Re: polar vs equatorial gravity

From: Edward Green (spamspamspam3_at_netzero.com)
Date: 10/27/04 

Date: 26 Oct 2004 17:33:36 -0700

zxcvnosend@yahoo.com (zxcv) wrote in message news:<acae8a4d.0410240751.6fd3c5ac@posting.google.com>...
> spamspamspam3@netzero.com (Edward Green) wrote in message news:<eca320d0.0410231938.40b6954d@posting.google.com>...

> I think this is the first answer I can understand. Thank you.

You are very welcome.

> (Thank
> you to the others as well. The fact that I cannot understand is my
> failing, not theirs.)

I should mention that Gene Nygaard seems to have given by far the most
technically complete answer -- I only say "seems" because he also
seems to be an expert, and as such I lack standing.
 
> The big mistake I made was assuming that the formula for gravitation
> that I used was correct for any mass when in reality (as many
> respondents mentioned) it only applies for a point mass or a uniform
> sphere. Clearly which the earth is not.

Right. One question I had was whether this correction attributable to
deviation from sphericity is significant in calculating the surface
gravity of the Earth. Nygaard says it is.
 
> Your sentence "I know for sure that the [mean] _sea level_ must be an
> equipotential." says it all for me. That, and the fact that there IS
> sea level at the North Pole and the equator. Now I can relax.

Oh, well, don't get too complacent yet!

You seem to have been bothered in your original post that you
calculated a _different_ effective gravitational field at two points
on the Earth's surface. Various people assured you this is quite all
right, and Nygaard confirms that there is a variation, and that you
were in the ballpark:

           Pole Equator

 You 500 495 lbf

 Nygaard 502.7 500 lbf

The problem I have is, in thinking more about the spinning liquid drop
model, I have reached the tentative conclusion that there _cannot_ be
a variation!

Oops. :-/

Here's the argument in outline:

(1) the mean shape of the Earth can be understood as that of a
spinning gravitating liquid drop; and

(2) gravity and centrifugal force can be combined to form an effective
joint potential for a spinning massive system; and

(3) a condition of equilibrium for a liquid drop in a potential is
that the free surface be an equipotential surface; and

(4) a second condition of equilibrium for a liquid drop in a potential
is that the potential gradient be equal at all points on the free
surface.

The "potential gradient" is what gives us the effective weight.
Obviously there is a little problem here. I am confident in (3) and
(4), so that leaves (1) or (2) as the likely culprits -- either the
Earth is able to freeze in long-term non-hydrostatic stress, or else
the alleged combined potential does not act like a bonafide potential
after all.

I wonder if anybody can help resolve this.

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