ok in morning light it looks like we can proceed further already
even without having to look for much more topographic detail
because all the highest equatorial areas of ecuador are far
higher as well as far steeper generally than anything on sumatra
in fact the most equatorial stripe of andean cordillera antipodizes
to the lowlands of sumatra
while the most equatorial highlands of sumatra antipodize to
areas of ecuador that are not nearly so steep
so it appears our quest is leading us to the highest equatorial &
pene equatorial peaks of the cordillera
a preliminary survey of ecuador at peakware etc suggests we
have a leading candidate in mount cayambe
which is ecuadors 3rd highest mountain
& which offers the highest elevations in the world on the equator
while peaking at only 2 minutes north latitude
but there are evidently 3 others in all that cant be ruled out
here are the raw & still unconfirmed data
1
chimborazo
elev 6310 or 6267 meters
slat 01d28m x wlong 78d48m
2
cotopaxi
elev 5897 meters
slat 00d40m x wlong 78d26m
3
cayambe
elev 5786 or 5780 meters
nlat 00d02m x wlong 77d58m
4
antisana
elev 5752 or 5705 meters
slat 00d29m x wlong 78d08m
possibly close enough to stay in the running
at the minimum bulge gradient of 477 meters per degree
just in case there happens to be a high enough hill at the
sumatran antipodes for the diametric length to exceed the
diametric lengths produced from all 3 of ecuadors higher peaks
5 etc
evidently all lower than 5315 meters
which would easily disqualify them all
even at the minimum bulge gradient of 477 meters per degree
& tho we still dont know the actual gradient of the bulge
it is clear that cayambe would not be overtaken by any of these
other peaks even at the minimum gradient
but it just isnt clear yet what boost any of the 4 diametric trials
would get from their antipodal partner elevation in sumatra
most probably not nearly enough boost to matter tho
so for now it sure likes like the summit point of cayambe & its
antipodal counterpart are the winners
obviously tho
more & better detail
as well as the most exact measurement possible
are needed before resting completely satisfied that we have
done it
--- In
BoundaryPoint@yahoogroups.com, "acroorca2002"
<orc@o...> wrote:
> 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