In order to find the Keplerian orbit elements, we must first know the satellite's position and velocity. In order to determine those, we will first need to determine the satellite's topocentric ranges (distance from the observer to the satellite) for all three observations. This can be done by using the following equations: c_{1} =
t_{1}
+ mt_{2
}/ (r_{2})^{3
}c_{2} = -1 c_{1} =
0.5403414 Now we can determine the actual topocentric ranges of the satellite at all three observation times: r_{1}
= (M_{12} - M_{11}c_{1 }- M_{13}c_{3}) /
c_{1} r_{1}
= 2,373.1528 km Note that the second topocentric range (828 km) is very near the estimated altitude of the satellite (816 km) determined in Step 7. This is encouraging, as the second observation of the satellite occurred when the satellite was at the location's zenith and therefore its topocentric range at that point would nearly be the orbit altitude of the satellite at that specific time. The other two topocentric ranges (r_{1} and r_{2}) also look encouraging since the other two observations were made when the satellite was only 10 degrees above the local horizon. |
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Step 8: Topocentric Ranges Was Last Modified On September 23, 2013 |