Earth and Its Orbit - The Science of Navigation - page 17

because of the centrifugal force that arises from rotation. The planet must
bulge slightly at the equator and be flattened a little at the poles. On the
basis of his law of gravity and an assumption that the earth is a fluid, he
calculated that the bulge was about 1 ⁄ 230 ; that is, the earth's diameter at the
equator is larger than the diameter between the poles by this fraction. In
fact, we now know that the earth is not really (or not wholly) a fluid, and so
the deviation of its shape from a sphere is less than Newton calculated: it is
about 1 ⁄ 298 . (The bulging e√ect of the centrifugal force is less pronounced
than it would be for a fluid because solid material is more resistant to
deformation.) A century after Newton, two French expeditions were sent
out to di√erent parts of the world to see if his idea about the bulging earth
was correct. A controversy raged at the time concerning the shape of the
earth, with some eminent French physicists opining that our planet was a
prolate spheroid, like an egg (a stretched sphere, instead of a squashed
one). We will meet up with these French expeditions in the next chapter.
In the twentieth century, yet more accuracy was needed. For the pur-
poses of geodesy , 11 it was no longer su≈cient to say that the earth was an
ellipsoid. A better definition came by considering gravitational contours.
Imagine a large number of plumb lines, all over the earth, the oceans as
well as the land—let us say one plumb line on every square meter of the
planet. Imagine now a surface that is perpendicular to all those plumb
lines. Physicists call this an equipotential surface . There are many equi-
potential surfaces, but one is special. The geoid is the equipotential surface
that coincides with mean (average) sea level. It is considered to be the true
shape of the earth.
Clearly, the geoid must be very similar to the earlier ellipsoid, because it
pretty much coincides with it over the sea. 12 There are slight deviations, es-
pecially over land, due to the uneven distribution of mass within the earth.
A large deposit of dense metallic ore will cause the geoid to bulge outward
11. According to the Oxford English Dictionary , ''That branch of applied mathematics
which determines the figures and areas of large portions of the Earth's surface, and the
figure of the Earth as a whole.''
12. The seas, being fluid, flow if a force acts on them. Consequently, the sea surface must
coincide with a gravitational equipotential surface. Think about it (and let's suspend the
moon's influence for a moment): if there were a horizontal component of the gravitational
force on one part of the sea surface, the sea would move under the action of this force to a
position where there was no such horizontal force. That is, the sea would flow until its
surface was equipotential (in practice, very close to the geoid). Note that the geoid is
not necessarily a surface of equal gravitational strength because of the e√ect of the centrifu-
gal force.