great
thanx
i get it
so we should drop the circumferential pursuit
because even if we could determine the exact longitudes of the
longest meridional circuit
which we cant
no single pair of points on that circuit would present themselves
as being any farther apart along the earths surface than any
other pair
& this regardless of whether they were actually antipodal or not
hahaha
& therefore we can cut back to the only chase that we still have
left to us
by examining & comparing topographical maps of the sumatra &
ecuador neighborhoods
so as to try to find the pair of antipodes thereabouts with the
greatest combined elevation above sea level
to be continued no doubt
--- In
BoundaryPoint@yahoogroups.com, "Lowell G. McManus"
<mcmanus71496@m...> wrote:
> Insertions below between lines marked thus: +++++++++
>
>
>
> ----- Original Message -----
> From: "m06079" <barbaria_longa@h...>
> To: <BoundaryPoint@yahoogroups.com>
> Sent: Wednesday, March 10, 2004 8:00 PM
> Subject: [BoundaryPoint] Re: How far is it?
>
>
> --- In BoundaryPoint@yahoogroups.com, "Lowell G. McManus"
> <mcmanus71496@m...> wrote:
> > I seem to have misconstrued the original quest as pertaining
> to tripoints.
> >
> > If it pertained to [just] points, then I think that the two points
> farthest
> > apart diametetrically would be the two equatorial or very
nearly
> equatorial
> > antipodes with the greatest combined elevation above sea
> level. The bulging
> > equatorial diameter would easily overcome any elevational
> advantages of
> > non-equatorial points. I would nominate some Ecuadorian
> peak and its Sumatran
> > antipode.
>
> good thinking
>
> i also realized the diametric maximum would fall within the
> famous equatorial bulge
> just as the diametric minimum would fall within the equally
> famous area of polar compression
> but have no idea how broad or how locally steep this bulge &
this
> compression are
>
> like
> are they very nearly as linear & perpendicular as the equator &
> axis themselves are
> being confined to say only a very few degrees of spheroidal arc
> or
> do they perhaps spread out much more broadly & blend much
> more gradually with their surrounding regions until finally
> disappearing somewhere around the 45th parallel
>
> ++++++++++++++++
> If the solid structure of the earth were a perfect sphere,
centrifugal force
> from the diurnal rotation would cause our fluid seas to pile up
27 miles deep at
> the Equator, swamping everything there while leaving the polar
regions high and
> dry. Centrifugal force being what it is, the seas do pile up 27
miles deep
> there anyway, but the sea floors and the dry lands of the
equatorial regions
> providently bulge upward to precisely match their swell! Since
solid structure
> and centrifugal effects on fluid must be in perfect agreement,
the equatorial
> bulge and the polar flats must necessarily spread broadly and
blend gradually.
> I doubt that the rate of bulging is constant throughout. I would
expect the
> rate to be greatest near the equator where the centrifugal force
is greatest.
> If it were constant, though, that rate would be 477 meters per
degree of
> latitude. If so, then just a few degrees of latitude from the
equator would
> negate the effects of some fairly pronounced differences in
relief.
> ++++++++++++++++
>
> if the former
> then you must be right on with ecuador & sumatra
> & we might proceed to narrow the possibilities further
>
> & if the latter
> then we might have to consider peaks of the entire equatorial
> region
> conceivably even as far afield as the tropics
>
> ++++++++++++++++
> It wouldn't be nearly that far.
> ++++++++++++++++
>
> still guessing wildly here of course
>
> in other words
> i do realize lowness of latitude will generally trump height of
> altitude
> but dont know yet at what latitude this advantage begins to
taper
> off
>
> so can you think of any way to evaluate these parameters
> or to at least bridge the apparent data gap
> because i think this additional understanding could be
essential
> before proceeding further
>
> more below
>
>
>
> > The two most circumferentially distant antipodes present an
> entirely different
> > question. The polar flattening causes the shortest
> circumferential routes
> > between any two antipodes to be along a great circle through
> the poles.
>
> ok but thats the shortest & we want the longest
>
> ++++++++++++++++
> Yes, but what we want to find is the longest of the shortest
(most direct
> possible) circumferential routes--as opposed to those that
take unnecessarily
> long and scenic paths just to make themselves longer.
Imagine two equatorial
> antipodes and the question of the circumferential distance
between them. They
> could be joined by an equatorial route, a polar route, or
anything in between.
