98
4.3
TRANSFORMATION FROM ORBITAL TO AVERAGE TERRESTRIAL SYSTEM
The orbital plane does not rotate with the earth, but remains fixed
in the celestial system.
The orbital system and the apparent celestial
both have their origins at the centre of gravity of
107
5.3 DUALITY PARADOX IN THE APPARENT AND
OBSERVED CELESTIAL
The reason there are apparent and observed systems is because
the observer is not at the centre of the celestial sphere (the centre
of the sun) and this must
be accounted for.
There are two
wa
71
From the Greenwich meridian counterclockwise to the celestial meridian
is called the astronomic longitude cfw_A).
From the celestial meridian
clockwise to the hour circle is called the hour angle (h).
LST
= GST
LST
=h
Therefore,
37
+ A
+ a
38
+ A a
NCP(T0 )
80
NCP(T)
MIN EOtJaTOR
. 't)\ .
PftECESSION
Gl. .
.
Figure 39. MEAN
CELESTIAL
MC.To
COOftOINATE SYSTMS
81
as rates of changes in right ascension and declination) must therefore
be included in the conversion of mean place at T
o
3.5.3
to mean pla
Zenith
North
celestial
pole
Hour angle
Horizon
North
celestial
pole
North
ecliptic.
pole
Primary pole
(zaxis)
North point
Vernal eq_uinox
Vernal eq_uinox
Secondary Pole
(xaxis)
Reference Poles
Right ascensio
Ecliptic
System

Celestial
horizon
Celestial
62
the celestial sphere at the celestial eguator.
The gravity vertical
at a station on the earth is extended upwards to intersect the celestial
sphere at the zenith (Z), and downwards to intersect at the nadir (N).
The plane of the earth's orbit around th
53
260
"
Note that so far no translation!; have taken place.
We have merely
rotated the position vector (rk1 ) of station 1 with respect to station
k
into the average terrestrial system.
If the position vector of
station k with respect to the centre of g
36
2.3.1
Datum Position Parameters
In order to establish an ellipsoid as the reference surface for
a system of control we must specify its size and shape (usually by assigning
values to the semimajor axis and flattening) and we must specify its position
19
2. 2
RELATIONSHIP BETWEEN CARTESIAN AliD CURVILINEAR COORDIIIATES
In this section we first describe the Cartesian (x, y, z) and
curvilinear (latitude, longitude, height) coordinates for a point on the
reference ellipsoid.
We then develop expressions fo
44
Table 21
PARAMETERS DEFINING THE
1927 NORTH AMERICAN DATUM
Date Ado;eted
Clarke 1866 Ellipsoid semimajor axis
Clarke 1866 Ellipsoid semiminor axis
= 6378206.4
a
b
Initial Point Latitude of Meade's Ranch
0
Initial Point Meridian Deflection
Component
28
Rotating the coordinate system to introduce longitunes
x*
X
r =
y
= R3(A.)
COSA
a case
=
0
z
2.2.4
a case
sin>.
z
226
b sine
Relationships between Geodetic, Geocentric and Reduced Latitudes
From equations 224, 225, and 226
z
 =
X
b
a
tan$ cosA.
c
10
The last specification is unambiguous.
three are not.
As we shall see the other
We will first discuss problems in defining the earth's
axis of rotation and the Greenwich meridian.
we will discuss
translations of the origin from the centre of the earth.
l.
INTRODUCTION
These notes discuss the precise definitions of, and transformations
between, the coordinate systems to which coordinates of stations on or
above the surface of the earth are referred.
To define a coordinate
system we must specify:
a)
the l