Angular Momentum
Angular mass momentum is the spin analog of Newton’s first law. We
start an object spinning in free (unencumbered) space and it will
continue to spin at uniform velocity, perhaps forever. We start an
object moving rectilinearly in free space and it will continue to
uniformly move, perhaps forever. We have angular and linear momentum.

So my question was “How do we get from the first law single body, spin
angular momentum, to a two body orbital angular momentum”? Obviously
something must support such a “jump”.

Section 4 in this series subsumes angular momentum in terms of
Kepler’s law of areas, and Newton’s uniform motion, describing a
perfectly circular orbit. Recall that Newton used a perfect circle and
uniform motion as the basis for the derivation (See Section 4, this
series of posts). A 2D perfect circle in a uniform spinning motion is
the 2D kinematic equivalent of a 3D solid, uniformly spinning sphere,
and a 2D solid, spinning disk. Recall that Newton used Kepler’s least
action consistent, law of areas, to support his supposition for a mass
derived centripetal force, as his mathematical argument that carried
that force to the entire universe, as the means to generalize his
notion of gravity, as the cause of the least action order we observe
in the celestial least action universe (See Section 4, this series of
posts).

Kepler’s law of areas is the naturally occurring, celestial orbit
least action consistent, kinematic analog, of the uniform spinning
circle, and the kinematic properties of the spinning sphere and disk.
The common constant kinematic connection between the four is angular
velocity, which is an artifact of the spinning circle and spinning
sphere, and spinning disk, and is met by the celestial, least action
consistent, orbital (conic section) motion. These are all least action
consistent properties.  Three of which are artifacts of a uniformly
spinning circle, sphere and disk. One of which (Kepler’s law of areas)
apparently obeys a time function independent of mass, to maintain
angular velocity.

I asked, “So how do we get planet surface mass into the celestial time
controlled orbits”?  Well, we just multiply two sides of a least
action consistent equation by unity in the form of [m/m]. In other
words we hitchhike (Hijack or commandeer are perhaps better terms).
The least action consistent angular velocity, picked us up (gave us a
ride), and became least action consistent angular momentum, by
mathematical decree. Our least action consistent mathematics, carried
our conserved planet surface object mass, as an “independent”, to the
least action consistent, celestial orbit. Consequently, the idea for
angular momentum as a causal descriptor for celestial orbital motion,
is kinematically consistent with the celestial angular, time
controlled velocity, and the conserved but celestial, velocity
independent, planet surface object mass. Here angular orbital momentum
does not speak to a controlling mass, much less a proportional to
planet surface object, controlling mass.

Note that our planet surface object mass (this includes our artificial
satellites) is conserved, and operates within the least action
consistent, time controlled orbits, without an orbit causal effect.
We just put planet surface object mass in the least action consistent
orbit. Therefore the idea for angular momentum,, as a causal
descriptor for orbital motion, is kinematically consistent with the
angular time controlled velocity, and the conserved, but independent,
planet surface object mass momentum, that we measure.

Since the Earth attractor does not act on mass during orbit, escape
velocity and freefall, we can easily quantify its celestial presence,
solely in terms of what it (planet surface mass) does act on. That is
planet surface mass objects, which we qualify as. Isaac Newton
justified this operation by stating “Since it is true for all objects
we can measure, it is true for all objects whatsoever”. Paraphrased.
Consequently, we defined the universe in terms of the force we had to
exert to duplicate the least action events. This is regarded today as
Newton’s Great Syntheses. The principle has been incorporated into the
atomic study known as particle physics.

Afterword
The tendency for the massive orbital body to fly off into space is a
consequence of mass and possibly the cause of the eccentricity in
orbit, but is not necessarily proportional to planet surface object
mass, and is subject to the time function of the least action
consistent, attractive mechanism, probably initiated by
electromagnetic causes.  Therefore the idea for angular momentum as a
causal descriptor for orbital motion is kinematically consistent with
the angular time controlled velocity, and again, the conserved, but
independent planet surface object mass momentum, that we measure

A supremely functional working “subjective” quantitative concept, that
initiated the scientific age for mankind. Even with the qualifying
statements Isaac Newton increasingly put forward as he aged, those who
followed, ultimately led us to conceptual flights of frivolous
fantasy, as well as intellectual dead ends, like; Big Bangs and Black
Holes, etc.  All of it based on our tactile sense, or “feel” of force.
johnreed,  November 20, 2009