The Oval Earth Theory
Martha Bridegam
person's inability to prove the earth is round. Had forgotten GO
anticipates Rowland's objection by saying that while it obviously isn't
flat, perhaps it could be oval.
Herewith, from "As I Please," December 1946 (he was already writing
"1984"):
"Somewhere or other -- I think it is in the preface to 'Saint Joan' --
Bernard Shaw remarks that we are more gullible and superstitious today
than we were in the Middle Ages, and as an example of modern credulity
he cites the widespread belief that the earth is round. The average man,
says Shaw, can advance not a single reason for thinking that the earth
is found. He merely swallows this theory because there is something
about it that appeals ot the twentiety-century mentality.
Now, Shaw is exaggerating, but there is something in what he says, and
the question is worth following up, for the sake of the light it throws
on modern knowledge. Just why *do* we believe that the earth is found? I
am not speaking of the few thousand astronomers, geographers and so
forth who could give ocular proof, or have a theoretical knowledge of
the proof, but of the ordinary newspaper-reading citizen, such as you or
me.
As for the Flat Earth theory, I believe I could refute it. If you stand
by the seashore on a clear day, you can see the masts and funnels of
invisible ships passing along the horizon. This phenomenon can only be
explained by assuming that the earth's surface is curved. But it does
not follow that the earth is spherical. Imagine another theory called
the Oval Earth theory, which claims that the earth is shaped like an
egg. What can I say against it?
Against the Oval Earth man, the first card I can play is the analogy of
the sun and moon. The Oval Earth man promptly answers that I don't know,
by my own observation, that those bodies are spherical. I only know that
they are round, and they may perfectly well be flat discs. I hve no
answer to that one. Besides, he goes on, what reason have I for thinking
that the earth must be the same shape as the sun and moon? I can't
answer that one either.
My second card is the earth's shadow: when cast on the moon during
eclipses, it appears to be the shadow of a round object. But how do I
know, demands the Oval Earth man, that eclipses of the moon are caused
by the shadow of the earth? The answer is that I don't know, but have
taken this piece of information blindly from newspaper articles and
science booklets.
Defeated in the minor exchanges, I now play my queen of trumps: the
opinion of the experts. The Astronomer Royal, who ought to know, tells
me that the earth is round. The Oval Earth man covers the queen with his
king. Have I tested the Astronomer Royal's statement, and would I even
know a way of testing it? Here I bring out my ace. Yes, I do know one
test. The astronomers can foretell eclipses, and this suggests that
their opinions about the solar system are pretty sound. I am therefore
justified in accepting their say-so about the shape of the earth.
If the Oval Earth man answers -- what I believe is true -- that the
ancient Egyptians, who though the sun goes round the earth, could also
predict eclipses, then bang goes my ace. I have only one card left:
navigation. People can sail ships round the world, and reach the places
they aim at, by calculations which assume that the earth is spherical. I
believe that finishes the Oval Earth man, though even then he may
possibly have some kind of counter.
It will be seen that my reasons for thinking that the earth is round are
rather precarious ones. Yet this is an exceptionally elementary piece of
information. On most other questions I should have to fall back on the
expert much earlier, and would be less able to test his pronouncements.
And much the greater part of our knowledge is at this level. It does not
rest on reasoning or on experiment, but on authority. And how can it be
otherwise, when the range of knowledge is so vast that the expert
himself is an ignoramus as soon as he strays away from his own
specialty? Most people, if asked to prove that the earth is round, would
not even bother to produce the rather weak arguments I have outlined
above. They would start off by saying that 'everyone knows" the earth to
be round, and if pressed further, would become angry. In a way Shaw is
right. This *is* a credulous age, and the burden of knowledge which we
now have to carry is partly responsible."
Alan Allport
<36B407...@sirius.com>...
> Ran across the bit we were discussing a couple weeks ago re: average
> person's inability to prove the earth is round. Had forgotten GO
> anticipates Rowland's objection by saying that while it obviously isn't
> flat, perhaps it could be oval.
This did occur to me at the time, I confess, but I hesitated in pointing it
out on the grounds that an extended flame-baiting competition about
geometry seemed too gruesome to contemplate. (Besides, I've lost my
protractor).
Alan.
Rebecca and Rowland
Weeelll.... On this subject, I once seconded the opposition to a
college debate, which proposed that `This house believes that the Earth
is flat'. We argued very successfully for the `odd shaped Earth'
hypothesis, `proving' that the Earth did in fact have a beer gut (while
being otherwise flat), and won the debate.
Having said that, the Earth isn't in fact anything like a perfect
sphere: it's an `oblate spheroid' according to one definition I've read
(bulges around the equator) and does of course have countless minor
irregularities like mountains and so on.
To demonstrate the *precise* shape of the Earth, you need to take lots
and lots of measurements all over the globe. From such measurements and
others, you can derive a theoretical model of the Earth's composition
(in terms of solid crust and so on) which can explain the observed
overall shape, but... You get nowhere without the measurements. These
days, the observations are mostly done from satellites. Assuming that
you trust the published literature to present true data, a `normal'
person can demonstrate that the Earth is round with a few days in a
research library.
