Why is gravity strongest at the center of the Mass ?

On 11 Dec 2006 11:18:50 -0800, "Bill Hudson"
wrote:


wrote:
G=EMC^2 Glazier wrote:
On the Earth's surface gravity is the strongest. Strongest as
measured by objects not sitting on the earth's surface? Go figure Bert

not sure what your driving at G, but i've been wondering.....

How does gravity change below the surface of the earth? In outer
space, a person is weightless or zero G's, on earth's surface gravity
is 1 G. I assume somewhere like 50 or 100 miles up, its like 1/2 G.
(1) say you dig a hole down toward the center of the earth and weigh
yourself 2,000 miles down. Do you weigh more or less? It seems you
would
weigh less as a good portion of earths mass is now above you and that
much less is below you.

An answer from the art and science of surveying: Surveyors must be
careful of the 'local vertical' when shooting a bearing. Nearby masses
such as mountains, cliffs or even igneous intrusions underground can
throw off the 'vertical' by a statistically significant amount.

Yes, if you were to tunnel downward 2000 miles, the mass of the earth
above you would exert a gravitational pull in opposition to the mass
below you, and thereby decrease your weight (not mass, weight).

Not quite. For a uniform spherical shell (the earth can be
approximated as series of such shells), the gravitational force
exerted on an object outside the shell is exactly equal to the force
that would be exerted if all the mass of the shell were concentrated
at the center of the shell. For an object inside the shell, the force
is exactly 0 (all the force vectors cancel each other out).

It is true that your weight would decrease, but the reason is less of
the earth's mass is tugging at you with a net effect.



(2) say you hollow out 1 mile diameter spherical cavity in the center
of the earth, would you float to the center of this cavity and be
suspended in "midair"?

Yes, but it would most likely not be stable. Eventually the mass one

Inside the cavity (in the idealized approximation), there is no net
force pulling you to the center of the cavity.

one side or the other would win and you would fall for half a mile
before you smacked into the inside of the sphere. Better make it 10
meters in diameter. :-) As a side note, I hear sprained wrists are an
occupational hazard in microgravity environments, because the astronaut
tends to push off too hard, until they get their 'space legs'.

... And, if so, would you again be weightless?

Essentially, yes.

... and
would you be able to walk around "upside down" on the surface of this
hollowed out sphere?

Not very easily. You'd be able to push off and fall across the 1 mile
sphere pretty easily. Probably just flexing your calf muscles would do
it.


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G=EMC^2 Glazier wrote:
On the Earth's surface gravity is the strongest. Strongest as
measured by objects not sitting on the earth's surface? Go figure
Bert

not sure what your driving at G, but i've been wondering.....

How does gravity change below the surface of the earth? In outer
space, a person is weightless or zero G's, on earth's surface gravity
is 1 G. I assume somewhere like 50 or 100 miles up, its like 1/2 G.
(1) say you dig a hole down toward the center of the earth and weigh
yourself 2,000 miles down. Do you weigh more or less? It seems you
would
weigh less as a good portion of earths mass is now above you and that
much less is below you.
(2) say you hollow out 1 mile diameter spherical cavity in the center
of the earth, would you float to the center of this cavity and be
suspended in "midair"? And, if so, would you again be weightless? and
would you be able to walk around "upside down" on the surface of this
hollowed out sphere?
You seem to think that astronauts are 'weightless'. They are not.
A person in Orbit, is _not_ weightless. This is a common 'misnaming' of
what is going on. They are in 'free fall'. The satellite, and them, are
both falling towards the Earth with the same acceleration. It is just that
they effectively 'fall and miss' all the time. Remember the Moon is being
held in it's orbit by the Earth's gravity.
Now your question about a hollow in the centre of the Earth, would not
work, because of the Moon. The actual centre of mass of the Earth-Moon
system, is moving all the time as the Moon orbits, and also moving as the
Earth orbits the Sun. However on a imaginary planet, without a Moon, or
Sun, you would experience no gravitational acceleration at the centre of
the sphere.

Best Wishes

To You All (Florida talk) If you are 13 miles closer to the Earth's
center you would weigh half of one percent more. That is the reason a
199 lb man at the equator,weighs 200 lb at the poles Go figure Bert

From Roger H.:
You seem to think that astronauts are 'weightless'. They are not. A
person in Orbit, is _not_ weightless.

This is a common 'misnaming' of what is
going on. They are in 'free fall'.

So? Suffice it to say they are de facto weightless.

...your question about a hollow in the
centre of the Earth, would not work,
because of the Moon. The actual centre
of mass of the Earth-Moon system, is
moving all the time as the Moon orbits,
and also moving as the Earth orbits the
Sun.

What do such minor perturbatioins have to do with the point of the
thought experiment?
oc

"Bill Sheppard" wrote in message
...
From Roger H.:
You seem to think that astronauts are 'weightless'. They are not. A
person in Orbit, is _not_ weightless.

This is a common 'misnaming' of what is
going on. They are in 'free fall'.

So? Suffice it to say they are de facto weightless.
The point was that the poster had the idea that an object at a height like
50 miles, would be only experiencing perhaps 0.5g acceleration, because
objects in space were 'weightless'. This is a complete misunderstanding of
what is happening.

...your question about a hollow in the
centre of the Earth, would not work,
because of the Moon. The actual centre
of mass of the Earth-Moon system, is
moving all the time as the Moon orbits,
and also moving as the Earth orbits the
Sun.

What do such minor perturbatioins have to do with the point of the
thought experiment?
Hardly minor. For the one mile sphere suggested, the centre of mass, would
always fall outside the sphere. In fact the barycentre of the Earth Moon
system, is closer to the surface of the Earth, than it is to the centre of
the planet...

Best Wishes

Roger Hamlett wrote:
"Bill Sheppard" wrote in message
...
From Roger H.:
You seem to think that astronauts are 'weightless'. They are not. A
person in Orbit, is _not_ weightless.

This is a common 'misnaming' of what is
going on. They are in 'free fall'.

So? Suffice it to say they are de facto weightless.
The point was that the poster had the idea that an object at a height like
50 miles, would be only experiencing perhaps 0.5g acceleration, because
objects in space were 'weightless'. This is a complete misunderstanding of
what is happening.

...your question about a hollow in the
centre of the Earth, would not work,
because of the Moon. The actual centre
of mass of the Earth-Moon system, is
moving all the time as the Moon orbits,
and also moving as the Earth orbits the
Sun.

What do such minor perturbatioins have to do with the point of the
thought experiment?
Hardly minor. For the one mile sphere suggested, the centre of mass, would
always fall outside the sphere. In fact the barycentre of the Earth Moon
system, is closer to the surface of the Earth, than it is to the centre of
the planet...

Best Wishes

as Bill S said, it is just a thought experiment. my only point of
bringing up the weight (i'm not even sure if "weight" is the correct
term but i think i'm getting the point across) factor in outer space or
somewhere a few miles above the surface of the earth was to show that
weight increases from essentially zero somewhere far enough out in
space to 1g at the earth's surface. i then wanted to know how this
"weight" factor changes below the surface of a planet.
i suppose i should have used a hypothetical planet of uniform
density with no other objects within 1 billion lightyears and any
weight measuring device sitting on an imaginary stationary platform.
this imaginary planet is also not spinning or accelerating.
i can see how all the various factors of Earth's real life
attributes (nearby moon,sun, etc, the earth spinning, etc) affect the
answer i was looking for.
lol- i'm still not sure i've set the hypothetical up correctly but i
think i got the point across. a lot of interesting answers. i
appreciate everybody's input.