Re: [Phys-l] A question about the Earth's gravity

[John Denker <jsd@av8n.com>]

On 05/07/2009 08:51 AM, Fakhruddin, Hasan wrote:
> I sure was referring to change in g due to deviation (however small)
> from a perfectly spherical shape.

OK, now we know that's what you meant.  But it's not what you said.

On 05/07/2009 05:46 AM, Fakhruddin, Hasan wrote:
> > We claim that the earth's gravity at its poles is slightly greater
> > than that at its equator. 

First of all, if you ask about "the earth's gravity" in a thread 
where the Subject: is "the earth's gravity" you shouldn't be surprised 
if you get answers that describe the earth's gravity.

Secondly, you cannot separate the centrifugal effects from the
shape effects.  Physics does not permit it.  To a good approximation,
more than good enough for present purposes, the surface of the earth
is an equipotential.  When quantitatively calculating (or just 
qualitatively explaining) the departure from sphericity, the dominant
contribution is the centrifugal field.

This result does not depend on modern physics, but rather on basic,
practical, operational definitions of "gravity" and "vertical" that 
predate Newton by thousands of years.  If you drop something, it tends
to go "down".  If you build a monument, you want the centerline to be
mostly "vertical".  If you build a pool, you want the deck to be
"horizontal".  Operationally, the vertical directions is:
 a) not determined by drawing a straight line to the center of the 
  earth, but rather 
 b) determined by the local gravitational acceleration, i.e. the local 
  g field.

In temperate latitudes, (b) differs from (a) very significantly, and
the dominant contribution to the difference is the centrifugal field.

Newton's theory of universal gravitation simply cannot change this basic,
practical, operational, observable fact.  No amount of sophistic pedantic
PER "theory" can change it.  Down is down.  Vertical is vertical.  Horizontal
is horizontal.  Gravity is gravity, and ever more shall be so.  The
centrifugal terms are necessarily included.

If you choose to /approximate/ gravity using the Newtonian GMm/r formula, 
that's good enough for some purposes but not others.  It is absolutely
not good enough for understanding the departure from sphericity.  It is
not even good enough for day-to-day architectural engineering.

For more on this, including some quantitative numbers, see
  http://www.av8n.com/physics/weight.htm