Rowland.
--
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Alan Allport
<1dmibbw.18w...@p123.nas2.is3.u-net.net>...
> Assuming that
> you trust the published literature to present true data, a `normal'
> person can demonstrate that the Earth is round with a few days in a
> research library.
That, of course, was Orwell's point - one has to resort to the commentary
of experts.
From what I recall of my Earth Science classes many moons ago, the Earth is
shaped like a peach - fatter in the Southern Hemisphere with a sort of
dimple at the South Pole.
Alan.
Rebecca and Rowland
> Rebecca and Rowland <real-addr...@flur.bltigibbet> wrote in article
> <1dmibbw.18w...@p123.nas2.is3.u-net.net>...
>
> > Assuming that
> > you trust the published literature to present true data, a `normal'
> > person can demonstrate that the Earth is round with a few days in a
> > research library.
>
> That, of course, was Orwell's point - one has to resort to the commentary
> of experts.
Not at all - all you need is the raw data and you can work it out
yourself. You need to trust the *data*, not the commentary. Since the
measurements can be repeated and reproduced by way of verification, this
is a fairly reliable way of doing things - even if you can't check the
data yourself, *someone* will be able to re-do the measurements.
Because of this, very few modern[1] scientists attempt to fiddle the
data, and almost all of them are working in fields like medicine and
biology.
If you want to demonstrate that the Earth is round off your own back,
you've got to make measurements all over the world. Local measurements
can only give information on the bits of the planet that you can see.
(you seem to be confusing science with your woolly area of academe[2] -
you don't need to depend on anyone's commentary or opinion in science,
because you can work it out yourself. Nor do you need to trust anyone's
reports, because you can (in principle at least) reproduce the
experiment and measurements yourself.)
> From what I recall of my Earth Science classes many moons ago, the Earth is
> shaped like a peach - fatter in the Southern Hemisphere with a sort of
> dimple at the South Pole.
Hmm... I won't say `impossible', but it doesn't seem very likely to me.
There's certainly a bulge at the equator caused by the Earth's rotation,
and that same effect leads to flattening at the poles. I can't see any
reason for any large scale north/south asymmetry, nor can I see any way
there could be a *dimple* at either pole.
Rowland.
[1] Newton fiddled his optics results, amongst others. But it was all
in a good cause...
[2] I know I shouldn't say things like this, but I just can't help
myself sometimes.
Alan Allport
> [2] I know I shouldn't say things like this, but I just can't help
> myself sometimes.
Similarly, I know I shouldn't get involved in these kind of threads, and I
am going to do my damndest to avoid them from now on.
Alan.
Martha Bridegam
>
> Of course, if the Party *does* want to introduce an alternative cosmology
> then it could do worse than to dust off the Ptolemaic system, a perfectly
> sound empirical explanation (from an Earth-centered perspective) of the
> rotations of the heavenly bodies which has gotten a rather bad press over
> the last few centuries. There is a reason beyond blind ignorance why
> Christendom held on to this scheme for so long; and that's that it works
> pretty well, only breaking down at the fringes (much the same could be said
> of Newtonian mechanics).
I'm sure that was intended. People don't compare O'Brien to
Dostoyevsky's Grand Inquisitor for nothing.
/MAB
Martha Bridegam
>
... Seems the
> hot irons and pincers stuff is mostly a lot of (highly effective)
> Protestant propaganda. I guess another Monty Python sketch bites the dust.
Hm. I guess nobody'd expect that from the Spanish Inquisition!
Joseph C Fineman
>Having said that, the Earth isn't in fact anything like a perfect
>sphere:
A bit of an overstatement. It is something _very like_ a perfect
sphere by ordinary standards -- as good an approximation as a marble;
much better than a soccer ball.
>it's an `oblate spheroid' according to one definition I've read
>(bulges around the equator)
Yes, but you wouldn't know it to look at it. The difference is only a
bit over 26 miles in diameter out of nearly 8000. If somebody took
the trouble to make an ordinary classroom globe (say 12 inches) to
true scale, that would amount to a difference of 0.04 inches -- about
the thickness of a filing card. You would have to use calipers and be
pretty careful if you wanted to check it.
Jupiter, which is a lot bigger & rotates faster, is out of round to
the eye.
>and does of course have countless minor irregularities like mountains
>and so on.
The Himalayas would be barely rough to the touch.
