  The body of work presented here revolves around the investigation of the
existence and nature of extra-solar planetary systems. The fitting of stellar
radial velocity time series data is attempted by constructing a model to
quantify the orbital properties of a star-planetary system. This is achieved
with the Planetary Orbit Fitting Process (POFP). Though specific to the
investigated problem, the POFP is founded on two separate, more general ideas.
One is a Solver producing the gravitational dynamics of a Three-Body system by
integrating its Newtonian equations of motion. The other is an independent
optimisation scheme. Both have been devised using MATLAB. Applying the
optimisation to the Solver results in a realistic Three-Body dynamics that best
describes the radial velocity data under the model-specific
orbital-observational constraints. Combining these aspects also allows for the
study of dynamical instability derived from interaction, which is reaffirmed as
a necessary criterion for evaluating the fit. The validity of POFP solutions
with respect to the observations and other models is discussed in this context.
The underlying generality and fundamental principles demonstrate a larger frame
of operation where problems in Physics and Mathematics can be solved with a
multitude of techniques.
