Center of Gravity? LOL

If, protected against heat and pressure, you descend into the Earth,
towards that center of gravity - you'll start weighing less again!

Halfway down (cherry colored figure) you 're surprised to see you weigh
only 30 to 40 kilos

Why?

Mo
http://www.perceptions.couk.com/uef/graveffect.html

Maybe because assuming gravity acts as a point source starts to fail?
I hope you're not confusing mass with weight! Your mass won't change.

Saul Levy


On Tue, 14 Sep 2004 03:21:07 GMT, Imperishable Stars
wrote:

If, protected against heat and pressure, you descend into the Earth,
towards that center of gravity - you'll start weighing less again!

Halfway down (cherry colored figure) you 're surprised to see you weigh
only 30 to 40 kilos

Why?

Mo
http://www.perceptions.couk.com/uef/graveffect.html

"Barry Schwarz" wrote...
in message ...

On Tue, 14 Sep 2004 03:21:07 GMT, Imperishable Stars
wrote:

If, protected against heat and pressure, you descend into the Earth,
towards that center of gravity - you'll start weighing less again!

Halfway down (cherry colored figure) you 're surprised to see you weigh
only 30 to 40 kilos

Why?

A shell of uniform density has two interesting properties (these are
relatively easy calculus exercises that I had to do in school but that
was way too long ago):

A point mass outside the shell experiences the same gravitational
force as if the entire mass of the shell was located at the center of
the shell.

A point mass inside the shell experiences no gravitational force
from the shell.

For many practical applications, the Earth can be considered a series
of such concentric shells and most objects are comparatively small
enough to treated as point masses. Consequently:

A person on the surface experiences a gravitational force the same
as if the entire mass of the Earth is concentrated at its center.

A person some distance inside the Earth experiences a force
equivalent to only the fraction of the mass that is still closer to
the center than he is.

Just as an example, if we consider the Earth to be spherical and
uniformly dense and have a mass M and a radius R:

The volume is given by V = 4/3*pi*R^3

The density is given by D = M/V = 3*M/(4*pi*R^3)

The gravitation force exerted on an object of mass q on the
surface is given by F = G*M*q/R^2

For the same object 1/2 way down to the center of the Earth:

The volume of the sphere with radius r = R/2 is
v = 4/3*pi*(R/2)^3 = V/8

The mass of this smaller sphere is m = v*D = M/8

The gravitation force exerted on the object is
f = G*m*q/r^2 = G*(M/8)*q/(R/2)^2 = (G*M*q/R^2)*(4/8) = F/2

The gravitational force is what we call weight. So the object weighs
half as much.

The ratio changes when you factor in the complication that the Earth
is not uniformly dense but the principle remains the same as long as
you treat each concentric shell as having constant density.


Remove the del for email

This made me think of the effect of the mass *above*. Barry,
you said...

A person some distance inside the Earth experiences a force
equivalent to only the fraction of the mass that is still closer to
the center than he is.

How about the fraction of the mass that is farther from the center
than he is? Will this not have a tendency to pull upward on him
and reduce his weight more?

And when he is about halfway between the center and the
surface, would he be pulled equally from above as from below
and be essentially weightless?

I sense that complications arise from the Earthmass that is also
pulling on the front, rear and sides of the subject?

happy days and...
starry starry nights!

--
Be very wary...
For Life will zoom past ya,
Pay heed when I say--
Tempus fugit ad astra!

Indelibly yours,
Paine@ http://painellsworth.net

In article ,
Painius wrote:


How about the fraction of the mass that is farther from the center
than he is? Will this not have a tendency to pull upward on him
and reduce his weight more?

Wouldn't any pull from above be cancelled by the fact that much more mass
is below? Most of the shell that is above continues all around, though
slightly further away.

Jochen

"Jochen Lueg" wrote...
in message ...

In article ,
Painius wrote:

How about the fraction of the mass that is farther from the center
than he is? Will this not have a tendency to pull upward on him
and reduce his weight more?

Wouldn't any pull from above be cancelled by the fact that much more mass
is below? Most of the shell that is above continues all around, though
slightly further away.

Jochen

Not sure, Jochen... but you raise the question, "What happens as
you go deeper and nearer to the center?"

happy days and...
starry starry nights!

--
Be very wary...
For Life will zoom past ya,
Pay heed when I say--
Tempus fugit ad astra!

Indelibly yours,
Paine@ http://painellsworth.net

Hi Stars Quantum gravity answers this. Interesting if the Earth was
completely hollow(like a balloon) its surface shell would be where
gravity is located. If we had a tunnel going through one end of the
Earth to the other,and dropped a ball in this tunnel(hole) and take
away air friction it would almost reach the other end,and then fall
back,and do this back and forth many times until it comes to rest in the
gravitational center of the earth. This action is the same as a
pendulum. At the Earth's center the ball has no weight,but its
inertia(mass) stays the same. Bert

Imperishable Stars wrote:
If, protected against heat and pressure, you descend into the Earth,
towards that center of gravity - you'll start weighing less again!

Halfway down (cherry colored figure) you 're surprised to see you
weigh only 30 to 40 kilos

Why?

Mo
http://www.perceptions.couk.com/uef/graveffect.html

See your own link. It is explained there. It is hard to read it out loud for
you across the internet :-)

"Painius" wrote in message
...
"Jochen Lueg" wrote...
in message ...

In article
,
Painius wrote:

How about the fraction of the mass that is farther from the center
than he is? Will this not have a tendency to pull upward on him
and reduce his weight more?

Wouldn't any pull from above be cancelled by the fact that much more
mass
is below? Most of the shell that is above continues all around,
though
slightly further away.

Jochen

Not sure, Jochen... but you raise the question, "What happens as
you go deeper and nearer to the center?"


For the answer re-read Barry's answer

Barry Schwarz wrote:

I sense that complications arise from the Earthmass that is also
pulling on the front, rear and sides of the subject?

Complications arise because the Earth is not uniformly dense nor is it
made up of concentric shells which can be considered uniform.
However, for many practical applications it can be idealized this way
and, to this level of accuracy, you only feel the gravity of the mass
of the shells closer to the center than you are.



In addition to Barry's explanation, a the gravitational potential due to a
point source can ve described as a monopole, the potential of which falls as
1/r (Force proportional to 1/r^2). Any nonuniformities can be modelled as
dipoles, quadrupoles etc., the potential of which falls more rapidly than
1/r. eg, for a dipole, the potential falls as 1/r^2. In other words, the
further you are from the earth, the more it looks like a point source.


DaveL