Newtonian physics was, of course, discovered by Isaac Newton (1643--1727) (see the figure below (local link / general link: newton_principia_2.html) and it continues to be regarded as a true emergent theory in the classical limit where the effects of relativistic physics (combined special relativity (1905) general relativity (1915)) and quantum mechanics become vanishingly small.
Some Qualifications are needed:
Newtonian physics is primarily based on Newton's 3 laws of motion and Newton's law of universal gravitation which we discuss below in section Newton's Law of Universal Gravitation.
There is whole lot of Newtonian physics formalism developed on the basis of the primary bases.
Newton's 3 laws of motion are:
LOCAL means in the same place or nearly the same place. Context as usual determines the exact meaning. Here the meaning is "in the same place".
(vec F_net_ext) = m(vec a_CM) or (vec a_CM) = (vec F_net_ext)/m ,where "vec" means vector (a quantity with a magnitude and a direction), vec F_net_ext is a NET EXTERNAL a href="http://en.wikipedia.org/wiki/Force">force
The Newton's 2nd law of motion is often just referred to as F=ma.
In fact, the internal forces on a body do cancel out pairwise and this is why they do NOT affect the motion of the CM though they certainly affect the motion of the body parts.
Newtonian physics is strongly believed to hold (exactly) asymptotically in the classical limit and to be an emergent theory from TOE-Plus.
Note that Newton's 3 laws of motion are referenced to inertial frames. It is just part of their statements just as we gave them above. However, inertial frames are often omitted in initial presentations of the Newton's 3 laws of motion to students. They should NOT be omitted.
What "referenced to" means is that the laws do NOT work if NOT applied relative to inertial frames.
This does NOT mean the physical laws are wrong somehow since they are explicitly or implicitly formulated as referenced to inertial frames.
Much more explication of inertial frames is given above in Mechanics file: frame_basics.html: Inertial Frames in General.
More general theories can be applied when Newtonian physics fails: e.g., for atoms and molecules, black holes, and the observable universe.
We give explication of the some of the keywords of
Newtonian physics
in subsections below:
mass,
center of mass (CM),
acceleration,
force,
etc.
Formally mass is just defined
as the resistance of
a body to acceleration
relative to an inertial frame
and the body's
gravitational "charge"
(i.e., the strength parameter
of its gravitational effects).
That the two aspects of
mass are the same is just a coincidence
in Newtonian physics, but
general relativity shows that
is a fundmental fact.
Now in the classical limit,
the mass of a body equals the
sum of the rest mass
of baryonic matter particles
(i.e., protons,
neutrons,
and electrons)
that make it up.
Because of this statement,
mass is often defined as the
quantity
of matter
as a shorthand.
Note the rest mass is
the mass-energy
of existence for
massive particles
(i.e., those particles
with rest mass).
Note also that by the dictate of
quantum mechanics,
subatomic particles
and unperturbed
atoms
and
molecules
of a given type are absolutely identical---they have NO freedom to be different.
So each such particle of a given type has exactly the same
rest mass.
Note also again, there are
massless particles:
the photon being the best known.
But actually,
massless particles have
mass since they have
energy as implied by
mass-energy equivalence E=mc2.
They do NOT have
rest mass since they
do NOT exist
at rest
in inertial frames.
Relative to any
inertial frames,
they always move at the
vacuum light speed c = 2.99792458*10**8 m/s
(exact by definition) ≅ 3*10**8 m/s = 3*10**5 km/s ≅ 1 ft/ns
in vacuum and
more slowly in a
media-dependent way
in media.
What the heck is center of mass
and why do we need it?
Short answer: To clear the bar
(see the figure below
(local link /
general link: center_of_mass_fosbury_flop.html).
What about the parts of a body?
The parts of the body are their own bodies with their own
centers of mass
and their own
NET EXTERNAL forces
which include those forces
due to other parts of the whole body.
In the astrophysical realm, there is hierarchy of
systems
of astro-bodies.
Each systems
has its own
centers of mass
which moves under the net EXTERNAL
of a larger system
of astro-bodies.
A system can be analyzed
in a celestial frame
which name can be used as a synonym
for the system itself.
Top of the hierarchy are
comoving frames.
For further explication on the hierarchy,
celestial frames,
and comoving frames,
see file: Mechanics file:
frame_hierarchy_astro.html.
Don't panic,
we'll
NEVER calculate a center of mass---we
just need to understand the
concept
center of mass
and learn how to find it without
calculating it in some simple cases.
Since a center of mass
is a mass-weighted
average position,
for bodies of sufficiently high symmetry,
centers of mass
must be at the obvious centers of symmetry.
There is NO place else centers of mass
could be given that they are mass-weighted
average positions.
So one can find the centers of mass
by inspection
in the figure below
(local link /
general link: center_of_mass_2d.html).
