Conformal gravity was proposed by Weyl shortly after Einstein's discovery of the general theory of relative. However the model remained stagnant for a number of decades. In the late 1980s a number of interesting and physically relevant spherically symmetric solutions were found. These compared well against observational tests with better results than general relativity for the most part. In this work a review is given of the status of conformal gravity with progress and current problems in the first chapter. The next two chapters follow in this tradition of finding new solutions. Here two solutions are found for the cylindrical topology. After this a number of interesting binary system tests are investigated. The first being that of perihelion precession while the second being related to the affect rotation has on the constancy of direction. Called the geodetic and Lense-Thirring effects, when an observer or source orbits of rotates a number of interesting effects are found which may serve as a test of modified gravity. This is followed by a discussion of the main results and their place in the current work going into the work and testing of Weyl conformal gravity.

I graduated in mathematics and physics in 2010 from the University of Malta. Following this I entered the PhD programme directly and spent the next few years studying some of the general to modifications of Einstein's general theory of relativity. In 2014 I graduated from the PhD degree and am now a lecturer at the University of Malta.