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Fred Hebard quoted my remark-

>> Even the ellipsoidal
>> effects caused by the Earth's spin give rise to changes which are less
>> than
>> 1%. And the hills and dips, that we've been discussing in such detail,
>> are
>> molehills on that ellipsoid. So the gravity variations that we have
>> been
>> discussing are small, and the surfaces of equal potential and the
>> surfaces
>> of equal gravity, though not spherical shells, are pretty damn near to
>> that.

 and asked-

>So, once again, just how big are these molehills?  200 meters is about
>.001% of the earth's radius, if my calculation is correct, which is
>pretty insignificant.  But that would be a fair-sized skyscraper or
>hill.

Fred has asked this before, and by now deserves some sort of answer. In the
absence of a specialist on geophysics or geodesy, I will do the best I can;
but note my limitations.

However, I hope by now that everyone can accept that the hills and dips we
refer to in the ocean surface are just variations in the distance to the
Earth's centre. They are not hills and dips in the sense that there's any
uphill and downhill, requiring or giving back energy in order to transit
them. In gravitational terms, they are as flat as flat can be: perfect
territory for a bike ride, if the surface was hard enough.

Until the 1700's a spherical model for the Earth was all that was needed,
but then it was realised that its spin caused it to bulge a bit at the
equator, and the spin itself slightly modified the effect of gravity at the
surface. For mapmakers and astronomers, an ellipsoid, with a difference of
about 1 in 300 between the equatorial radius and the polar radius, provided
a good approximation. This implies that the distance from the ocean surface
to the Earth's centre varies from its mid-value (at a latitude of about 45
degrees) of about 6367 km, by roughly +11km at the equator and -11km at the
poles. These effects are the biggest of the "hills and dips".

It's long been realised that because the Earth is made of such non-uniform
stuff, of continental masses of granites and limestones swimming around in
molten magma, such an ellipsoid can only be a crude approximation, and the
coming of satellites has allowed the ocean surface to be mapped much more
precisely. That sea-level equipotential surface, which is known as the
"geoid", extends, inaccessibly, under the surface of the continents. The
difference between the geoid and the standard ellipsoid is presumably what
is referred to in the papers originally quoted by David Hoyte, which
started this whole business off on Nav-l. Here's what he said, again-

===========

> The joint NASA-German GRACE project has released the most
>accurate map yet of Earth's gravity field. It shows Gravity Anomaly,
>(mGal), on a global map at the URL:
>http://photojournal.jpl.nasa.gov/catalog/PIA04652
>
>        These gravity anomalies cause the geodic heigh of the ocean's
>surface to vary around the world by up to 200 meters, 650 feet. Ref:
>http://www.csr.utexas.edu/grace/publications/press/03-07-21-ggm01-nasa.html
>
>        In the Atlantic ocean, for example, there is a hill South of
>Greenland of +200 feet, and a dip in the Caribbean of -250 feet, approx.

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

That extract was the only part of David Hoyte's mailings that I didn't
question. I haven't followed up the refs, but have no reason to doubt what
he says here.

It's rather puzzling why Fred Hebard finds such figures hard to accept, it
he can accept the ? 11 km deviation of the ellipsoid from a sphere. Perhaps
it's the use of the words "hill" and "dip". These deviations, of hundreds
of feet, are spread out over thousands of square miles of surface. The
deviations of the curvature of the horizon from its normal value would be
so small as to be undetectable. The features are so spread-out that any
resulting tilt of the horizontal is insufficient to affect star altitudes
for navigational purposes. When Fred compares these shallow deviations with
a "skyscraper" he has quite the wrong picture in his mind. He seems to be
thinking of something like the parting of the Red Sea...

But I make the point once again, that on the ocean surface, over these
"hills and dips" there is NO component of gravitation force, NONE AT ALL,
urging you toward the nearest "dip". And it's NOT because these deviations
from the ellipsoid are such shallow ones, it would be just as true if the
deviations were vastly greater. I think many of the misunderstandings arise
from the use of the words "hills and dips" in an inappropriate context.
They are just deviations, positive and negative ones, from the standard
ellipsoid. You don't go up them, and you don't go down them.

George.

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contact George Huxtable by email at george@huxtable.u-net.com, by phone at
01865 820222 (from outside UK, +44 1865 820222), or by mail at 1 Sandy
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