Keskustelujen arkisto

THERESA:

> The further down you dig yourself, the smaller the earth-'ball' that
> creates a gravity on you gets. THe mass that is above you, a 'shell' of
> earth, wouldn't affect you.

Why?

> So the downwards pull of gravity gets less and less, until in the middle
> you'd be weightless.

If the gravity arises from mass only, you'd certainly be affected by
those upper shells as well, in other words, you'd experience
weightlessness long before you reach the middle of the Earth.

All this reminds me of a beautiful P. L. de Vita story, where Scrooge
finds the biggest gold occurrence in ze world.

S?ren

THERESA:

>> So the downwards pull of gravity gets less and less, until in the middle
>> you'd be weightless.
>
>
> If the gravity arises from mass only, you'd certainly be affected by
> those upper shells as well, in other words, you'd experience
> weightlessness long before you reach the middle of the Earth.

Oops, I forgot the symmetry. Clearly at the absolute center of Earth all
forces are equally distributed in all direction, hence the gravity must
equal zero. Still those "shells" you mention do have an influence.

Sorry, no more OT from my hand...for now :-)

S?ren

Olaf Solstrand wrote:

> > > Unless... Did Mae-Wang have any blue powder left at the end of the
> > story?
>
> She didn't, no. Not according to Kim.

Argh! Well, there went that idea...

> So even if Kim was wrong about this and she HAD powder left, she would
> never offer to give it away for a new camera anyway... But I'm sure it
> was a great story idea, Lars. :-)

Well, I haven't gotten beyond a vague opening, so who knows how good
it'll become?! It *will* be scary, though -- I hope. Anyway, I've come
up with two different ways of getting around this particular problem --
and they may even turn out to be one! The only problem is, due to the
solution(s), it will probably take several years before I can get the
story done. (Assuming it *gets* done, of course.)

Thanks to all for your help, especially a certain somebody, who emailed
me privately with a suggestion.

Lars

CORD WILJES to SOREN KRARUP OLESEN, 20-03-2004:

>> If the gravity arises from mass only, you'd certainly be
>> affected by those upper shells as well, in other words,
>> you'd experience weightlessness long before you reach the
>> middle of the Earth.

> Please find my reply here:
> http://www.dcml-talk.org/read.php?f=1&i=226&t=226

Why do you put your reply elsewhere? The subject about the center of the
Earth, is an exploration of matters in a Disney story. It's still related.
If people for no reason would write about the center of the "new planet"
Sedna, *then* it would be off-topic.

Please, I don't want to go to do different places to read about one
subject. That will result in messages like: "If you want to know more,
visit www.this-or-that-site.com!"

Story-related subjects like these, are part of the reasons why I'm
subscribed to DCML.

I hope you won't mind if I fully quote your message from the above
mentioned URL. It makes it easier for me to archive your interesting
message.

And it makes it easier for me to reply to the subject.
(See the end of this e-mail.)

=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=

Center of the earth
Author:?Cord?(---.dip.t-dialin.net)
Date:???03-20-04 04:00

Theresa wrote:

>> The further down you dig yourself, the smaller the earth-'ball' that
>> creates a gravity on you gets. THe mass that is above you,
>> a 'shell' of earth, wouldn't affect you.
>> So the downwards pull of gravity gets less and less, until
>> in the middle you'd be weightless.

If you were in space in the middle between two planets of equal mass then
both planets gravitational pull would cancel out. Essentially there would be
no net force at all. (I know that you know that better than me)

But in the case of digging to the earth's core you have to consider that
those layers of the earth you already digged through are (a little bit)
nearer to you than the mass in the equivalent layer on the other side of the
earth. As the gravitational pull decreases with the square of the distance
they do not exactly cancel out. There is little less net force pulling you to
the core than the imaginary "small earth ball" under you would extract
without the layers of earth above you.

S?ren wrote:
> If the gravity arises from mass only, you'd certainly be affected by
> those upper shells as well, in other words, you'd experience
> weightlessness long before you reach the middle of the Earth.

The effect I described above decreases as you get nearer to the center of the
earth because the layers of earth above you (pulling you "up") get further
away and their equivalent mass on the other site of the earth's center
(pulling you "down") gets nearer. Only at the eath's center do you have zero
gravity because only there you have equal mass "above" and "below" you.

It would be quite interesting to experience the YoYo-effect of falling down a
tunnel through to the center of the earth (zero gravity) where the energy of
motion would carry you to the other side of the earth (losses by air friction
deducted) and then back again.

You would feel like falling all the time: execept in the middle of the earth
and at the two return points on each side. At all of theses three points you
would feel weightless.

Cord

=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=

I want to note that there's a (Dutch?) story about Donald falling through the
Earth, like a YoYo, going from one side to the other, and back. It must be a
story from the early 1980s or the mid-1980s. At least that was when it must
have been published in the Dutch weekly. It was about ten pages, I think.