Something which everyone knows (even if they don't know they know it) is to
balance body, the
center of mass must be above
the balance point.
A balance is, of course,
an unstable equilibrium.
A stable equilibrium
is when a body is hanging and at rest.
The center of mass
must be below the hanging point.
Remember bodies always hang the same way from a given hanging point.
We will NOT prove the above statements.
However, there is a simple
empirical method for
finding the
center of mass for
rigid objects.
The method is illustrated in the figure below
(local link /
general link: center_of_mass_hanging.html).
To further explicate
Newtonian physics
we need to define what we mean by
acceleration
and
force.
An acceleration
of a body
is a change in speed AND/OR a change in direction
relative to an inertial frame
caused by a net force acting on the body.
In non-inertial frames,
there can
be accelerations
without a net force: i.e.,
an ordinary net force.
In fact, all
non-inertial frames
can be converted into
inertial frames by
the introduction
of inertial forces
which are NOT ordinary
forces, but they act exactly as if they were.
The upshot is that you can always use an intrinsic
inertial frame
or a converted-to inertial frame,
and you NEVER need to use
non-inertial frames
and we do NOT usually mention them again below.
By physical relationship, one means that the
force depends on the
nature of the bodies and the states of the bodies.
A force can depend on
mass (gravity),
electric charge
(the electromagnetic force),
relative position (gravity,
the electromagnetic force),
velocity
(the magnetic force),
and other things.
If you are NOT
in the classical limit,
you have to use
relativistic mechanics
and/or quantum mechanics.
Newton's law of universal gravitation
for 2
point masses:
Explication:
However, the
gravitational force
between kilogram
masses can be measured
in high sensitivity experiments.
and so is grows small as r increases.
The 1/r**2 behavior is an
inverse-square law.
Double the distance and the force decreases by a factor of 4;
triple the distance and the force decreases by a factor of 9; etc.
But formally the gravitational force
does NOT go to zero until r → ∞.
So, in fact,
gravity is a
long-range force.
The inverse-square law behavior
is illustrated in the figure below
(local link /
general link: function_behaviors_plot.html).
The short answer is to understand all the astrophysical structures, in particular
gravitationally bound systems
which are full of
gravitationally bound
orbits:
i.e., more or less revolving motions relative to
the center of mass
of
center-of-mass inertial frames
constituted by the
gravitationally bound systems.
For a sufficiently isolated
gravitationally-bound system,
all the
astro-bodies
orbit
gravitationally-bound system
center of mass
unaffected by the rest of
observable universe
to high accuracy/precision,
except that the
center of mass
is in free-fall
in the EXTERNAL
gravitational field
due to the rest of
observable universe.
For a NOT sufficiently isolated
gravitationally-bound system,
the EXTERNAL
gravitational field
will exert a tidal force
on a gravitationally-bound system
that will effect the INTERNAL motions (i.e., motions
relative to the center of mass).
A fairly general explication of
orbits is given
in the figure below
(local link /
general link: orbit_defined.html).
For an explication of
rest mass,
mass-energy,
and
E=mc2
(the only physics
formula knows), see
file Relativity file:
e_mc2.html.
Somewhat longer answer: a
center of mass is
the mass-weighted
average position
of a body and we need it since
Newton's 2nd law of motion
(AKA F=ma)
controls the motion of the
center of mass
of a body via the
NET EXTERNAL force on the body.
What if a center of mass
CANNOT be found
by inspection.
The center of mass can be located
deceptively as shown in the figure below
(local link /
general link: center_of_mass_balancing_bird.html).
Of course, you can calculate the center of mass.
How this is done in general is illustrated in the figure below
(local link /
general link: center_of_mass_illustrated.html).
Note inertial frames
are explicated in detial in
file
Mechanics file:
frame_basics.html.
These two kinds of change included in the
definition of acceleration
are illustrated in the two figures just below
(local link /
general link: gravity_acceleration_little_g.html;
local link /
general link: newton_2nd_law.html).
If you know the forces
acting on a body from known force laws, then
physical law
will predict the acceleration
relative to the inertial frame you are using.
The physical law
in the classical limit is
Newton's 2nd law of motion (AKA F=ma).
G * M_1 * M_2
F = --------------- ,
r**2
where
F is size of the pulling gravitational force
each point mass exerts on the other,
gravitational constant G=6.67430(15)*10**(-11) (MKS units),
(M_1 * M_2) is the product of the
point mass
masses,
and r is their separation.
M_1 * M_2 .
It is also inversely proportional to the square of the distance
between the bodies:
1/r**2
The fall-off of the gravitational attraction with distance---the
inverse-square law behavior---in
one sense is rapid.
There is a whole hierarchy of such isolated
gravitationally-bound systems.
To give an example of
gravitationally-bound systems
in the hierarchy consider the following cases:
Local file: local link: frame_basics.html.
File: Mechanics file:
newtonian_physics.html.