"El Enrrabadore-mor" wrote in message


Wait, you're confused about the equivalence
principle and you confuse gravity with centrifugal
force?
I've a secret for you, gravity and centrifugal force
are not equivalent in nature. Gravity follows an
inverse SQUARED radius function. Centrifugal
follows an inverse LINEAR radius.

No! The inverse square relationship for gravity
is the consequence of a particular geometry of
the source mass. The field from a point source
or spherically symmetric source diverges. For
spherically symmetric sources the resulting field
varies as the inverse square.

Consider instead an infinite sheet of mass. In
such a case the field lines are parallel and the
potential drops linearly with distance. Or
consider the hypothetical hole bored through a
hypothetically uniform density planet (go pole
to pole to avoid coriolis complications). Thus,
as Einstein said, acceleration (centrifugal
included) is equivalent to a *uniform*
gravitational field.

Only for
stable orbits, where a body can be considered
to be in free-fall (no forces), one can make
such approximation.

Any force that results in a uniform acceleration
will be equivalent to a uniform gravitational field.
A time varying force would be equivalent to a time
varying gravitational field, which we don't find a
lot of in our day to day experience, but we can
certainly concoct hypothetical situations where it
can happen.