Is it true that two bodies fall simoultaneously in earth?
Does this fact prove the equivalence of mass inertia and gravitational mass?

"nonzero" wrote in message
om...
Is it true that two bodies fall simoultaneously in earth?

If the body can be considered a particle, and it is not charged, then two
bodies dropped from rest at the same height will hit the ground at the same
time if in a vacuum. You can actually see this if you have a vacuum chamber
designed for this. In the Boston Museum of Science they have a setup for
that. They have two vey high tubes. Each tube is evacuated of air. In one
tube there are feathers, in the other a ball. When the two are released from
the same height each falls at the same rate. I've known for a long time that
all objects fall at the same rate. But to watch feathers drop like a brick
is weird! :-)

Does this fact prove the equivalence of mass inertia and gravitational
mass?

The closer we can measure their times of fall the closer we can measure this
equality. There is no measured difference whatsoever. And the precision of
those experiments are extremely high.

Pmb

"nonzero" wrote in message
om...
Is it true that two bodies fall simoultaneously in earth?
Yes, two bodies will fall at the same rate, if no other force such as air
resistance interferes. A feather and a hammer will not land at the same
instance here on Earth, but they did on the airless moon.
Does this fact prove the equivalence of mass inertia and gravitational
mass?
No.
Androcles

"Androcles" wrote in message ...

"nonzero" wrote in message
om...
Is it true that two bodies fall simoultaneously in earth?

Yes, two bodies will fall at the same rate, if no other force such as air
resistance interferes. A feather and a hammer will not land at the same
instance here on Earth, but they did on the airless moon.

Does this fact prove the equivalence of mass inertia and gravitational
mass?

No.

This fact is more or less *called*
"the equivalence of inertial mass and gravitational mass"

Androcles is something that thinks that definitions can
be true or false.
And for some reason it never leaves a blank line to
separate his comments, so I have done that.

Dirk Vdm

On Mon, 20 Oct 2003 16:37:31 +0200, "Dirk Van de moortel"
wrote:

"Androcles" wrote:
"nonzero" wrote:
Is it true that two bodies fall simoultaneously in earth?

Yes, two bodies will fall at the same rate, if no other force such as air
resistance interferes. A feather and a hammer will not land at the same
instance here on Earth, but they did on the airless moon.

Does this fact prove the equivalence of mass inertia and gravitational
mass?

No.

This fact is more or less *called*
"the equivalence of inertial mass and gravitational mass"

And in Newtonian gravitation it may be correct. But this
"fact" requires that the mechanism of gravitation be some kind
of attractive force acting, or some mechanism by which space
or space-time is caused to curve by the presence of matter
and energy.

Androcles is something that thinks that definitions can
be true or false.
And for some reason it never leaves a blank line to
separate his comments, so I have done that.
Dirk Vdm

It can be true that gravitational mass does not exist,
and that there is only inertial mass or rest mass.
That is how the statement can be false.

It seems completely unreasonable to have both
the concept of gravitational mass and also have dynamic
space-time geometry.
Much of Newtonian terminology and physical
concepts remains in discussions of gravity, but a good
text will try to move from the historical perspective to
the terminology only needed in General Relativity.

It seems many posters forget that General
Relativity is about physics in the presence of
gravitation, and very little of Newtonian theory
is needed for General Relativity.

Joe Fischer

"Pmb" wrote in message ...
"nonzero" wrote in message
om...
Is it true that two bodies fall simoultaneously in earth?

If the body can be considered a particle, and it is not charged, then two
bodies dropped from rest at the same height will hit the ground at the same
time if in a vacuum. You can actually see this if you have a vacuum chamber
designed for this. In the Boston Museum of Science they have a setup for
that. They have two vey high tubes. Each tube is evacuated of air. In one
tube there are feathers, in the other a ball. When the two are released from
the same height each falls at the same rate. I've known for a long time that
all objects fall at the same rate. But to watch feathers drop like a brick
is weird! :-)

Does this fact prove the equivalence of mass inertia and gravitational
mass?

The closer we can measure their times of fall the closer we can measure this
equality. There is no measured difference whatsoever. And the precision of
those experiments are extremely high.

Pmb

Thank's for answering.
It's weird for me also that a feather falls like a brick in the
region near earth or in the moon, and as you said there are
experiments that prove that with a very good precision. My problem is
the following:
The behaviour of bodies falling at the same time in a gravitational
field (for example earth's)isn't it a local behaviour (due to the fact
that bodies are very close to earth?)? What if we were examining two
bodies outside in free space?
For example let's assume the following systems:
System1 consists of one body with the mass of earth and one body with
the mass of the moon in a certain distance, and we let these bodies
fall.

System2 consists of two bodies with each of the mass of earth and in
the same distance as in System1, we also let the bodies fall to each
other.
Let's assume also that the two systems are far away each from the
other.
Will the bodies fall at the same speed and at the same time in both
systems?
I believe that the answer is no!
If this is correct then the equivalence of mass inertia and
gravitational mass
has a stictly defined region of existence.
If it is not correct i would like to have a proof of that.

best regards

"nonzero" wrote in message
om...
"Pmb" wrote in message
...
"nonzero" wrote in message
om...
Is it true that two bodies fall simoultaneously in earth?

