Global Positioning System Reference
In-Depth Information
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is defined by coordinates of a smaller set of essentially stationary quasars whose
positions are accurately known.
We denote the directions of the instantaneous rotation axis by the celestial ephe-
meris pole (CEP) and the normal of the ecliptic by the north ecliptic pole (NEP). The
angle between both directions, or the obliquity, is about 23.5°, which, by virtue of
geometry, is also the angle between the instantaneous equator and the ecliptic. As
shown in Figure 2.4, the rotation axis can be viewed as moving on a mantle of a cone
whose axis coincides with the ecliptic normal.
Mathematically, the motion is split into a smooth long-periodic motion called lu-
nisolar precession and short-periodic motions called nutations. Precession and nuta-
tion therefore refer to the motion of the earth's instantaneous rotation axis in space. It
takes about 26,000 years for the rotation axis to complete one motion around the cone.
The nutations can be viewed as ripples on the circular cone. The longest nutation is
18.6 years and has the largest amplitude of about 20
. The cause of precession and
nutation is the ever-changing gravitational attraction of the sun, the moon, and the
planets on the earth. Newton's law of gravitation states that the gravitational force
between two bodies is proportional to their masses and is inversely proportional to
the square of their separation. Because of the earth's and the moon's orbital motions,
the separation between the sun, the moon, and the earth changes continuously. Since
these changes are periodic, the resulting precession and nutations are periodic in time
as well, reflecting the periodic orbital motions. The only exception is a small plan-
etary precession stemming from a motion of the ecliptic. Because of Newton's law
of gravitation, the distribution of the earth's mass also critically impacts precession
and nutation. Important features are the flattening of the earth, the noncoincidence of
the equatorial plane with the ecliptic, and the noncoincidence of the orbital plane of
the moon with the ecliptic. Nonrigidity effects of the earth on the nutations can be
observed with today's high-precision measurement systems. A spherical earth with
homogeneous density distribution would neither precess nor nutate.
[20
Lin
—
0.9
——
Sho
PgE
[20
NEP
CEP
ε
= 23.5
o
Figure 2.4 Lunisolar precession and nutation.
The spatial
motion of the CEP is parameterized in terms of precession and
nutation.
