Fragments:
To be precise, the mass-dependent forces are all linearly dependent on the mass of an object in a force field. Only gravity has a special name for its force field: i.e., the gravitational field.
Mass-dependent forces are subclass of body forces.
The fixed stars were on average at rest in absolute space.
All reference frames unaccelerated with respect to absolute space were also exact inertial frames.
All other reference frames could only be approximate inertial frames.
and all the old celestial mechanics practitioners from his day until general relativity (discovered 1915) actually knew that free-fall frames acted just like exact inertial frames or their calculations would never have been correct.
What they did and what we still do (because it is exactly right to do it) is just take the center of mass (see subsection Center of Mass below) of an astronomical object in free fall and that use that center of mass as the origin of an inertial frame for the calculation of the motions of the parts of the astronomical object.
Note when we say an astronomical object is in free fall, we almost always mean that its center of mass is in free fall in the force field of mass-dependent forces due to external astronomical objects.
Usually, the force field is just the gravitational field.
The astronomical objects could be pressure-supported astronomical objects (e.g., planets or stars) or kinetic energy-supported astronomical objects (e.g., planet-moon systems, planetary systems, star clusters, galaxies, galaxy clusters).
Why is this procedure exactly right. Because general relativity tells us free-fall frames are exact inertial frames.
General relativity plus modern cosmology tells us there is a continuum of fundamental inertial frames defined by points that participate in the mean expansion of the universe. These inertial frames are called comoving frames. We consider comoving frames in IAL 30: Cosmology.
But there are lots more inertial frames since all free-fall frames are exact inertial frames.
So there is NO absolute space, but there is absolute rotation: i.e., rotation with respect to the bulk mass-energy of the observable universe (see also Wikipedia: Inertial frame of reference: General relativity).
This absolute rotation is usually just assumed understood without bothering to explicate what one means.
But there may be exceptions to absolute rotation just described. In very strong gravitational fields (like very near black holes) maybe inertial frames do rotate with respect to the bulk mass-energy of the observable universe???---but yours truly has to guess about this since no one explicates this factoid.
For somewhat less accurate/precise, but usually adequate, measurements of absolute rotation, we use the fixed stars (which in traditional meaning used by yours truly are just the naked-eye stars). The system of fixed stars has a very low absolute rotation and is effectively zero for most purposes.
But that treatment is very inconvenient
So special inertial forces have been devised to ????? UNDER RECONSTRUCTION BELOW ?????
In fact, at location on the surface of the Earth, one can ignore inertial forces to good approximation for most purposes---but NOT all purposes.
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That is why they are free-falling.
If other forces act on the reference frame, then the reference frame CANNOT be exactly a free-fall frame---but it might be approximately one for some purposes---like any location on the surface of the Earth.
Other forces include, e.g., the pressure force, the normal force (i.e., a rigid body force), and the electromagnetic force.
If these other forces cause small enough accelerations, then a reference frame, may be approximately a free-fall frame for some purposes.
Note that a uniform external gravitational field does NOT include gravitational fields internal to the reference frame which are just treated as causing internal gravitational forces.
Note also a uniform external gravitational field is actually caused by everything in the universe external to the reference frame---as far as we know.
Note moveover that a uniform external gravitational field is an ideal limit that is approached as the reference frame becomes small compared to the size scale over which the external gravitational field varies.
In fact, we can say the observable universe (i.e., its average behavior) defines the absolutely non-rotating frame for us.
The expansion of the universe (meaning the expansion of the observable universe) is a scaling up of space WITHOUT any twisting which is consistent with our saying the observable universe (i.e., its average behavior) defines the absolutely non-rotating frame for us.
The mysterious "body forces" are NOT real forces, but they sure act like real body forces. They are called inertial forces) and are used as trick to treat non-inertial frames as if they were inertial frames.
For important example, consider a rigid rotator: the bits of it at any radius are NOT in free fall (NOT moving under the gravitation force ONLY) and they are rotating relative to the observable universe which inertial frames do NOT do.
Now the center of mass of an orbiting astro-body does define inertial frame---when that point is NOT taken as rotating relative to the observable universe per usual.
The surfaces of orbiting astro-bodies are in general NOT inertial frames because they are rotating relative to the observable universe, except in very rare cases.
But the surface locations may be approximately inertial frames just as the surface locations on the Earth are if their acceleration relative a local (i.e., at the same place) inertial frame is sufficiently small.
Note that a Earth surface location is in rotation around the Earth's axis, but that rotation NOT an orbit around the Earth's axis because it is NOT caused by gravity ONLY, but by gravity and the normal force of the ground.
Another complication for being on the surface of the Earth is that external gravitational field on the Earth is NOT uniform over the Earth. But this effect is also small for most purposes.
So for most purposes, we can treat every location on the surface of the Earth as being an inertial frame.
The same is true for the surface locations, mutatis mutandis, of almost all planets or stars.
Weather and long-range artillery are affected by non-inertial frame effects which are treated by using inertial forces. Note these phenomena have noticeable non-inertial frame effects because they have such a large size scale compared to most human scale activities.
You can notice non-inertial frame effects on a small scale by special equipment: e.g., Foucault pendulum (see the figure below: local link / general link: pendulum_foucault.html).
In the following sections, we elaborate on the above points elaborately.
The very next section, takes up some salient features of Newtonian physics.
Inertial frames of reference
are reference frames
with a physical nature.
They are essential for understanding all of
physics even though
high-school presentations
of physics often
gloss over them.
We explicate
inertial frames
in the multi-image figure below
(local link /
general link: frame_inertial_free_fall.html)
See the figure below
(local link /
general link: alpine_tundra.html)
for a picturesque zone
of the rotating reference frame
of the surface of the
Earth
that can be treated as
inertial frame for
many purposes.
We consider
non-inertial-frame effects
on the surface of the Earth at some length
below in
subsection Inertial Forces on the Earth's Surface