Global Positioning System Reference
In-Depth Information
four generations of Cassinis would dominate the observatory and also the
Académie Royale des Sciences. They would eventually produce an accurate
map that showed France to be significantly smaller than had been thought.
Over the period 1683-1716 Giovanni Cassini and his son Jacques extended
Picard's meridian arc southward to Collioure, while Philippe de Lahire
extended it northward to Dunkirk. These measurements resulted in two
estimates of the length of a degree longitude (that is, of the length of 1\ of
arc running north-south). The length of a degree north of Paris was found
to be less than the length south of Paris (see the caption to fig. 2.8a for the
reason). Because they felt that the survey had been conducted very accu-
rately, the Cassinis concluded that the earth was not a sphere, but was
instead a prolate spheroid, stretched at the poles like an egg. This was the
first evidence that the earth was not spherical.
We have seen that Newton also thought the earth was not quite spheri-
FIGURE 2.8.
Prolate and oblate
spheroids. (a) The Cassinis believed
that the earth was stretched at the
poles. (The stretch is greatly exag-
gerated here.) The dashed lines 1-4
are all perpendicular to the prolate
spheroid; if the angle between line
1 and line 2 is the same as the angle
between 3 and 4 (say 1
\
), then the
meridian arc length
d
will be
shorter than
D
, because the curva-
ture of the surface is greater at 1-2
than at 3-4. (b) This oblate spheroid
is flattened by
1
⁄
5
. The earth is much
closer to being a sphere: it is flat-
tened by about
1
⁄
300
.
