Gravitational force and gravitational acceleration

[Luigi Fortunati]

Gravity manifests itself as gravitational force if there is an obstacle
(the stone on the wall of the well) and as gravitational acceleration if
the obstacle is not there (the same stone as before that detaches from
the wall and falls).

In the first case there is gravitational force (and there is no
acceleration), in the second case there is gravitational acceleration
(and there is no force).

When in my animation https://www.geogebra.org/m/eybpyx4d we click on the
"Detach the stone from the wall" button, the stones A and B detach from
the walls and fall.

In this phase of free fall, the two stones A and B accelerate towards
each other and, therefore, they are two mutually accelerated reference
systems: how can they both be declared inertial if they are accelerating
towards each other? Can inertia and acceleration coexist?

Note that I am talking about (gravitational) acceleration and not force.

Luigi Fortunati

[Mikko]

[[Mod. note -- I apologise for the delay in processing this article,
which arrived on my computer on 2024-02-15, but was mistakenly classified
as spam.
-- jt]]

On 2024-02-15 12:31:18 +0000, Luigi Fortunati said:
> Gravity manifests itself as gravitational force if there is an obstacle
> (the stone on the wall of the well) and as gravitational acceleration if
> the obstacle is not there (the same stone as before that detaches from
> the wall and falls).

>=20

> In the first case there is gravitational force (and there is no
> acceleration), in the second case there is gravitational acceleration
> (and there is no force).

In the sencond case there is a force: the acceleration means a change
in the momentum (i.e. the quantition of the motion) and the time
derivative of the momentum is the force. That force is equal to the
force in the first case.

However, gravitation is best understood as an acceleration field and
the force as secondary.

Mikko

[Richard Livingston]

[[Mod. note -- I apologise for the delay in processing this article,
which arrived on my computer on 2024-02-15, but was mistakenly classified
as spam.
-- jt]]

Others have tried to explain this to you, but I will give it a try. You are
making it all too complex. There is always gravitational acceleration,
when viewed in a frame stationary with the gravitating mass. The
only force is the one that stops a mass from accelerating.

That does seem a bit contradictory at first, but if you think about it
correctly it isn't. When you are falling freely (i.e. no air friction) you
are in an inertial frame (at least locally). Astronauts in orbit cannot
tell if they are in orbit or moving in a straight line at uniform speed
in deep space (i.e. far from gravitating masses), unless they look
out the window. The same would be true in an elevator car falling
in a deep shaft in a vacuum.

In both cases an observer on the ground (i.e. stationary wrt the
gravitating mass) would see the orbiting or falling observer
accelerating. But the standing observer is not in an inertial
frame! He is accelerating due to the force of the earth on his
feet.

This is just like an observer on an accelerating rocket watching
someone floating free in space. To the rocket observer the
free floating person is accelerating downward. But the free
floating person is in an inertial frame, they experience no
force.

The person in a falling elevator is in exactly the same
situation. They are in an inertial frame while the observer
standing on the surface of the earth sees them as
accelerating. The person in the elevator can release an
object in mid air and it will appear to float there just
like an astronaut would see if they did the same experiment.

The observer in the accelerating rocket knows he is not in an
inertial frame because if they release an object in the air, it
will immediately start accelerating. Likewise the observer on
the surface of the earth. The observer floating in space, or in
orbit, or in the falling elevator, will know they are in an inertial
frame because if they release an object is will float in mid
air without accelerating.

The only force present in all these cases is the force on the feet
of the accelerating observer; that is, the person standing on the
ground or in the accelerating rocket watching the free falling
objects.

I suspect part of your problem getting all this is the concept
of relativity. The relativity principle maintains that physics is
the same in all inertial frames. Whether an observer sees
OTHER people accelerating is irrelevant, it is only the state
of motion of the observer that is important for their physics.

When an inertial observer sees something accelerating, then
they can attribute that to either a force or a difference in the
curvature of space-time. Which it is depends on the distribution
of mass or the presence of mechanisms that can impart a force,
such as electric charges or collisions with other masses.

For your two elevators, one at the center of the earth and the
other falling towards it, they are both in inertial frames, because
if they release an object it will appear to float mid air wrt each
observer. The reason they see the other accelerating towards
them is the distribution of mass that is distorting space-time.

If the two elevators were in empty space and were still accelerating
towards each other, there would have to be some mechanism
imparting a force on one or both elevators. In that case
one or both would no longer be an inertial reference frame,
and whichever elevator was being accelerated by a force, they
would know it because if they released an object in mid air
the object would immediately start "accelerating" wrt to that
accelerating frame.

Rich L.