> The equatorial route would be unnecessarily long because it
runs the bulge all
> the way around. The polar route would clearly be shortest
(most direct), and
> thus the truest answer to the question of the distance between
any pair of
> antipodes.
> ++++++++++++++++
>
> & does your next statement follow from this
>
> you seem to follow now by saying there are none shorter than
> any others
> which seems a contradiction of the above
>
> ++++++++++++++++
> What I say is that none of the most direct (polar) routes would
differ in length
> from each other on an earth without relief. They would certainly
differ from
> unnecessarily longer indirect (non-polar) routes.
> ++++++++++++++++
>
> or do both of these propositions make sense independently
>
> On a
> > smooth oblate spheroid (an earth without relief), any pair of
> antipodes would be
> > equally interdistant one from the other. This is because any
> imaginable great
> > circle connecting them would make two crossings of the
> bulging equatorial region
> > and two of the flattened polar regions. On the real world, only
> the matter of
> > elevational relief crossed in the process would differentiate
the
> distances
> > between any pair of antipodes. You would want to pick the
> diametrically
> > opposite pair of west and east longitudes that cross the
> maximum amount of
> > continental relief during their circuit of the earth, then choose
> any two
> > antipodes on that circuit--perhaps something like 70° W and
> 110° E.
>
> interesting too
> tho i am not sure i understand
>
> are you saying here that all circumferential differences are
> levelled except for those presented by relief
>
> ++++++++++++++++
> Unfortunately, yes. I am saying that all direct polar routes
between any two
> true antipodes should be equal except for the effects of
intervening relief.
> ++++++++++++++++
>
> but in that case it seems to me we face the difficulty of having
to
> measure in detail the actual terrain crossed by every possible
> great circle in the world
>
> or rather not just the difficulty but the ultimate imponderability &
> practical impossibility of it
>
> so maybe the supposed answerability of this question actually
> evaporates under the heat of scrutiny
>
> ++++++++++++++++
> Yes, it does! Of course, there would be no way to effectively
measure such
> relief. One could only generalize that a route running the length
of the Andes
> would be considerably longer than one skimming the smooth
waters of the Pacific,
> etc. That is why we would probably do best to disregard relief
as a factor and
> simply bask in the sheer wonder of this proposition: The
equality of
> circumferential distance between any two antipodes
(something that we would
> expect to find on a perfect sphere) obtains nevertheless on our
oblately
> spheroidal earth! End of my insertions.
> ++++++++++++++++
>
> but i am sure i dont fully understand this yet
> so please clarify further if you can
>
> thanx
>
> end insertions
>
> >
> > Lowell G. McManus
> > Leesville, Louisiana, USA
> >
> >
> > ----- Original Message -----
> > From: "acroorca2002" <orc@o...>
> > To: <BoundaryPoint@yahoogroups.com>
> > Sent: Wednesday, March 10, 2004 12:41 PM
> > Subject: [BoundaryPoint] Re: How far is it?
> >
> >
> > > in bp terms
> > > you have improved as well as redeemed what was only a
try
> > > pointing quest by turning it into an actual tripointing quest
> > >
> > > moreover your upgraded version is interesting in its own
right
> > >
> > > & it holds forth some promise of being ultimately
answerable
> too
> > >
> > >
> > > so have a leading pair of candidates suggested
themselves
> yet
> > >
> > >
> > >
> > > & having tried a few things too
> > > i can report that the original quest
> > > namely
> > > which points on earth are farthest apart
> > > & exactly how far apart are they
> > > remains as hard to make any real headway with as it is
hard
> to
> > > improve upon in curiosity value & elegance
> > >
> > >
> > > --- In BoundaryPoint@yahoogroups.com, "Lowell G.
> McManus"
> > > <mcmanus71496@m...> wrote:
> > > > If one wanted to determine the two tripoints that are
farthest
> > > apart, one should
> > > > first determine which few pairs are the most likely
> candidates
> > > based on their
> > > > relative antipodality from each other. This would take
some
> > > trial and error.
> > > > However, since the antipodes of most continents are
> oceanic,
> > > there shouldn't be
> > > > an abundance of likely candidates.
