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".
A uniform motion is more usually described as a CONSTANT velocity.
And velocity is a vector: a quantity with both a magnitude and a direction.
(vec F_net_ext) = m(vec a_CM) or (vec a_CM) = (vec F_net_ext)/m ,where "vec" means vector (a quantity with both a magnitude and a direction recall), vec F_net_ext is a NET EXTERNAL force, vec a_CM is CM acceleration, and m is mass (i.e., the body's resistance to acceleration).
The Newton's 2nd law of motion is often just referred to as F=ma.
Note, yours truly holds the perspective that Newton's 1st law of motion is a special case of Newton's 2nd law of motion, and so there are, in fact, really only 2 Newton's laws of motion. Many agree with this perspective and many do NOT. For yours truly a main reason for the held perspective, see below section Newtonian Physics as a Package.
Note also, it does take a proof to show that an "ELEMENTARY" Newton's 2nd law that refers to point masses (ideal bodies of zero size) combined with Newton's 3rd law of motion yields the Newton's 2nd law given here that refers to centers of mass of finite bodies. But this proof is beyond our scope. For the proof, see, e.g., Lecture Notes 5, p. 17. However, you could inverse that proof and show that Newton's 3rd law is a corollary of the Newton's 2nd law given here. This may be the more fundamental way of the treating Newton's 2nd law and Newton's 3rd law.
In fact, the internal forces on a body do cancel out pairwise and this is part of the proof as to why they do NOT affect the motion of the CM though they certainly affect the motion of the body parts.
Actually, there are exceptions to the Newton's 3rd law as simply stated. However, those exceptions are treated by the more general principle of conservation of momemtum (see Wikipedia: Newton's laws of motion: Newton's third law; Go-7--8).
Newtonian physics is strongly believed to hold (exactly) asymptotically in the classical limit and to be an emergent theory from TOE-Plus.
Now most of everyday life and most astro-bodies from interstellar medium (ISM) to large-scale structure of the universe are close enough to the classical limit that they obey Newtonian physics to a high accuracy/precision.
More general theories can be applied when Newtonian physics fails: e.g., for atoms and molecules, black holes, and the observable universe.
Note, Newton's 3 laws of motion
are referenced to inertial frames.
It is just part of their statements just as we gave them in
above section Newton 3 Laws of Motion.
However, inertial frames
are often omitted in
initial presentations of the
Newton's 3 laws of motion
to students.
They should NOT be omitted.
Actually, all physical laws
are referenced to
inertial frames, except
general relativity
(which tells us what inertial frames are)
as discussed in
Mechanics file:
frame_basics.html: Inertial Frames and Physics.
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.
For this presentation
(i.e., Newtonian Physics),
we are just going to assume
inertial frames
as the reference frames
for physical laws
and, in fact, they
are the reference frames we think of
all the time in everyday life.
A very full explication of inertial frames
is given in
Mechanics file:
frame_basics.html.
Yours truly holds the perspective that
Newtonian physics
is a package and must be accepted as such.
This means the basic entities of
Newtonian physics
and also more general physics
(e.g.,
Euclidean geometry,
time,
velocity,
acceleration,
mass,
force,
inertial frames,
Newton's 3 laws of motion,
etc.)
CANNOT be defined independently of each other, at least NOT completely.
So although you must introduce the entities in some order,
they only exist in relationship to each other as specified
by Newtonian physics
or some more general physics.
To learn Newtonian physics,
you just jump into the
pool
and swim.
This is what we do in this presentation (i.e.,
Newtonian Physics) usually without
mention.
Note, a main reason for yours truly
holds the perspective that
Newton's 1st law of motion
is a special case of
Newton's 2nd law of motion (as mentioned above in
section Newton 3 Laws of Motion), and so there are, in fact, really only
2
Newton's laws of motion
is that you need to
be able to measure time in order to
identify uniform motion.
But in order to measure time, you need
some motion that you believe measures time.
Newtonian physics
tells us there are such motions, but
you need the whole package of
Newtonian physics
(excepting
Newton's 1st law of motion, but
NOT excepting
Newton's 2nd law of motion)
to believe those motions measure time.
Formally, mass is 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 have the same value 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).
In the classical limit,
mass and
rest mass have the
same value; i.e., in the limit as
velocities go small,
their values asymptotically become the same.
However, special relativity
tells us that mass increases
relative to an inertial frame
as velocity increases.
This effect is usually too small to notice until you reach
velocities that
are a significant fraction of 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.
Note also, by a 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 system
has its own
center of mass
which moves under the net EXTERNAL
of a larger system
of astro-bodies.
A system can be analyzed
in an astrophysical
center-of-mass (CM)
inertial frame
which name can be used as a synonym
for the system itself.
Top of the hierarchy are
comoving frames.
For further explication of the hierarchy,
astrophysical
center-of-mass (CM)
inertial 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 in order to
balance a 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
velocity.
Both velocity
and acceleration
are vectors.
By acceleration,
we always mean
acceleration relative
to an inertial frame, unless
we say otherwise explicilty.
As per
Newton's 2nd law of motion
(AKA F=ma)
(see above section
Newton 3 Laws of Motion),
an acceleration of a body
is caused by a net (EXTERNAL)
force acting on the body.
Now force is also a
vector
and net force is the
vector sum of
all individual forces on a body.
If the net force on a body is
zero, there is NO
acceleration NO
matter what the
individual force are.
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 affect 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 detail in
Mechanics file:
frame_basics.html.
The two kinds of change included in the
definition of acceleration
(i.e., change in magnitude
and direction)
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: