Re: [Phys-L] field of an ellipsoidal distribution

["Donald G Polvani" <dgpolvani@verizon.net>]

On August 8, 2015 at 5:14 pm, David Bowman wrote:

"Another consequence of this result is that the surface gravity g as a
function of geodetic latitude, è must acquire the form:

g(è) = g_0*(1 + k*sin^2(è))/sqrt(1 - e^2 *sin^2(è))

where g_0 is the surface gravity on the equator, e is the spheroid's
eccentricity, and k is a nonnegative constant that depends on how the mass
is distributed internally.  If the internal mass distribution has a constant
density then k is zero.  For Earth k = 0.00193185 indicating that the Earth
is denser in its inside than on its outside.  Also Earth's values for the
other two parameters are e = 0.081819191 & g_0 = 9.7803268 m/s^2.  I believe
the the above equation for g(è) is called the Somigliana equation."

The equation doesn't seem to apply to a spherical (e = 0), constant density
(k = 0) object which is rotating, since you get:

g(theta) = g_0

which is correct if the object is not rotating but shows no dependence of g
on latitude (theta) due to the rotation.   Is k not zero for a rotating
object even if the density is constant?  Or ???

Don

Dr. Donald G. Polvani
Adjunct Faculty, Physics, Retired
Anne Arundel Community College
Arnold, MD 21012