Geoscience Reference
In-Depth Information
2
3
sinL
N
cosL
N
0
4
5
ð
þ
H
Þ
ð
þ
H
Þ
2
4
3
5 new
2
4
3
5
ʷ
N
Δ
X 0
sinBcosL
M
sinBsinL
M
cosB
M
Δ
Y 0
ð
þ
H
Þ
ð
þ
H
Þ
ð
þ
H
Þ
Δ
Z 0
cosBcosL
cosBsinL
sinB
2
3
old
0
0
4
5
N
e 2 sin 2 B
M 2
ð
Þ
a e 2 sinBcosB
Δ
a
sinBcosB
ð
M
þ
H
Þ
þ
ð
M
þ
H
Þ
ð
1
f
Þ
Δ
f
sin 2 B
N
a
M
e 2 sin 2 B
e 2 sin 2 B
1
1
1
f
2
3
old
ð
ʻ
L old
Þ
cosB old
4
5
þ
ˆ
B old
,
N old
This gives ʾ, ʷ, andN at each astro-geodetic point, including at the geodetic
origin, and eventually provides the new geodetic origin data.
The result of the astro-geodetic orientation indicates that, at the geodetic origin,
the direction of the normal to the ellipsoid does not coincide with that of the plumb
line, and the ellipsoid is no longer a tangent to the geoid. However, the ellipsoid
surface is the best fit to the geoid over an area of interest.
When determining the ellipsoid orientation in an area (non-global) of interest
based on
N 2
minimum, the ellipsoid center will not coincide with the Earth's
center of mass. Thus, we get a local orientation or non-geocentric orientation. The
established coordinate system is called the local coordinate system or
non-geocentric coordinate system.
Differing from the above neoteric methods for arc measurement, the concepts of
arc measurement in modern times have greatly expanded. Integrating the gravity
and spatial geodetic surveying data worldwide, the arc measurement in modern
times studies the Earth from both geometric and physical perspectives, including
the geometric shape and size of the Earth ellipsoid as well as the gravity field of the
Earth.
Another four fundamental parameters are used to describe the Earth,
a (semimajor axis of the ellipsoid), GM (the product of gravitational constant and
the mass of the Earth), J 2 (second-order zonal harmonic coefficient of the Earth's
gravity field),
(angular velocity of the Earth's rotation), and a series of geometric
and physical constants derived from these as well as the Earth gravity field model.
ˉ
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