Obtaining Fractional Fringe Shift in LIGO Type Interferometers using Newtonian Laws of Vector Addition

The LIGO interferometers which are inspired by a setup of Michelson interferometer which consists of a beam splitter, light source, frequency resonators and mirrors as their basic working tools. LIGO-type interferometers which are used to detect gravitational waves are installed in LIGO-Hanford and LIGO-Livingston. Light travelling in the arms of the interferometers should experience a change in time dilation due to uniform rotation of the earth as inertial gravitational forces come into picture. By using Newtonian method of vector addition, we find the path of light with respect to rotation of earth whilst neglecting third-degree order terms of angular velocity of the earth. The change in time of arrival and fractional fringe shift induced in LIGO-type interferometer due to the uniform rotation of the earth is obtained in this paper. A direct relationship between the fractional fringe shift and the angular velocity of the earth is found, and other parameters dependent are arm�s length, latitude of object placed, wavelength of light source and speed of light.