None of this rebuts Orwell's point: that you have to take a lot on
faith to believe even some pretty simple & well-known facts. But that
(quite aside from the fact that since his time a few of us have been
up & seen for ourselves) glosses over the important role of theory in
the evaluation of evidence. Any one piece of evidence could be faked
or explained away, but it would be quite a job, even for Minitrue
working night & day, to produce a "dual system of astronomy" as
claimed by O'Brien. I think he must have been bluffing. The job is a
good deal worse than moving a war from one part of the earth to
another. Things are relevant to each other in too many ways. For
example, looking up in the sky, one sees first the sun & moon, and
then, with a telescope, a lot of other objects more than a few hundred
miles across, and they are all pretty good spheres. This suggests
that, tho small rocks can be any shape, for sufficiently big ones
there is only one design. There is a reason for that. It is that
God, being Himself spherical, thinks spheres are beautiful -- ah, no,
that's the old explanation. In our time, the conclusion follows from
what we know about gravity & the strength of materials, and what we
know about those things can be checked in a lot of ways that do not
even involve looking out the window. An oval earth is as preposterous
as 6-foot flea. It's out of scale. The arguments are not
particularly sophisticated, go back to Galileo & Newton, and were
surely accessible to Orwell.
--- Joe Fineman j...@world.std.com
||: If you don't like the fortune, don't eat the cookie. :||
Alan Allport
Joseph C Fineman <j...@world.std.com> wrote in article
<F6G8w...@world.std.com>...
> Any one piece of evidence could be faked
> or explained away, but it would be quite a job, even for Minitrue
> working night & day, to produce a "dual system of astronomy" as
> claimed by O'Brien. I think he must have been bluffing.
Ah, but that ignores the role of Doublethink in Party doctrine. O'Brien
doesn't need to produce a sophisticated work of fakery to demonstrate his
flat earth theorem; it is enough that the willing Oceanian accepts a priori
Big Brother's assurances that the world is flat, even perhaps while
simultaneously piloting an aircraft or navigating a ship using techniques
that demand spherical navigation techniques.
Of course, if the Party *does* want to introduce an alternative cosmology
then it could do worse than to dust off the Ptolemaic system, a perfectly
sound empirical explanation (from an Earth-centered perspective) of the
rotations of the heavenly bodies which has gotten a rather bad press over
the last few centuries. There is a reason beyond blind ignorance why
Christendom held on to this scheme for so long; and that's that it works
pretty well, only breaking down at the fringes (much the same could be said
of Newtonian mechanics).
Alan.
Rebecca and Rowland
> real-addr...@flur.bltigibbet (Rebecca and Rowland) writes:
>
> >Having said that, the Earth isn't in fact anything like a perfect
> >sphere:
>
> A bit of an overstatement. It is something _very like_ a perfect
> sphere by ordinary standards -- as good an approximation as a marble;
> much better than a soccer ball.
(I think I should mention my degree's in physics. I don't have much
truck with ordinary standards)
> >it's an `oblate spheroid' according to one definition I've read
> >(bulges around the equator)
>
> Yes, but you wouldn't know it to look at it. The difference is only a
> bit over 26 miles in diameter out of nearly 8000. If somebody took
> the trouble to make an ordinary classroom globe (say 12 inches) to
> true scale, that would amount to a difference of 0.04 inches -- about
> the thickness of a filing card. You would have to use calipers and be
> pretty careful if you wanted to check it.
Hmm... 0.3% isn't that small a difference; 0.04 inches is about 1mm,
which isn't *that* hard to spot on a scale of about 1 foot using normal
calipers and a ruler. No need for any care at all really - you wouldn't
even need to use vernier calipers to spot the difference.
> Jupiter, which is a lot bigger & rotates faster, is out of round to
> the eye.
Mainly because it's gaseous. And does it *really* have a day that's
less than 24 hours? If so, wow!
> >and does of course have countless minor irregularities like mountains
> >and so on.
>
> The Himalayas would be barely rough to the touch.
On a 12" globe, Everest would be about 0.008" high - much more than
`barely rough to the touch'. A 0.008" valve clearance in my bike engine
is enough to cause horrible nasty rattles - the 0.003" and 0.004" feeler
gauges I use to set the specified clearances are hardly foil-thin, and I
can easily feel a 0.001" irregularity, which I've heard described as `a
pretty big step' in some contexts.
> None of this rebuts Orwell's point: that you have to take a lot on
> faith to believe even some pretty simple & well-known facts.
Hmm... I'm still unconvinced.
> But that
> (quite aside from the fact that since his time a few of us have been
> up & seen for ourselves) glosses over the important role of theory in
> the evaluation of evidence. Any one piece of evidence could be faked
> or explained away, but it would be quite a job, even for Minitrue
> working night & day, to produce a "dual system of astronomy" as
> claimed by O'Brien. I think he must have been bluffing. The job is a
> good deal worse than moving a war from one part of the earth to
> another. Things are relevant to each other in too many ways. For
> example, looking up in the sky, one sees first the sun & moon, and
> then, with a telescope, a lot of other objects more than a few hundred
> miles across, and they are all pretty good spheres.
But you can't tell, surely? They all look pretty circular to be sure,
but that's not the same as spherical.
> This suggests
> that, tho small rocks can be any shape, for sufficiently big ones
> there is only one design. There is a reason for that. It is that
> God, being Himself spherical, thinks spheres are beautiful -- ah, no,
> that's the old explanation.
Does that mean it's wrong, though?
