The prediction of the position of a planet, comet, or any other member of the Solar System, depends upon knowing its orbital elements. The orbit is completely defined by these elements (in the absence of perturbations) and hence the position of the body can be calculated for any moment in the future or the past. Sometimes, however, you may not know the elements, particularly if you have been fortunate enough to have discovered a new comet. In that case, you can measure the position of the comet on at least three separate occasions as far apart as possible and then apply one of a number of methods to deduce the set of elements which are consistent with your observations. Unfortunately, the standard methods are neither particularly easy to apply, nor to understand, so I have adopted a more obvious, if perhaps rather flat-footed, approach to the problem which makes use of the mindless number-crunching ability of a computer.

The method is best understood by first considering a simpler problem in one dimension only. Suppose that we have a mathematical relationship between the variables VO and P such that VO is a function of P i.e. given any value of P we can immediately calculate the value of VO.