A concise, novel description is presented of near-circular satellite motion at arbitrary inclination in resonance with a single dominant tesseral harmonic of a gravitational potential. A practical method is then given for determining the validity of the ideal resonance assumption in specific regions of phase space. The model has been designed to be potentially sufficiently accurate for use in orbit determination yet computationally concise enough for implementation on-board small satellites. Unlike more traditional, mathematically rigorous approaches the orbit description has a relatively simple geometric interpretation making it ideal for use in mission analysis and design. It also facilitates a summary of the factors determining and affecting the nature of resonant motion experienced by satellites. This resonance model is incorporated into a curvilinear relative orbit framework to characterize the effects of tesseral resonance on the relative motion of formations of satellites. The results show that these effects can be the same magnitude as that due to short periodic J2 motion, or secular motion due to small inclination differences for close LEO satellite formations. The analytical relative resonant orbit model also allows the key factors determining the relative resonant motion to be isolated. Finally, the intuitive nature of the resonant orbit model is exploited in two ways. Firstly, the analogy between the non-linear motion of a satellite in resonance to that of a simple pendulum is exploited to develop control strategies for maintaining both spatial and temporal separations between satellites in a resonant formation. Secondly, a simple mission analysis tool is developed to allow orbit analysts to determine whether a given satellite mission could encounter a resonance of significant strength. The output of this software tool is also used to identify the limitations of the resonance model for describing motion about other celestial bodies such as the Moon, Venus and Mars.

I numerically investigate the dynamics of orbits in 3D circumbinary phase-space as a function of binary eccentricity and mass fraction. I find that inclined circumbinary orbits in the elliptically-restricted three-body problem display a nodal libration mechanism in the longitude of the ascending node and in the inclination to the plane of the binary. I analyse and quantify the behaviour of these orbits and investigate their stability over time. This work is the first dynamically aware analysis of the stability of circumbinary orbits across both binary mass fraction and binary eccentricity. This work also has implications for exoplanetary astronomy in the existence and determination of stable orbits around binary systems. I also present an examination of the so-called radio ruff around the microquasar SS433, which I show to precess on a timescale of approximately 550 days. The observed precession in the projected angle of the ruff on the sky may be explained if the ruff feature arises from an inclined circumbinary excretion disk. In addition, I describe a pilot study in the near-infrared waveband in search of circumbinary material around other microquasars.

MSc (Chemistry) / Department of Chemistry

- / -