The first integral yields 7cJ0(Q). All other terms vanish due to the symmetrical limits on the integral. The second integral yields All subsequent terms vanish. Hence, Since (r) was previously calculated, it is instructive that the result be verified using the characteristic function. This agrees with the previous results. II. Analysis of Orbital Statistics, Distance from a Satellite to a Reference Sphere At this point we wish to determine the average (or expected) distance of a satellite at some arbitrary point in its orbit, to a sensor placed at some random location on the surface of a sphere, about which the satellite is orbiting. The result could be applied to determining the average slant range distance from a satellite to a randomly located sensor. From the geometric considerations of Fig. 1 we have: since the random variable to be considered here is the location of a sensor on the surface of the sphere, the differential of the random variable is: with 6 in this problem defined as the angle of rotation about the line of measurement r. The expression for I2 can be rewritten as:
RkJQdWJsaXNoZXIy MTU5NjU0Mg==