>In our time, the conclusion follows from
> what we know about gravity & the strength of materials, and what we
> know about those things can be checked in a lot of ways that do not
> even involve looking out the window. An oval earth is as preposterous
> as 6-foot flea. It's out of scale. The arguments are not
> particularly sophisticated, go back to Galileo & Newton, and were
> surely accessible to Orwell.
Hmm.... again. Surely an oval Earth is at least theoretically
conceivable, assuming that the Earth itself is a solid lump of rock?
(not long-term stable by any means, of course, but couldn't a solid
Earth hold itself significantly oval for a short while? If I could be
bothered, I'd do some calculations myself, but I'm feeling lazy at the
moment).
But never mind that - to test this idea, you need to use a model of
gravity, a model of the Earth's composition (still untested by direct
observation), and several models of the mechanical behaviour of
materials. I think a fair degree of sophistication is needed for all
that, and again, you've either got to take rather a lot on trust, or do
an awful lot of your own research and checking to verify the various
models yourself - not something the man on the Clapham Omnibus is likely
to be able or willing to do.
Rowland.
Alan Allport
> I'm sure that was intended. People don't compare O'Brien to
> Dostoyevsky's Grand Inquisitor for nothing.
And talking of bad press... guess who else has been rehabilitated of late?
Yes, Torquemada's mob. Early-modern history is not my area by any means,
but according to a BBC Timewatch documentary there's significant evidence
to suggest that the Spanish Inquisition was, for its day, a model of
judicial impartiality and gaolkeeping enlightenment. Unlike the secular
legal system, which ran on graft and apathy, the Inquisition was policed by
scholarly academics who took principles of evidence and due process very
seriously, and maintained relatively humane prison conditions - records
exist of criminals deliberately blaspheming so that they could be
transferred into the religious court system as a cushy number. Seems the
hot irons and pincers stuff is mostly a lot of (highly effective)
Protestant propaganda. I guess another Monty Python sketch bites the dust.
Alan.
Joseph C Fineman
>> Jupiter, which is a lot bigger & rotates faster, is out of round to
>> the eye.
>Mainly because it's gaseous.
Not so. When something gets that big, it doesn't matter what it's
made of. If Jupiter were made of steel & rotating at the same rate,
it would have the same shape as it actually does. The size of the
irregularities that solidity can support is pretty small even on earth
-- on the order of the size of actual mountains (see below). On
Jupiter it would be much smaller, because the gravitational field is
more intense. (On the moon, it is larger. A rough calculation shows
that for fixed composition the maximum mountain height is inversely
proportional to the diameter of the planet. When those two numbers
become comparable -- which seems to happen when they are both a few
hundred miles -- any shape is possible.)
>And does it *really* have a day that's less than 24 hours? If so,
>wow!
About 10 hours, IIRC. Yes, it is quite a spectacle. When that string
of comets hit it just over the limb, we didn't have to wait long to
see the mess it made.
>> >and does of course have countless minor irregularities like mountains
>> >and so on.
>>
>> The Himalayas would be barely rough to the touch.
>On a 12" globe, Everest would be about 0.008" high - much more than
>`barely rough to the touch'.
If you say so. I grant, on a steel globe, you could probably catch
your fingernail on Everest. But running your finger over the whole
region would be more like running your finger over an orange peel.
>> Any one piece of evidence could be faked or explained away, but it
>> would be quite a job, even for Minitrue working night & day, to
>> produce a "dual system of astronomy" as claimed by O'Brien. I
>> think he must have been bluffing. The job is a good deal worse
>> than moving a war from one part of the earth to another. Things
>> are relevant to each other in too many ways. For example, looking
>> up in the sky, one sees first the sun & moon, and then, with a
>> telescope, a lot of other objects more than a few hundred miles
>> across, and they are all pretty good spheres.
>But you can't tell, surely? They all look pretty circular to be sure,
>but that's not the same as spherical.
You can see them rotate (even the moon, to some extent).
>> This suggests that, tho small rocks can be any shape, for
>> sufficiently big ones there is only one design. There is a reason
>> for that. It is that God, being Himself spherical, thinks spheres
>> are beautiful -- ah, no, that's the old explanation.
>Does that mean it's wrong, though?
If you find it consoling, be my guest. It would not have stopped
Orwell for long. %^)
>> In our time, the conclusion follows from what we know about gravity
>> & the strength of materials, and what we know about those things
>> can be checked in a lot of ways that do not even involve looking
>> out the window. An oval earth is as preposterous as 6-foot flea.
>> It's out of scale. The arguments are not particularly
>> sophisticated, go back to Galileo & Newton, and were surely
>> accessible to Orwell.
>Hmm.... again. Surely an oval Earth is at least theoretically
>conceivable, assuming that the Earth itself is a solid lump of rock?
>(not long-term stable by any means, of course, but couldn't a solid
>Earth hold itself significantly oval for a short while? If I could
>be bothered, I'd do some calculations myself, but I'm feeling lazy at
>the moment).
It would slump right away. The stresses would be enormous.
