It is instructive to look at an example in which we shall compare two search patterns. Pattern 1 will be to search between f<r<f+<5r and Pattern 2 will be to search between r~3r<r<r+dr, where: Assuming the plane of the orbit to be known, the volume function is thus ^(r) = 7tr28h, that is to say, a thin disk. For pattern 1 where ^(r) is the cumulative probability function for density function equation 1.8 (see appendix equation J2). In evaluating the semimajor axis variable factors out, making a function of eccentricity only. Table I shows the value of £ as a function of e for both cases. Examining Table I, one finds search Pattern 1 intrinsically more efficient than search Pattern 2 for virtually all values of e. If we consider the case where the inclination or (if the inclination is not zero) the right ascention of the orbit plane is unknown, the search volume becomes:
RkJQdWJsaXNoZXIy MTU5NjU0Mg==