__Particles, Newton’s Laws and
Gravitomagnetic Theory
__

__Newton
1.
__

Newton’s 1^{st}
law of mechanics essentially
distinguishes inertial frames of reference from non-inertial frames. By
implication his other laws apply only from the perspective of inertial frames.
All of the rules/equations of gravitomagnetic theory are also cast in inertial
frames of reference, as are Maxwell’s equations and the Lorentz force law
(from which much of gravitomagnetic theory has evolved).

__Newton
3.
__

Newton’s 3^{rd}
law states that in general every particle in nature can experience *two*
kinds of force: (1) *action* forces, as
a consequence of the particle being acted upon by others in its environment, and
(2) *reaction* forces, as a consequence
of the particle being acted upon by its own acceleration-induced gravitomagnetic
fields. The general idea is that these reaction (or “self”) forces are
passed through to the particles exerting the action forces. The law states that
whenever one of these forces is present, so is the other. Furthermore, these two
forces are always equal in magnitude and oppositely directed.

__Newton
2.
__

Newton’s 2^{nd}
law states that whenever an action force acts on a particle, the particle’s
time rate of change of ** P**, its
“quantity of motion”, (

** F**
= d

In cases
where v<<c, m is practically constant at m_{0} (the so-called rest
mass) and it is convenient to say more simply that

** F**
= m

__Newton’s
Law of Universal Gravitation.
__

Newton
finished his theory with his Law of Universal Gravitation. The idea in this case
is that every particle has an intrinsic quantity of matter or mass, m. Given two
particles, separated by a displacement ** r**
from the acting to the reacting particle, each particle experiences a
gravitational force

__F___{1}
= Gm_{1}m_{2}__r___{1,2}/r_{1,2}^{3},

__F___{2}
= Gm_{1}m_{2}__r___{2,1}/r_{2,1}^{3}.

Since the
force is always *attractive*, the
particle masses are assumed to be mathematically *imaginary
*in gravitomagnetic theory. On the other hand, the force in Newton’s 2^{nd}
law is real, and it must accordingly be
that the particle’s *inertial* mass is
real. Thus in gravitomagnetic theory every particle has an imaginary
gravitational mass, m_{grav}, and a real inertial mass, m_{inert}.
For any given particle, the inertial mass equals the magnitude of the
gravitational mass:

m_{inert}
= |m_{grav}|.

__The
Mechanics Paradigm.
__

The general
paradigm for analyzing the behavior of a given particle is to calculate the
imaginary gravitational and gravitomagnetic fields (** g**
and

** F**
= m(

Note that
since m and ** O** are imaginary, a

Newton’s
gravitational force law is replaced by much more difficult equations for ** g** and