Re: [Phys-l] polar grid navigation

[John Denker <jsd@av8n.com>]

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.