Global Positioning System Reference
In-Depth Information
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calendar), 1582, was labeled October 15 (Gregorian calendar). The proceedings of
the conference to commemorate the 400th anniversary of the Gregorian calendar
(Coyne et al., 1983) give background information on the Gregorian calendar. The
astronomic justification for the leap year rules stems from the fact that the tropical
year consists of 365
d
.
24219879 mean solar days. The tropical year equals the time it
take the mean (fictitious) sun to make two consecutive passages over the mean vernal
equinox.
2.
3 DATUM
Th
e complete definition of a geodetic datum includes the size and shape of the ellip-
so
id, its location and orientation, and its relation to the geoid by means of geoid un-
du
lations and deflection of the vertical. The datum currently used in the United States
is
NAD83, which was developed by the NGS (NGS, 2002). In the discussion below
we
briefly introduce the geoid and the ellipsoid. A discussion of geoid undulations
an
d deflection of the vertical follows, with emphasis on how to use these elements to
re
duce observations to the ellipsoidal normal and the geodetic horizon. Finally, the 3D
ge
odetic model is introduced as a general and unified model that not only deals with
ob
servations in all three dimensions, but is also mathematically the simplest of all.
[29
Lin
—
-
——
Sho
*PgE
2.3.1 Geoid
Th
e geoid is a fundamental physical reference surface to which all observations refer
if
they depend on gravity. Because its shape is a result of the mass distribution inside
th
e earth, the geoid is not only of interest to the measurement specialist but also to
sc
ientists who study the interior of the earth. Consider two point masses
m
1
and
m
2
se
parated by a distance
s
. According to Newton's law of gravitation, they attract each
ot
her with the force
[29
k
2
m
1
m
2
s
2
F
=
(2.41)
where
k
2
is the universal gravitational constant. The attraction between the point
masses is symmetric and opposite in direction. As a matter of convenience, we
consider one mass to be the “attracting” mass and the other to be the “attracted” mass.
Furthermore, we assign to the attracted mass the unit mass
(m
2
=
1
)
and denote the
attracting mass with
m
. The force equation then becomes
k
2
m
s
2
F
=
(2.42)
and we speak about the force between an attracting mass and a unit mass being at-
tracted. Introducing an arbitrary coordinate system, as seen in Figure 2.8, we decom-
pose the force vector into Cartesian components. Thus,