>But never mind that - to test this idea, you need to use a model of
>gravity, a model of the Earth's composition (still untested by direct
>observation), and several models of the mechanical behaviour of
>materials.
Make the most extravagant assumptions you like.
>I think a fair degree of sophistication is needed for all that, and
>again, you've either got to take rather a lot on trust,
That's for sure. But no more than the scientists themselves do.
>or do an awful lot of your own research and checking to verify the
>various models yourself - not something the man on the Clapham
>Omnibus is likely to be able or willing to do.
Well, he could read up on what various scientists, trusting one
another in various combinations, have said, and see if it looks
plausible. And the whole argument we have gotten embroiled in is just
one of the possible channels thru which the truth might leak in.
Closing them all off, I still maintain, would be an excessive job for
an Ingsocful mathematician. (The Soviet government somehow avoided
making that demand on its mathematicians. Its geneticists &
cosmologists were not so lucky.)
--- Joe Fineman j...@world.std.com
||: A cosmology is an autobiography of the universe. :||
Rebecca and Rowland
> real-addr...@flur.bltigibbet (Rebecca and Rowland) writes:
>
> >> Jupiter, which is a lot bigger & rotates faster, is out of round to
> >> the eye.
>
> >Mainly because it's gaseous.
>
> Not so. When something gets that big, it doesn't matter what it's
> made of. If Jupiter were made of steel & rotating at the same rate,
> it would have the same shape as it actually does.
I find that pretty hard to believe - care to point me in the general
direction of a mathematical model that demonstrates this?
> The size of the
> irregularities that solidity can support is pretty small even on earth
> -- on the order of the size of actual mountains (see below). On
> Jupiter it would be much smaller, because the gravitational field is
> more intense. (On the moon, it is larger. A rough calculation shows
> that for fixed composition the maximum mountain height is inversely
> proportional to the diameter of the planet. When those two numbers
> become comparable -- which seems to happen when they are both a few
> hundred miles -- any shape is possible.)
Can you post the outline of the calculation?
> >And does it *really* have a day that's less than 24 hours? If so,
> >wow!
>
> About 10 hours, IIRC. Yes, it is quite a spectacle. When that string
> of comets hit it just over the limb, we didn't have to wait long to
> see the mess it made.
>
> >> >and does of course have countless minor irregularities like mountains
> >> >and so on.
> >>
> >> The Himalayas would be barely rough to the touch.
>
> >On a 12" globe, Everest would be about 0.008" high - much more than
> >`barely rough to the touch'.
>
> If you say so. I grant, on a steel globe, you could probably catch
> your fingernail on Everest. But running your finger over the whole
> region would be more like running your finger over an orange peel.
I think not, because orange peel doesn't have sharp edges. I can catch
my fingernail on a 0.001 inch irregularity with no trouble.
> >> Any one piece of evidence could be faked or explained away, but it
> >> would be quite a job, even for Minitrue working night & day, to
> >> produce a "dual system of astronomy" as claimed by O'Brien. I
> >> think he must have been bluffing. The job is a good deal worse
> >> than moving a war from one part of the earth to another. Things
> >> are relevant to each other in too many ways. For example, looking
> >> up in the sky, one sees first the sun & moon, and then, with a
> >> telescope, a lot of other objects more than a few hundred miles
> >> across, and they are all pretty good spheres.
>
> >But you can't tell, surely? They all look pretty circular to be sure,
> >but that's not the same as spherical.
>
> You can see them rotate (even the moon, to some extent).
Hmm... You can see that they look different at different times. Is
that really the same as seeing them rotating (admittedly, this line of
reasoning is beginning to get seriously tenuous)?
> >> This suggests that, tho small rocks can be any shape, for
> >> sufficiently big ones there is only one design. There is a reason
> >> for that. It is that God, being Himself spherical, thinks spheres
> >> are beautiful -- ah, no, that's the old explanation.
>
> >Does that mean it's wrong, though?
>
> If you find it consoling, be my guest. It would not have stopped
> Orwell for long. %^)
I'm not sure about consoling, but it does seem like an amusing idea to
me.
[snip]
> >Hmm.... again. Surely an oval Earth is at least theoretically
> >conceivable, assuming that the Earth itself is a solid lump of rock?
> >(not long-term stable by any means, of course, but couldn't a solid
> >Earth hold itself significantly oval for a short while? If I could
> >be bothered, I'd do some calculations myself, but I'm feeling lazy at
> >the moment).
>
> It would slump right away. The stresses would be enormous.
I can see I'm going to have to heat up the calculus parts of my brain
again.
[snip]
> >I think a fair degree of sophistication is needed for all that, and
> >again, you've either got to take rather a lot on trust,
>
> That's for sure. But no more than the scientists themselves do.
Erm... Ish, very ish - scientists aren't especially trusting creatures,
and they're inclined to check things very carefully at times.
> >or do an awful lot of your own research and checking to verify the
> >various models yourself - not something the man on the Clapham
> >Omnibus is likely to be able or willing to do.
