Step 13 - Determining the Location`s Geocentric Cartesian 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

We now need to find the distance from the Earth's center to the observing location:

r_g = { [ cosd_i / R_E ]² + [ sind_i / R_P ]² }^-1/2 + A

where: R_E = the Equatorial Radius of the Earth = 6378.135 km
R_P = the Polar Radius of the Earth = 6356.752 km; and
A = the Altitude Above Sea Level of the Observing Location = 0.1 km

r_g = 6367.669472 km

The Geocentric Equatorial Cartesian coordinates of the observing location can now be calculated by using the following equations:

a_g = r_gcosa_icosd_i
b_g = r_gsina_icosd_i
c_g = r_gsind_i

a_g = 4371.468712 km
b_g = 1205.734692 km
c_g = 4470.310913 km

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PROCEED TO STEP #14

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Step 13: Location's Cartesian Was Last Modified On April 01, 2014