Are there people here who recognize this story?

BTW. I remember the story as very funny. But I was still a kid back then,
and kids are not capable to judge whether a Duck story is good or not. They
have to re-read the story as adult collectors, before they can give a good
judgement. Right? :-) I'm saying this, because this is often the feeling I
get, after recommending a story from my youth without rereading it. People
might jump on me and ask if I'm blind or crazy, for appreciating such a lousy
story. And then I automatically start to defend myself by saying that I was
only a kid back then... As if kids are not old and wise enough to fully enjoy
children's stories! :-)

--- Dani?l

"Stop! You don't know what you're doing to yourself"
(Which Barks story?) :-)
Hint #1: These words are spoken by Donald.
Hint #2: Donald is talking to an animal.
Hint #3: Loss of hair.

Hi everyone!

Quite unfortunately, I haven't had time to read through all the messages on
this intriguing subject, but I am saving them for later.

As I was browsing through the Cornell University collection of scanned
nineteenth-century American magazines & newspapers
(http://cdl.library.cornell.edu/moa/moa_browse.html) for my research, I
started going through the first issues of the Scientific American- and gues
what I saw on the first page of Vol 2 issue 1 (Oct 3, 1846)
(http://cdl.library.cornell.edu/cgi-bin/moa/pageviewer?root=%2Fmoa%2Fscia%2F
scia0002%2F&tif=00011.TIF&cite=http%3A%2F%2Fcdl.library.cornell.edu%2Fcgi-bi
n%2Fmoa%2Fmoa-cgi%3Fnotisid%3DABF2204-0002-2&coll=moa&frames=1&view=75) (can
be viewed as a gif image or a pdf document) ? ...

"

Philosophy of Gravity

A body carried beneath the surface of the earth becomes lighter, because
the matter then above it, is drawing it up, instead of down, as before. A
descent of a few hundred feet makes a sensible difference, and at the
centre of the earth, if a man could reach it, he would find things have
no weight at all; and there would be neither up nor down, because bodies
would be equally attracted in all directions.

"

Have a nice week!

Olivier

Hans Kiesl (from the University of Bamberg) asks me:

<< Leafing through your papers in the December 2003 issue
of the Journal of the American Statistical Association, I noticed
the following reference:

Hjort, N.L., and Rosa, D. (1999), "Who won?",
Speedskating World 4, 15-18.

I guess the article is about the influence of a skater's last track
(inner vs. outer track) on the outcome of speedskating competitions;
this is of course completely off topic here. What I'd like to know,
though, is Mr. "Rosa, D."'s contribution to the paper (and whether
it makes this posting on topic). >>

Thanks for noticing, and for looking at these articles in the JASA.
I'm very proud of them, and of the many discussion contributions
that followed. I was also happy to be able to bring both
speedskating and a connection to Mr Rosa D onto the gravely
serious pages of JASA, devoted here to mathematical discussions
of statistical-probabilitistical model selection and model averaging
methodology. It was to clarify the sometimes conflicting roles
and uses of statistical regression models in applied scientific practice
that I pointed to my speedskating work (causing the Olympic
rules to be changed, from Nagano 1998 onwards), and where
one of the related points is being nicely illustrated in the mentioned
Hjort & Rosa publication. It turned out that Mr Rosa D has a good
grasp of certain engineering aspects of the problems that sometimes
conspire to confront speedskaters.

Yes, this should qualify as on-topic, I believe, and the serious
Rosa D reader should not be without a copy of the above publication.
I think *some* copies might still be had from the Dutch editor of
SpeedSkating World, Irene Postma, also an occasional reader of
the DCML pages. She might be contacted at "irenep at bos.nl" .

(And no, the direct sample average is not always the most efficient
estimator of the mean of an unknown distribution. For the double
exponential family, for example, the standard deviation of the
sample mean is sqrt(2) bigger than that of the median, for large n.)

Nils Lid Hjort

Frank Bubacz wrote:

> Barks will be
> excluded completely from the German 'Hall of Fame', because those in power
> decided we've already suffered a Barks-overdose within the last ten years or
> so. Which is rubbish, of course, although maybe not from a business point of
> view. ;-)

So you're saying they did NOT print too much Barks in Germany?
But the Germans had several Barks series: Tollsten Geschichten ("Sonderheft"), Bound volumes of the Tollsten Geschichten, Besten Geschichten, Hard-cover reprints of the Besten Geschichten, Barks Library.
With all these series, I wouldn't need yet-another-one, if I were German.

--Harry.

Harry Fluks -- TNO Telecom -- Delft -- Nederland
h.w.fluks at telecom.tno.nl -- http://dd50.inducks.org
"Wie ben ik? Wat doe ik hier? Waar is mijn Roddelflop?"