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And you thereby recognize the real force, F=mg, of the Earth's1) Newtonian response:
<snip>
In this paradigm, an object in free fall at the earth's surface is
impelled by the gravitational force of the earth. In searching for an
inertial frame, this force must be taken into account.
As you mentioned, in searching for an inertial frame, we look for a
way to write F=ma. If we choose rotating frames, we quickly run into
problems doing this. But it is easy enough to find a frame in which
we can write F=mg.
. . .