From: nospam@de-ster.demon.nl (J. J. Lodder)
Subject: Re: This Week's Finds in Mathematical Physics (Week 175)
Date: Mon, 31 Dec 2001 00:08:47 +0000 (UTC)
Newsgroups: sci.physics.research,sci.physics,sci.math
Summary: Fine-tuning geometric models of the Earth

John Baez <baez@math.ucr.edu> wrote:

snip
> Four of the last five sentences are true.  In particular, you really
> *can* see a green laser beam shining due north from the Royal 
> Observatory, across the Thames, past the Citigroup Building and out 
> into the night.  And speaking of longitude, the day before Christmas
> I visited this observatory and had a wonderful time learning how John
> Harrison solved the longitude problem.  

Sure, but it can't be the zero meridian, as anyone who has been there
carrying a GPS receiver can tell you. The brass line in Greenwich
observatory is about a 100 m off from 0^o0'00'' nowadays.
How this can be is a FAQ in sci.geo.satellite-nav:
In order to define a grid on the earth a 'datum' is needed,
actually a parameterization of the 'best fiting' ellipsoid.
(Best fitting to the geoid that is)

As it happened, the man who did the work originally,
Airy (indeed -the-), used an ellipsoid that fitted well in England.
Unfortunately this ellipsoid is off-center with repect to the current
internationally accepted datum (WGS84). To make both systems fit the
common reference point was chosen to be the intersection of Airy's zero
meridian with the equator, with the consequence that it is off in
Greenwich.
(It is in the Altantic ocean, no complaints from the residents)
The mark on the ground at Greenwich is of historical interest only.
Some of the 'equator marks' in Africa are off for the same reason.

> The longitude problem?  Ah, how soon we forget!  It's pretty easy to
> tell your latitude by looking at the sun or the stars.  However, it's
> pretty hard to tell your longitude, unless you have a clock that keeps
> good time.  After all, if you know what time it is in a fixed place,
> like Greenwich, you can figure out how far east or west you've gone by
> comparing the time you see the sun rise to the time it would rise there.

Actually seeing the sun rise won't do, for various reasons.
You should time the higest point at midday instead.
That's what these guys with sextants in the old sea paintings are doing.

> Unfortunately, until the late 1700's, pendulum clocks didn't work well
> at sea, due to the rocking waves.  This was a real problem!  Ships would
> lose track of their longitude, go astray, and sometimes even run aground,
> killing hundreds of sailors.  

Pendulum clocks still won't do their thing at sea :-)
However, they were quite useful to keep time at fixed stations.
Using them in observatories made it possible to determine the longitude
of at least a couple of fixed points very accurately.

Getting the timing correct was done by watching the motions
(eclipses) of the Jovian moons, which could be accurately predicted.
(After Romer had sorted out the finite speed of light mess).

Best,

Jan