# [time-nuts] Information on the Danjon Astrolab

James Maynard james.h.maynard at usa.net
Tue Aug 8 19:18:30 EDT 2006

```Rasputin Novgorod wrote:
>>ofcourse they have a different local gravity and the

> Wait a minute. The center of gravity ~is~ the center of gravity.
> You can't have two, or multiple centers. The strength of gravity
> varies from place to place, but that doesn't change the direction.
> If I'm wrong; please explain...
>
You are wrong. Here's my attempt at an explanation.

The direction of gravity -- the direction of the plumb line -- is
everywhere normal to the local gravitational equipotential surface. (The
particular gravitational equipotential surface that corresponds to mean
sea level is called the "geoid.")  The geoid is is not exactly an
ellipsoid of revolution, although such as ellipsoid (such as the WGS-84
ellipsoid, for example) is used to define the location of the
"graticule" - the grid of meridians of longitude and parallels of
latitude that we use for a horizontal datum. For many surveying
purposes, a different reference surface, the geoid, is used instead of
the ellipsoid. The direction of the plumb line (the "down" direction) is
normal to the local gravitational equipotential surface -- that is,
normal to the geoid if you're location is at sea level.

The normal to the ellipsoid andthe normal to the geoid do not point
directly at the earth's center of mass (the "geocentre").  They might
point at the geocentre if the earth did not rotate on its axis, but the
earth's rotation, and the centrifugal force that we observe as we rotate
with it, causes the geoid to fit more closely to an ellipsoid than to a
perfect sphere.

The angular difference between the normal to the ellipsoid and the plumb
line (the normal to the geoid) is called the "deflection of the
vertical," and is typically a few seconds of arc.  (The deflection of
the vertical was discovered during the 19th century by British surveyors
during the great survey of India. The same survey organization, also
discovered that Mount Everest was so tall, and named it after their leader.)

If the earth was a perfect sphere (which it could only be if it didn't
rotate on its axis), and was perfectly uniform in its mass density, then
all plumb lines would pass through the geocentre.  But the earth does
rotate, and it has mountains and seas with different densities of the
underlying rocks, so the geoid is not spherical, and the plumb lines do
not generally pass through the geocentre.

--
James Maynard
Salem, Oregon, USA

```