>
> Well, he could read up on what various scientists, trusting one
> another in various combinations, have said, and see if it looks
> plausible. And the whole argument we have gotten embroiled in is just
> one of the possible channels thru which the truth might leak in.
> Closing them all off, I still maintain, would be an excessive job for
> an Ingsocful mathematician.
[snip]
I suspect you're right on this point.
Joseph C Fineman
>Joseph C Fineman <j...@world.std.com> wrote:
>> real-addr...@flur.bltigibbet (Rebecca and Rowland) writes:
>>
>> >> Jupiter, which is a lot bigger & rotates faster, is out of round
>> >> to the eye.
>>
>> >Mainly because it's gaseous.
>>
>> Not so. When something gets that big, it doesn't matter what it's
>> made of. If Jupiter were made of steel & rotating at the same
>> rate, it would have the same shape as it actually does.
>I find that pretty hard to believe - care to point me in the general
>direction of a mathematical model that demonstrates this?
>> The size of the irregularities that solidity can support is pretty
>> small even on earth -- on the order of the size of actual mountains
>> (see below). On Jupiter it would be much smaller, because the
>> gravitational field is more intense. (On the moon, it is larger.
>> A rough calculation shows that for fixed composition the maximum
>> mountain height is inversely proportional to the diameter of the
>> planet. When those two numbers become comparable -- which seems to
>> happen when they are both a few hundred miles -- any shape is
>> possible.)
>Can you post the outline of the calculation?
Imagine piling up material to make a bump on an otherwise spherical
planet. To get it as high as possible, pile it up until it sags, like
a sandpile. Its base diameter will have the same order of magnitude
as its height. The shear stress at the base will be of the order of
its weight divided by the area of the base. The weight is
proportional to the volume, and thus to the bump size cubed, and also
to the acceleration of gravity, which for a constant-density planet is
proportional to the planet's radius. The biggest bump is one for
which the stress at the base equals the strength of the material. And
so on.
>> I grant, on a steel globe, you could probably catch your fingernail
>> on Everest. But running your finger over the whole region would be
>> more like running your finger over an orange peel.
>I think not, because orange peel doesn't have sharp edges. I can
>catch my fingernail on a 0.001 inch irregularity with no trouble.
As you please. My point is, as balls go in ordinary life, the earth
is a pretty good one.
>> >> For example, looking up in the sky, one sees first the sun &
>> >> moon, and then, with a telescope, a lot of other objects more
>> >> than a few hundred miles across, and they are all pretty good
>> >> spheres.
>>
>> >But you can't tell, surely? They all look pretty circular to be
>> >sure, but that's not the same as spherical.
>>
>> You can see them rotate (even the moon, to some extent).
>Hmm... You can see that they look different at different times. Is
>that really the same as seeing them rotating...?
Spots disappear around one limb and reappear on the other limb and
cross the disk again. They slow down in the right way as they
approach the limb. It _might_ all be done with mirrors. %^)
Also, in the case of the moon & Venus, you have something even more
compelling -- the terminator of the crescent, which is always just the
right ellipse to be the projection of a semicircle the same size as
the limb.
>> >Hmm.... again. Surely an oval Earth is at least theoretically
>> >conceivable, assuming that the Earth itself is a solid lump of
>> >rock? (not long-term stable by any means, of course, but couldn't
>> >a solid Earth hold itself significantly oval for a short while?
>> >If I could be bothered, I'd do some calculations myself, but I'm
>> >feeling lazy at the moment).
>>
>> It would slump right away. The stresses would be enormous.
>I can see I'm going to have to heat up the calculus parts of my brain
>again.
No calculus needed. Imagine a cold steel egg the size of the earth.
Scaling up one from my refrigerator (49 by 63 millimeters), we see
that this is roughly equivalent to a steel sphere with a mountain 3
million meters high that has a base on the order of 10^14 square
meters. The volume of the mountain is about 10^20 cubic meters, so
its mass is about 10^24 kilograms, and its weight is about 10^25
newtons. Thus, the stress at the base is about 10^11 pascals, about
1000 times the strength of steel.
Indeed, "it would slump right away" is a considerable understatement.
The potential energy released by the slump would be about 10^25
newtons times 10^6 meters = 10^31 joules, which is more than 10^5
joules per kilogram if spread over the entire egg -- enough to
vaporize the whole thing. Before it did much slumping, it would
explode.
>> >I think a fair degree of sophistication is needed for all that,
>> >and again, you've either got to take rather a lot on trust,
>>
>> That's for sure. But no more than the scientists themselves do.
>Erm... Ish, very ish - scientists aren't especially trusting
>creatures, and they're inclined to check things very carefully at
>times.
At times when something has clearly gone wrong. Otherwise, they
believe the Rubber Handbook as I have just done.
--- Joe Fineman j...@world.std.com
||: Where reasons are no reason, cause is true. ||
Rebecca and Rowland
> real-addr...@flur.bltigibbet (Rebecca and Rowland) writes:
[snip]
> >> The size of the irregularities that solidity can support is pretty
> >> small even on earth -- on the order of the size of actual mountains
> >> (see below). On Jupiter it would be much smaller, because the
> >> gravitational field is more intense. (On the moon, it is larger.
