Step 9 - Finding the Geocentric 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

The R.A. Difference is the difference between the Geocentric Right Ascension of the satellite and its (precessed) R.A. of Ascending Node:

Da = a_g - a_W(t)

Rearranging the terms, the Geocentric Right Ascension (a_g) coordinate of the Satellite can be found by using the following equation:

a_g= Da + a_W(t) - 360^o { INTEGER [ (Da + a_W(t)) / 360^o ] }

a_g = 14^o.9188694

The Geocentric Declination (d_g) coordinate of the satellite can be determined by using the following equation:

d_g = [SIGN (sinm(t))] cos^-1 [ cosm(t) / cosDa ]

IMPORTANT NOTE: When using this equation, please keep in mind that the SIGN (sinm(t)) term means that only the sign of the result is to be used (+1 or -1) and not the value of the sine itself. SIGN (sinm(t)) is used only to determine the sign of the geocentric declination (above or below the celestial equator).

d_g = +44^o.73125163

BACK TO STEP #8

PROCEED TO STEP #10

CASTOR HOME	SITE MAP	*ORBIT PROPAGATION*

Step 9: Finding the Geocentric Coordinates Was Last Modified On April 01, 2014