Re: Spheres



On Sep 28, 9:14 pm, Claude Hopper <boobooililili...@xxxxxxxxxxxxxx>
wrote:
Everything forms a  sphere. Atomic particles are spheres. Atoms are
spheres, water forms a sphere in space. Moons and planets are spheres.
Why aren't galaxies spheres? Why aren't galaxy clusters spheres? The
total universe is depicted as a sphere.

Everything that has one degree of freedom is spherically symmetric.
The major forces of the universe follow the inverse square law - which
has only one degree of freedom - 1/r^2 - r can be given as a scalar,
but if you want to draw pictures, you must give r as a vector -
usually of 3 dimensions,.

The universe is dominated by gravity from the smallest scale to the
largest; Newton figured out how force and geometry are related

F = G*M*m / r^2

Where G = gravitational constant = 6.67e-11
M = mass 1 = kg
m = mass 2 = kg
r = radius between both masses = meters

Only one degree of freedom,even if radius is 3 dimensional. That
means across those three dimensions the system must be sphericallly
symmetric.

Atomic particles on the scale of atoms are dominated by electrostatics
- this was first given by Coulomb's law;


F = (1 / (4 *pi)) * k * Q * q / r^2

Where pi = 3.1416
k = electric constant = 9e+9
Q = electrostatic charge Coulombs
q = electrostatic charge Coulombs
r = radius meters

And the smallest and largest of things are tied together by light
which is given by

I =( P / (4*pi)) * (1/r^2)

Where I = irradiance power /m2
P = power of light
r = radius meters

This is spherical because the area of a sphere is given by

A = 4 pi r^2

Now, galaxies are collections of free flying spherical objects, stars,
that act under mutual gravitatoin and conserve their angular momentum
around a common center of mass - this is not spherically symmetric -
in fact there is one orientation in space associated with their
combined angular momentum - the plane of the galaxy is the plane
normal to that orientation -

Angular momentum of a particle about a given origin is defined as:

L_ = SUM( R_i x Mi * V_i )
where:

L_ is the angular momentum vector of the particles,
R_i is the position vector of the ith particle relative to the
origin,
Mi is the mass of the ith particle
V_i is the velocity vector of the ith particle, and
x is the vector cross product.

If you carry out the cross product of all the particles locations and
their common center of mass you will find there is one orientation in
space associated with the particle collection and that the plane that
is defined as normal to that collection, is the plane of rotation.

The solar system also is a collection of bodies orbiting the sun, most
of which occupy the plane of the ecliptic.

Now, not all galaxies are planar, there are globular clusters,for
instance and the universe appears to have no rotation around its
center of mass. This is a function of interaction and interaction
times and on the scale of galaxies expansion of the cosmos.

That is,it takes time and collisions for a collection of bodies to
fall into a disk and collapse into a planar collection of coorbiting
objects around a central mass - either a black hole at the center of a
galaxy or a star at the center of a planetary system.

OIne might expect that the entire cosmos may some day be a collection
of galaxies orbiting a super-supermassive black hole - but that
requires that all the galaxies to have interacted with one another to
transfer momentum to one another - to create such a super-galaxy.
This takes time, and as that is going on, the universe is expanding -
which is a spherically symmetric sort of thing.
.



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