Although we have found the possible topocentric ranges of the satellite for all three observation times, we still have not found the Keplerian orbit elements. This will be done by first determining the "state vector", which comprises of the satellite's geocentric distance matrix (which will be determined in this step) and the velocity vector at the second observation time (which will be determined in the following steps). The geocentric matrix is determined by using the following equations: r_{11} = r_{1}L_{11} + R_{11 }r_{12} = r_{2}L_{12} + R_{12 }r_{13} = r_{3}L_{13} + R_{13 }r_{21} = r_{1}L_{21} + R_{21 }r_{22} = r_{2}L_{22} + R_{22 }r_{23} = r_{3}L_{23} + R_{23 }r_{31} = r_{1}L_{31} + R_{31 }r_{32} = r_{2}L_{32} + R_{32 }r_{33} = r_{3}L_{33} + R_{33 }
If you determine the sum of the squares of each column, you will find the estimated geocentric distances of the satellite at each observation time: r_{1} = [ (r_{11})^{2} + (r_{21})^{2} + (r_{31})^{2} ]^{ 1/2 }r_{2} = [ (r_{12})^{2} + (r_{22})^{2} + (r_{32})^{2} ]^{ 1/2 }r_{3} = [ (r_{13})^{2} + (r_{23})^{2} + (r_{33})^{2} ]^{ 1/2} r_{1} =
7,204.0002 km Note that the second
of these ranges (r_{2}) is the same as that determined from the 8th
order equation in Step 7. This is correct. In fact, in order to check your
algebra, the r_{2} value here should be very similar to that value
determined in Step 7. |
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SITE MAP | ||
Step 9: Geocentric Matrix Was Last Modified On September 23, 2013 |