ri

 Variable Symbol Value Time Coefficient 1 t1 0.5101194 Time Coefficient 2 t2 28233.955 s2 Time Coefficient 3 t3 0.4898806 Time Coefficient 4 t4 27855.560 s2 Geocentric Range r2 7,194.4100 km Gravitational Parameter m 398600.44 km3/s2

 -14028.095 km -20859.718 km -28020.276 km M = 11249.889 km 13626.673 km 16116.251 km -13733.543 km -20437.266 km -27465.919 km

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:

c1 = t1 + mt2 / (r2)3
c2 = -1
c3 =
t3 + mt4 / (r2)3

c1 = 0.5403414
c2 = -1
c3 = 0.5196976

Now we can determine the actual topocentric ranges of the satellite at all three observation times:

r1 = (M12 - M11c1 - M13c3) / c1
r2 = (M22 - M21c1 - M23c3) / c2
r3 = (M32 - M31c1 - M33c3) / c3

r1 = 2,373.1528 km
r2 = 827.68474 km
r3 = 2,419.6918 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 (r1 and r2) also look encouraging since the other two observations were made when the satellite was only 10 degrees above the local horizon.

BACK TO STEP #7

PROCEED TO STEP #9

 SITE MAP Step 8: Topocentric Ranges Was Last Modified On September 23, 2013