these are derived and we know nothing of their apriori statistics. Clearly from these equations, the momentum vector (f) statistics are related to (not independent of) the position vector statistics (r), as opposed to the case in the colliding bullet example. For every r there will be a unique set of r with unique probability density functions so as to satisfy Eqns. 1 a+b. At this point, the problem seems to demand a strictly numerical approach, which will be reviewed next. We start by considering the position vector of each satellite r as some random variable, consisting of the sum of some known mean position r with a random 5r . For a strictly numerical approach the three dimensional space about r is to be divided up into discrete volumes; each volume representing a statistically independent “test” if you will, and having associated with it some vector r; for the average position within the volume, and a probability of the satellite having this value of r . One strategy to partition the volume and to set up the discrete position momentum values over which the probability integration will take place is to establish a lower velocity cut off. The value of velocity less than which amounts to no more than an uncertainty in the initial position is:
RkJQdWJsaXNoZXIy MTU5NjU0Mg==