A critical examination of relativity theories

We give a brief critical examination of the special theory of relativity and a similar Newtonian framework to the first order of the $v\mathrm{/}c$ ratio, focusing on the phenomena of aberration, Fresnel dragging, and the Doppler effect. We will show that both frameworks yield the same equations modeling these phenomena up to first order. We do this at a level understandable to anyone with a working knowledge of calculus so that the underlying ideas do not get lost in abstruse mathematical formulations.