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Re: [Phys-l] polar grid navigation



So... after all the messages posted on this list-serv ridiculing the news reports... it turns out the news reports were correct. If you use the pseudo grid for Antarctica that navigators and scientists in Antarctica are known to use (where grid north aligns with the prime meridian), then Lake Vostok is indeed southeast of the south pole. Actually I would call it "east southeast".

If you Google "Antarctica map" you can find quite a few jpg images of maps of Antarctica. Many of them are gridded as Hugh Haskell described. On these gridded maps Lake Vostok is indeed east southeast of the south pole. The news folks didn't make those maps. The scientists and navigators and geographers made those maps.

Here is one such map... http://geology.com/world/antarctica-map.jpg and it shows Lake Vostok.


Michael D. Edmiston, PhD.
Professor of Chemistry and Physics
Chair, Division of Natural and Applied Sciences
Bluffton University
Bluffton, OH 45817
Office 419-358-3270
Cell 419-230-9657

-----Original Message-----
From: phys-l-bounces@carnot.physics.buffalo.edu [mailto:phys-l-bounces@carnot.physics.buffalo.edu] On Behalf Of John Denker
Sent: Wednesday, February 15, 2012 4:14 AM
To: Forum for Physics Educators
Subject: Re: [Phys-l] polar grid navigation

On 02/14/2012 09:51 PM, Hugh Haskell wrote:
In the polar regions air navigation is not by the Lat/Long convention,
but by a square grid oriented parallel to the 0/180 meridian, and
tangent to the earth near the mid point of the intended flight
path.Compases are set to O° parallel to the Greenwich meridian (180°
when heading north along the 180° meridian).

Right. This is called "polar grid navigation".

Another name for it is "displaced pole", which tells you something about the physics involved: Imagine a new set of spherical polar coordinates, where the pseudo-north pole is in the Gulf of Guinea, south of Ghana and west of Gabon. Then, if you are anywhere near Antarctica,
-- the direction toward the Gulf of Guinea is pseudo-north aka grid-north
-- the direction toward Guatemala is pseudo-west aka grid-west
-- the direction toward Fiji is pseudo-south aka grid-south
-- the direction toward Bangladesh is pseudo-east aka grid-east

For example, starting from the pole, to get to Vostok Station you have to go pseudo-east (to a first approximation). Once you get there, if you keep going true north, that is still pseudo-east.

It's hard to find accessible references about this, but here is a decent introduction:
http://sites.google.com/site/antarcticaclassproject/getting-around-in-antarctica

In the pictures, you can see the grid ... now that you know what to look for.

This
enables navigation to "look" reasonably normal, and gives a fixed
heading to a track between points near, but not crossing, the pole.

It works just fine even if you go directly over the true pole.

The true south pole is at the equator of the displaced coordinate system. There is nothing singular or even remotely weird happening anywhere near that point in the displaced coordinate system. Lines of (pseudo) longitude are straight and parallel near the (pseudo) equator.

===================

In case it is not 1000% obvious to everyone, this is relevant to many branches of physics ... from elementary particles to cosmology and lots of things in between.

The general idea is that there are lots of situations where you cannot find a coordinate system that is everywhere nonsingular ... but in any local region you can create a well-behaved /local/ coordinate system.

As the saying goes: "Physics is simple when analyzed locally."

==

This makes contact with a discussion from last week. This is one of the many reasons why you want to read Misner, Thorne & Wheeler _Gravitation_.

That book teaches you a lot of techniques that you get to use over and over again, in many branches of physics, not just gravitation and general relativity. The lessons include some specific, technical techniques, but also hints about how to think about physics in general, and a high-class /style/ of doing physics.

I reckon most physicists already know about local coordinate systems and overlapping coordinate systems, and already know that "Physics is simple when analyzed locally" ... but if you didn't already know that, how would you learn it? It's nice to have at least one book that discusses such things explicitly and emphatically.
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