Element 
_{
Symbol} 
Value 
Epoch 
t_{o} 
05:54:21.171 UTC December 16, 2007 
Inclination 
i 
51^{o}.9970 
R.A.
of
the
Ascending Node 
a_{W}_{0} 
251^{o}.0219 
Eccentricity 
e 
0.0001492 
Argument of Perigee 
w_{0} 
33^{o}.8641 
Mean Anomaly at TLE Epoch 
M_{o} 
326^{o}.2322 
Mean Motion 
n 
12.62256095
orbits /
solar day 
Propagation Time 
Dt 
1.7677141
solar days 
Mean Anomaly at Time t 
M(t) 
1.37777389 radians (78^{o}.940629) 
True Anomaly at
Time t 
n(t) 
78^{o}.95065818 
Semimajor Axis 
a 
7791.787473 km 
Perigee Distance 
P 
7790.624938 km 
Geocentric Distance 
r(t) 
7791.564499 km 
Precessed R.A. of Asc. Node 
a_{W}(t) 
245^{o}.6400244 
Precessed Arg. of Perigee 
w(t) 
37^{o}.77767416 
Argument of Latitude 
m(t) 
116^{o}.7283323 
R.A. Difference 
Da 
129^{o}.278845 
Geocentric R.A. 
a_{g} 
14^{o}.9188694 
Geocentric Declination 
d_{g} 
+44^{o}.73125163 
Geocentric Cartesian x 
x_{g} 
5348.663965 km 
Geocentric Cartesian y 
y_{g} 
1425.05581 km 
Geocentric Cartesian z 
z_{g} 
5483.565179 km 
Observer Geodetic Longitude 
q 
75^{o}.6883 
Observer Geodetic Latitude 
l 
+44^{o}.5903 
Observer Geocentric Dec. 
d_{i} 
+44^{o}.5903 
Observer Geocentric R.A. 
a_{i} 
15^{o}.419875 
Observer Geocentric Cart. x 
a_{g} 
4371.468712 km 
Observer Geocentric Cart. y 
b_{g} 
1205.734692 km 
Observer Geocentric Cart. z 
c_{g} 
4470.310913 km 
The Topocentric
Cartesian Coordinates of the satellite can be determined by using the following
equations:
x_{s} = x_{g}  a_{g
}y_{s} = y_{g}  b_{g
}z_{s} = z_{g}  c_{g}
x_{s} = 977.195253 km
y_{s} = 219.321118 km
z_{s} = 1013.254266 km
Finally, the Topocentric Equatorial Coordinates of the GlobalStar M047 satellite as seen
from the observing
location on the Earth can now be calculated using the following equations.
The calculation of the Topocentric Right Ascension is dependant on conditions
that relate to which quadrant the satellite is in at the time:
a
= tan^{1} [ y_{s} / x_{s} ]
FOR
y_{s}>0 AND x_{s}>0
a
=
180^{o} +
tan^{1} [ y_{s} / x_{s} ]
FOR
x_{s}<0
a
= 360^{o} +
tan^{1} [ y_{s} / x_{s} ]
FOR
y_{s}<0 AND x_{s}>0
r = [ x_{s}^{2} + y_{s}^{2}
+ z_{s}^{2} ]^{1/2}
d
= sin^{1} [ z_{s} / r ]
r = 1424.674181 km
a
= 12^{o}.64980763 = 00^{h} 50^{m} 35^{s}.95
d
= +45^{o}.32255686 = +45^{o} 20' 02".84
