and love. See the
orbitsphere diagrams in the book (although they aren't effective
enough in communicating the structure and motion IMO).

Note that strictly speaking these are not *point charges* but the sum
of an set of infinitesimal slices of a *surface charge*--an
integration approach. Therefore, while Mills talks in terms of these
great circles you have to keep in mind that they're just a
```

7 Apr 2000 02:49

Re: Re: Modeling the Orbitsphere

```--- In hydrino@..., "Steven Florek"
<florek <at> e.yahoo.invalid> wrote:

> Note that strictly speaking these are not
> *point charges* but the sum
> of an set of infinitesimal slices of a *surface charge*--an
> integration approach.

> Therefore, while Mills talks in terms of these
> great circles you have to keep in mind that they're just a
> mathematical device for describing in parts a
> non-rigid surface with
> multiple features (magnetic force lines,
> electric force lines, etc.)
> in superposition and possessing complicated rotations.

Complicated is right! Yikes! I've just finished my first stab at
modeling this in Mathcad. It's not complete, but I need some help.
The file is called "Orbitsphere.mcd" and is located at

I saved it in Mathcad 6 format. I hope the Mathcad types out there

If anyone can show me how to get both "baseline" orthogonal circles
onto the same scatter graph, I'd appreciate it. That'll be the first
step I need to model the entire orbitsphere onto one scatter graph.

Luke Setzer
```

7 Apr 2000 13:52

Re: Re: Modeling the Orbitsphere

```--- In hydrino@..., "Luther Setzer"
<luthersetzer <at> y.yahoo.invalid>
wrote:

> The file is called "Orbitsphere.mcd" and is located at
>
>
> I saved it in Mathcad 6 format. I hope the Mathcad types out there