xg yg zg

 Element Symbol Value Epoch to 05:54:21.171 UTC December 16, 2007 Inclination i 51o.9970 R.A. of the Ascending Node aW0 251o.0219 Eccentricity e 0.0001492 Argument of Perigee w0 33o.8641 Mean Anomaly at TLE Epoch Mo 326o.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 (78o.940629) True Anomaly at Time t n(t) 78o.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 aW(t) 245o.6400244 Precessed Arg. of Perigee w(t) 37o.77767416 Argument of Latitude m(t) 116o.7283323 R.A. Difference Da 129o.278845 Geocentric R.A. ag 14o.9188694 Geocentric Declination dg +44o.73125163

The geocentric equatorial coordinates (R.A. and Dec.) of the satellite are known, but they are useless to observers on the surface of the Earth. We need to translate these coordinates to a location on the surface of the Earth that we wish to observe the satellite from.

First, we need to convert the satellite polar coordinates (r(t), ag, dg) into their equivalent Geocentric Cartesian Coordinates (xg, yg, zg) using the following equations:

xg = r(t)cosagcosdg
yg = r(t)sin
agcosdg
zg = r(t)sin
dg

xg = 5348.663965 km
yg = 1425.05581 km
zg = 5483.565179 km

In order to confirm that the Cartesian coordinates have been calculated correctly, add the sum of the squares of the answers and take the number's square root. The number you finally arrive at should be the original geocentric satellite distance, r(t):

xg2 + yg2 + zg2 should = r(t)2

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 SITE MAP Step 10: Geocentric Cartesian Was Last Modified On April 01, 2014