Gravitational Waves from Slow Motion Binary Systems

Abstract: In this thesis we study gravitational waves in the domain of linearised general relativity. Wepresent the fundamental ideas and theory of general relativity, then, using the traditionalmeans of quadrupole approximation, we derive an expression for the power radiated as gravitationalwaves in a binary system. We limit ourselves to binary systems in the Newtonianlimit, and can therefore use Kepler’s laws in our calculations. We then use the derived expressionto explicitly predict the power radiated by the Sun-planet systems in our solar systemspecifically, regarding each system as a binary consisting of the planet and the Sun. Finally,we calculate the resulting orbital decay and find an expression for the time it would take forthe bodies to come into contact if gravitational radiation were the only means by which thesystem lost energy. As expected, the power radiated by gravitational waves is found to bevery small for systems in the Newtonian limit, and the corresponding time until impact isfound to be on the order of many times the age of the Universe.