> >> A rough calculation shows that for fixed composition the maximum
> >> mountain height is inversely proportional to the diameter of the
> >> planet. When those two numbers become comparable -- which seems to
> >> happen when they are both a few hundred miles -- any shape is
> >> possible.)
>
> >Can you post the outline of the calculation?
>
> Imagine piling up material to make a bump on an otherwise spherical
> planet. To get it as high as possible, pile it up until it sags, like
> a sandpile. Its base diameter will have the same order of magnitude
> as its height. The shear stress at the base will be of the order of
> its weight divided by the area of the base.
I think I spy an invalid assumption: where does this idea come from?
Vertical compression is given by weight/base area in this case, but
shear stress? Where does that come from?
> The weight is
> proportional to the volume, and thus to the bump size cubed, and also
> to the acceleration of gravity, which for a constant-density planet is
> proportional to the planet's radius. The biggest bump is one for
> which the stress at the base equals the strength of the material. And
> so on.
Okay, I follow your reasoning, but I don't like it. I've just draw a
picture of a pile of sand type of heap (rounded cone) and I can't see
that there need be much in the way of shear stress at the base at all,
if you assume a rigid, solid lump of material.
Now then... Obviously, real materials are perfectly rigid (etc), and
I'm familiar with the *idea* of heaps of stuff bulging out at the
bottom, but... How do you go about calculating the magnitude of the
forces concerned? A simple paper model of lots of particles in a heap
with gravity acting vertically downwards implies that there's *no* shear
force at the base. This is clearly wrong - so... How do you work it
out?
> >> I grant, on a steel globe, you could probably catch your fingernail
> >> on Everest. But running your finger over the whole region would be
> >> more like running your finger over an orange peel.
>
> >I think not, because orange peel doesn't have sharp edges. I can
> >catch my fingernail on a 0.001 inch irregularity with no trouble.
>
> As you please. My point is, as balls go in ordinary life, the earth
> is a pretty good one.
Well, yes.
[snip]
> >Hmm... You can see that they look different at different times. Is
> >that really the same as seeing them rotating...?
>
> Spots disappear around one limb and reappear on the other limb and
> cross the disk again. They slow down in the right way as they
> approach the limb. It _might_ all be done with mirrors. %^)
>
> Also, in the case of the moon & Venus, you have something even more
> compelling -- the terminator of the crescent, which is always just the
> right ellipse to be the projection of a semicircle the same size as
> the limb.
Hmm - okay, pretty hard to explain any other way.
> >> >Hmm.... again. Surely an oval Earth is at least theoretically
> >> >conceivable, assuming that the Earth itself is a solid lump of
> >> >rock? (not long-term stable by any means, of course, but couldn't
> >> >a solid Earth hold itself significantly oval for a short while?
> >> >If I could be bothered, I'd do some calculations myself, but I'm
> >> >feeling lazy at the moment).
> >>
> >> It would slump right away. The stresses would be enormous.
>
> >I can see I'm going to have to heat up the calculus parts of my brain
> >again.
>
> No calculus needed. Imagine a cold steel egg the size of the earth.
> Scaling up one from my refrigerator (49 by 63 millimeters), we see
> that this is roughly equivalent to a steel sphere with a mountain 3
> million meters high that has a base on the order of 10^14 square
> meters.
Eh? I thought you were talking about an egg shape? What size egg are
you considering?
> The volume of the mountain is about 10^20 cubic meters, so
> its mass is about 10^24 kilograms, and its weight is about 10^25
> newtons. Thus, the stress at the base is about 10^11 pascals, about
> 1000 times the strength of steel.
I don't follow this reasoning at all - what direction is the stress in?
If you've got a mountain of a size comparable to the planet it's `sat
on', you can't neglect the gravitational field of its own mass - that
estimate of weight is bound to be flawed in some way.
> Indeed, "it would slump right away" is a considerable understatement.
> The potential energy released by the slump would be about 10^25
> newtons times 10^6 meters = 10^31 joules, which is more than 10^5
> joules per kilogram if spread over the entire egg -- enough to
> vaporize the whole thing. Before it did much slumping, it would
> explode.
Hmm...... I think some calculus *is* needed, and some account needs to
be taken of gravity and suchlike. This *might* be right, but it does't
*feel* right.
> >> >I think a fair degree of sophistication is needed for all that,
> >> >and again, you've either got to take rather a lot on trust,
> >>
> >> That's for sure. But no more than the scientists themselves do.
>
> >Erm... Ish, very ish - scientists aren't especially trusting
> >creatures, and they're inclined to check things very carefully at
> >times.
>
> At times when something has clearly gone wrong. Otherwise, they
> believe the Rubber Handbook as I have just done.
