the cross-section of the search volume is shown in Fig. 3. Comparing Table I to Table II, one finds that when the search volume is r3, there is no such great distinction for favoring Pattern 1 over Pattern 2 (except when e>0.7). In fact, when e<0.5, Pattern 2 appears to be more efficient than Pattern 1. This is a reversal of the proposition advanced by Table I. As a practical example, consider the following situation: a satellite is launched into a circular low earth (LEO) parking orbit at 0° inclination. Ground control loses track of the satellite. It is assumed the upper stage kick motor was activated, and there is further reason to assume the vehicle remained at 0° inclination, with a 12 h period and eccentricity 0.7 (molynia-type). We know nothing else about the final orbit, and assume all other parameters to be uniformly random. Using finite step-sizes in Jr, the search volumes are a series of concentric rings (viewed from the top, or north pole, down on the equatorial plane). A sample simulation program is listed in Appendix II. The program output indicates that the search pattern which maximizes the probability of detection per unit volume searched is one which has the volume upper limit at apogee, and the lower limit at apogee less Jr which for this particular case is 200.66 NM.
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