STEP 1: ORBIT ELEMENTS

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Now that we have found an initial orbit for the mysterious satellite, can we trust it for general propagation? The only way to find out is to either propagate it and see if can be detected again or use an orbit element set from a reputable source. For this example, the latter will be done.

The satellite in this example was a Russian SL-16 rocket body that is catalogued as NORAD #19120 (or CASTOR #1627). The orbit elements (TLE) for this satellite were obtained and provided here next to the determined orbit elements for comparison purposes.

Keplerian Orbit Element Symbol Determined Value TLE Value
Epoch Time tepoch 23:05:28.22 UTC January 3, 2012 02:28:42.20 UTC January 2, 2012
Semi-major Axis a 7,310.8163 km 7207.1667 km
Semi-major Axis (Altitude) aalt 932.6793 km 829.02972 km
Period T 103.68323 min 101.4861 min
Mean Motion n 13.888456 orbits/day 14.189135822 orbits/day
Eccentricity e 0.0159858 0.0021379
Inclination i 71.048202 71.0128
Right Ascension of the Ascending Node aW 211.28377 215.2851
Argument of Perigee w 137.75619 358.8242
Mean Anomaly M 354.97240 1.2824

What does this table tell us about Gauss' method for use in initial orbit determination? What must be remembered here is that we only used three observations to arrive at our answer, so the orbit shape will certainly not be perfect. In order to arrive at a better orbit determination, more data must be collected and all of this data must be included, not just three tracking data points.

The orbit altitude is certainly not correct when compared to the TLE. It is off by nearly 100 km, which in today's standards is "light years away". The orbit period is off by two minutes so if you waited for one entire orbit and tried to detect it again (using the determined orbit elements), you will not detect it until 2 minutes after the predicted time.

The eccentricity of the determined orbit is higher than the TLE's, but it is still nearly circular.

The inclination and ascending node are quite good (as expected) because the orbit plane can easily be determined using two tracking data points. The difference in the R.A. of ascending node is most likely due to precession between the two epoch times and not inaccuracy of the determined orbit element.

There is no doubt that the errors of the argument of perigee and the mean anomaly are due to the inaccuracy of the initial orbit determination. Since the shape of the orbit was not determined accurately, these two values could not be trusted.

The elements generated using this initial orbit determination can be used as an initial guess for more accurate orbit determination methods, such as statistical methods, which will be covered at a later time.

If the satellite has never been tracked before, an initial orbit determination such as this will allow the observer to continue tracking the satellite so that additional tracking data can be collected for more accurate orbit determination.


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Step 15: Comparisons Was Last Modified On September 23, 2013