The Rubber Handbook? If that's the book I've heard Rebecca (of my email
address) refer to, I know at least one scientist who believes almost
none of it (she did her PhD in elastohydrodynamics - a wonderful field
in which almost all the theoretical models are almost completely
useless)
Joseph C Fineman
>Joseph C Fineman <j...@world.std.com> wrote:
>> Imagine piling up material to make a bump on an otherwise spherical
>> planet. To get it as high as possible, pile it up until it sags,
>> like a sandpile. Its base diameter will have the same order of
>> magnitude as its height. The shear stress at the base will be of
>> the order of its weight divided by the area of the base.
>I think I spy an invalid assumption: where does this idea come from?
>Vertical compression is given by weight/base area in this case, but
>shear stress? Where does that come from?
I don't know; I could never acquired much intuition for stress
analysis. I don't think it matters. The material, being distorted &
at the limit of its strength, would figure out some way of generating
a shear stress so it slump out at the bottom. (The Egyptians, I have
read, had some pretty spectacular pyramid failures before they learned
their limits.) For a big enough bump, an infinitesimal virtual slump
will lower the gravitational potential energy by more than it raises
the elastic energy. Then the virtual slump will become real, and the
bump doesn't get any bigger.
>Okay, I follow your reasoning, but I don't like it. I've just draw a
>picture of a pile of sand type of heap (rounded cone) and I can't see
>that there need be much in the way of shear stress at the base at
>all, if you assume a rigid, solid lump of material.
>> No calculus needed. Imagine a cold steel egg the size of the
>> earth. Scaling up one from my refrigerator (49 by 63 millimeters),
>> we see that this is roughly equivalent to a steel sphere with a
>> mountain 3 million meters high that has a base on the order of
>> 10^14 square meters.
>Eh? I thought you were talking about an egg shape? What size egg
>are you considering?
One about the size of the earth, as I said. The "mountain" is the
part of the egg that is outside a sphere inscribed in the big end.
That sphere, it is true, is a little smaller than the earth, but we
are talking orders of magnitude here.
>> The volume of the mountain is about 10^20 cubic meters, so its mass
>> is about 10^24 kilograms, and its weight is about 10^25 newtons.
>> Thus, the stress at the base is about 10^11 pascals, about 1000
>> times the strength of steel.
>I don't follow this reasoning at all - what direction is the stress
>in?
Whatever direction it needs to be to lower the gravitational potential
energy.
>If you've got a mountain of a size comparable to the planet it's `sat
>on', you can't neglect the gravitational field of its own mass -that
>estimate of weight is bound to be flawed in some way.
The mountain is enough smaller than the rest of the planet that its
internal gravitational cohesion is smaller than its attraction to the
main body.
>> Indeed, "it would slump right away" is a considerable
>> understatement. The potential energy released by the slump would
>> be about 10^25 newtons times 10^6 meters = 10^31 joules, which is
>> more than 10^5 joules per kilogram if spread over the entire egg --
>> enough to vaporize the whole thing. Before it did much slumping,
>> it would explode.
>Hmm...... I think some calculus *is* needed, and some account needs to
>be taken of gravity and suchlike. This *might* be right, but it does't
>*feel* right.
I was a little surprised by that last result myself. But I do not see
how any of the effects you have mentioned can make all that energy go
away.
>> >Erm... Ish, very ish - scientists aren't especially trusting
>> >creatures, and they're inclined to check things very carefully at
>> >times.
>>
>> At times when something has clearly gone wrong. Otherwise, they
>> believe the Rubber Handbook as I have just done.
>The Rubber Handbook? If that's the book I've heard Rebecca (of my
>email address) refer to, I know at least one scientist who believes
>almost none of it (she did her PhD in elastohydrodynamics - a
>wonderful field in which almost all the theoretical models are almost
>completely useless)
The _Handbook of Chemistry and Physics_, so nicknamed after the odd
name originally borne by its publisher, the Chemical Rubber Publishing
Co. (now CRC Press). Actually, I was speaking generically. I mostly
used the McGraw-Hill Encyclopedia. My point is that when scientists
need a number or some other fact, and it doesn't come out of their own
field of expertise, their first recourse is to the handbooks & review
articles that supposedly contain, at worst, the best guesses by people
who ought to know. Being skeptical of everything is a luxury reserved
for those who have a lot of time and an inordinate need to be right --
say, the people who decide what value of the fine-structure constant
shall get into the handbooks. (There was a guy at Caltech named Jesse
DuMond who was in that business. He would personally visit the
laboratories of eminent persons & ask rude questions such as "What did
you do to check the purity of this crystal?".)
When Millikan did his oil-drop experiment, he needed the viscosity of
air, and he got it out of a handbook. It later turned out that the
handbook's value was wrong, and so the received value of the charge on
the electron was wrong for several years. Bad luck, but it would have
been unreasonable to expect Millikan to remeasure the viscosity of air
before he published. Where would he have stopped?
I have not managed an obOrwell in this posting, so by my standards it
is off topic. I suggest we move this thread to sci.physics or to
email if you think it is worth continuing.
--- Joe Fineman j...@world.std.com
||: Threats are expensive when they fail; promises are expensive :||
||: when they succeed. :||