This thesis investigates the dynamical evolution of systems orbiting within deeper potentials. Initially we use a simple satellite-halo interaction to study the dynamical processes that act on orbiting systems and we compare these results to analytical theory. Deep images of the Centaurus cluster reveal a spectacular arc of diffuse light that stretches for over 100 kpc and yet is just a few kpc wide. We use numerical simulations to show that this feature can be produced by the tidal debris of a spiral galaxy that has been disrupted by the potential of one of the central cD galaxies of the cluster. The evolution of sub-halos is then studied in a cosmological context using high resolution N-body simulations of galactic mass halos that form in a cold dark matter (CDM) simulation. CDM halos form via a complex series of mergers, accretion events and violent relaxation. Halos are non-spherical, have steep singular density profiles and contain many thousands of surviving dark matter substructure clumps. This will lead to several unique signatures for experiments that aim to detect dark matter either indirectly, through particle annihilation, or directly in a laboratory. For the first time it is possible to construct maps of the gamma-ray sky that result from the annihilation of dark matter particles within simulated dark matter halo distributions.

A supernova explosion of a massive star at the end of its life leaves behind a compact object, either a black hole or a neutron star. We study a particular aspect of neutron stars in this project. A neutron star is a fast spinning, extremely dense object with a strong magnetic field. Neutron stars can emit lightbeams from their magnetic poles. For an observer on earth these beams appear as pulses of light. These pulses of light are practically the only way to gather information about neutron stars. We use a model of a neutron star showing how the pulses of radiation would appear from Earth based on a set of chosen parameter values. These parameters contain information regarding the geometry of the neutron star, its mass and radius, as well as some properties related to the way the radiation is emitted. We also use a particle swarm optimization method to fit the simulated pulse to the observed light pulse of the x-ray emitting Centaurus X-3 (Cen X-3) binary system. This is done In order to retrieve information about Cen X-3. Our resulting fits do not converge to a single solution, rather it shows that there are many possible configurations leading to the observed light pulses. This shows that while our model can be used to simulate the behavior of neutron stars it requires further development if one wishes to obtain reliable parameter estimates.