Step 14 - The Satellite's Equatorial Coordinates

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_W₀	251^o.0219
Eccentricity	e	0.0001492
Argument of Perigee	w₀	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
Semi-major 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_gy_s = y_g - b_gz_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_s² + y_s² + z_s² ]^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

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Step 14: Satellite's Equatorial Was Last Modified On May 29, 2015