If the body can be considered a particle, and it is not charged, then
two
bodies dropped from rest at the same height will hit the ground at the
same
time if in a vacuum. You can actually see this if you have a vacuum
chamber
designed for this. In the Boston Museum of Science they have a setup for
that. They have two vey high tubes. Each tube is evacuated of air. In
one
tube there are feathers, in the other a ball. When the two are released
from
the same height each falls at the same rate. I've known for a long time
that
all objects fall at the same rate. But to watch feathers drop like a
brick
is weird! :-)

Does this fact prove the equivalence of mass inertia and gravitational
mass?

The closer we can measure their times of fall the closer we can measure
this
equality. There is no measured difference whatsoever. And the precision
of
those experiments are extremely high.

Pmb

Thank's for answering.
It's weird for me also that a feather falls like a brick in the
region near earth or in the moon, and as you said there are
experiments that prove that with a very good precision. My problem is
the following:
The behaviour of bodies falling at the same time in a gravitational
field (for example earth's)isn't it a local behaviour (due to the fact
that bodies are very close to earth?)? What if we were examining two
bodies outside in free space?
For example let's assume the following systems:
System1 consists of one body with the mass of earth and one body with
the mass of the moon in a certain distance, and we let these bodies
fall.

System2 consists of two bodies with each of the mass of earth and in
the same distance as in System1, we also let the bodies fall to each
other.
Let's assume also that the two systems are far away each from the
other.
Will the bodies fall at the same speed and at the same time in both
systems?
I believe that the answer is no!
If this is correct then the equivalence of mass inertia and
gravitational mass
has a stictly defined region of existence.
If it is not correct i would like to have a proof of that.

Do you recall my first comment? I.e. "If the body can be considered a
particle.."

The Earth cannot be be considered a particle when it is falling in the
gravitational field of a body whose mass is the same as Earth.

The equivalence of inertial mass and gravitational mass assumes that one
body does not cause the other body to accelerate. That is not the situation
you've described.

Pmb

The question was:
" Does this fact prove the equivalence of mass inertia and gravitational
mass?"
My reply was "No."
To clarify my answer, one cannot prove a definition.
Dinky will a simple answer and read into it more than it implies.

Androcles

"Androcles" wrote in message ...

The question was:
" Does this fact prove the equivalence of mass inertia and gravitational
mass?"
My reply was "No."

That was a mighty helpful answer.

To clarify my answer, one cannot prove a definition.

Trying to weasel out, as usual.

Dinky will a simple answer and read into it more than it implies.

Don't reply through someone else's post to someone
you allegedly killfiled. That is silly.

Dirk Vdm

On 21 Oct 2003 00:33:28 -0700, (nonzero) wrote:

My problem is the following:
The behaviour of bodies falling at the same time in a gravitational
field (for example earth's)isn't it a local behaviour (due to the fact
that bodies are very close to earth?)? What if we were examining two
bodies outside in free space?
For example let's assume the following systems:
System1 consists of one body with the mass of earth and one body with
the mass of the moon in a certain distance, and we let these bodies
fall.

System2 consists of two bodies with each of the mass of earth and in
the same distance as in System1, we also let the bodies fall to each
other.
Let's assume also that the two systems are far away each from the
other.
Will the bodies fall at the same speed and at the same time in both
systems?
I believe that the answer is no!

You are correct. Actually the reason you even have
to discuss this results from the standard Newtonian formula
used on Earth in all Earth as the largest body problems.

There are other formulas, but most are not discussed
in undergraduate texts or classrooms, except in Celestial
Mechanics (orbital motion) and advanced mechanics.

My interest is gravity, not relativity, but General
Relativity is mostly about gravity, so I read and post here.
I don't think much of Newtonian concepts, and I
should not post in sci.physics because Newtonian gravitation
is used in essentially all texts and classrooms except for
the few people who have a reason to study General Relativity.

Newtonian gravitation is so simple most eighth grade
students can handle it. And for most uses it is accurate
enough.

Your question relates to what is called "reduced mass"
problems. All orbital equations should have a component
like "MASS(A) + mass(b)" in them.
This is different than formulas that contain M times m,
and the difference is in the assumption that M times m
is used in formulas where M is massive enough that it
can be considered NOT to move at all due the the gravity
of m (the smaller mass).

Many formulas, even in orbital mechanics, trivialize
the formula if a certain value is too small to change the result
by a significant amount.
That is why the formula F = GMm / d^2 works for
a dropped object and the Earth.
The Earth can be assumed to NOT move at all due to
the gravity of any object smaller than a mountain, and few
objects have the mass of a mountain.

The Newtonian formula for two Earths can be written
in almost the same form, A + a = G(M + m) / D^2

If this is correct then the equivalence of mass inertia and
gravitational mass
has a stictly defined region of existence.
If it is not correct i would like to have a proof of that.
best regards

It is correct, but ignored in most terrestial cases
because the Earth does NOT move (or at least did not
move in the minds of man before it was assumed the
Earth orbits the Sun.

I don't have much interest in existing math
because I believe when the physical cause of gravity
is known a new math will probably have to be invented.
But I think all formulas for gravity can be derived
from what is called the vis a vive equations.

Maybe you can find information to show you are
correct by searching

www.google.com

for

reduced mass

and

vis a vive (Try different spellings for this).

Joe Fischer