If we were to envelop the orbit within a sphere of radius 7? and find average distances (which would have application to finding the average distance between a satellite and a deep space sensor located in some randomlv oriented circular orbit) we would find the limits on I change to and then finding the average value of I over the whole (inner) orbit: For certain applications it would be of interest to solve for (t) only when the satellite position P is visible from the surface of the snhprp Thp intparanH remains thp samp but the limits of integration on range become The average value for this last quantity could be calculated over the whole orbit using the same techniques as in the previous two examples. III. Analysis of Orbital Statistics, Space Surveillance of a Spherical Surface Considering again the geometry of Fig. 1, we now wish to determine the maximum area in view of a spherical surface from a distance r. The average (or expected) value of the spherical surface in view from a surveillance satellite (measured from nadir to limb) is [8]: It is somewhat remarkable to note that the average area in view is dependent only on the spherical radius (R) and the orbit semi major axis (a). The average area is independent of the orbit eccentricity (e). For many applications (e.g. rotating reflecting space-based radar) measurement from nadir to limb is not possible. There is a minimum off-nadir angle (0O) and a maximum off-nadir angle
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