> > > >
> > > > Next, the few candidates might have to be evaluated for
the
> > > effects of the
> > > > spheroidicity of the earth and for elevation. The earth is
an
> > > oblate spheroid,
> > > > bulging at the Equator and flattened at the poles.
However,
> the
> > > difference
> > > > between sea level diameters pole-to-pole and Equator to
> > > Equator is typically
> > > > stated in the range of 40 to 43 km. The supposedly most
> > > precise model pegs the
> > > > figure at 42,952 meters, which is less than 27 miles. On
> top of
> > > this distance,
> > > > elevation could add a few more miles if one found a pair
of
> > > relatively antipodal
> > > > tripoints both in high mountains. Elevation would most
> affect
> > > diametric
> > > > distance and would be much less significant
> circumferentially.
> > > >
> > > > Considering the relative paucity of land-land antipodes
and
> the
> > > relative paucity
> > > > of tripoints near the poles, the variations due to
> spheriodicity
> > > and elevation
> > > > above sea level would probably be inconsequential in
> > > determining the two most
> > > > interdistant tripoints.
> > > >
> > > > At http://williams.best.vwh.net/gccalc.htm , you will find yet
> > > another
> > > > great-circle distance calculator into which one can enter
the
> > > coordinates of any
> > > > two points and get their circumferential distance apart.
> This
> > > calculator
> > > > differs from the others in that you can chose from various
> > > mathematical models
> > > > of the shape of the earth, from perfectly spherical through
a
> > > number of
> > > > spheroidal models. Among these last, the one currently
> > > accepted is
> > > > WGS84/NAD83/GRS80.
> > > >
> > > > Lowell G. McManus
> > > > Leesville, Louisiana, USA
> > > >
> > > >
> > > >
> > > > ----- Original Message -----
> > > > From: "acroorca2002" <orc@o...>
> > > > To: <BoundaryPoint@yahoogroups.com>
> > > > Sent: Wednesday, March 10, 2004 8:31 AM
> > > > Subject: [BoundaryPoint] Re: How far is it?
> > > >
> > > >
> > > > > really
> > > > > i dont remember that
> > > > >
> > > > > & it is an interesting question
> > > > > as well as a challenging try pointing quest
> > > > >
> > > > > perhaps even 2 of each
> > > > > since the farthest pair of points measured
> circumferentially
> > > > > might not be the same points as the diametrically
farthest
> > > pair
> > > > >
> > > > >
> > > > > yet exactly how to solve for either set
> > > > >
> > > > >
> > > > >
> > > > > alternatively
> > > > > someone may already have solved & posted answers
for
> > > them
> > > > >
> > > > > so perhaps a prior question is
> > > > > exactly how to search for any such ready made
answers
> > > > >
> > > > >
> > > > > &or
> > > > > failing that
> > > > > there must be some data on the geoid already
developed
> &
> > > > > available somewhere that might be useful toward these
> > > ends
> > > > > if we knew what to look for
> > > > >
> > > > > like
> > > > > greatest circumference & diameter figures might be a
> good
> > > > > place to start
> > > > > since these are likely to have been worked out to some
> > > degree
> > > > > of specificity & accuracy
> > > > >
> > > > > but where & how to find them
> > > > >
> > > > > & could we in fact approach the correct answers via
these
> > > data
> > > > >
> > > > > & if so
> > > > > by exactly what means could we get there from here
> > > > >
> > > > >
> > > > >
> > > > > but can anyone solve or advance this
> > > > >
> > > > > or even clearly see the right way to go
> > > > >
> > > > >
> > > > > --- In BoundaryPoint@yahoogroups.com, "L. A.
Nadybal"
> > > > > <lnadybal@c...> wrote:
> > > > > > We discussed some time back the maximum
distance
> that
> > > any
> > > > > two places
> > > > > > on earth could be from one another.
> > > > > >
> > > > > > This site claims to deliver the distances between two
> > > selected
> > > > > points:
> > > > > >
> > > > > > www.indo.com/distance/
> > > > > >
> > > > > > LN
> > > > >
> > > > >
> > > > >
> > > > >
> > > > > Yahoo! Groups Links
> > > > >
> > > > >
> > > > >
> > > > >
> > > > >
> > > > >
> > >
> > >
> > >
> > >
> > > Yahoo! Groups Links
> > >
> > >
> > >
> > >
> > >
> > >
>
>
>
>
>
> Yahoo! Groups Links