The meaning and significance of Mach's Principle and its dependence on ideas about relativistic rotating frame theory and the celestial sphere is explained and discussed. Two new relativistic rotation transformations are introduced by using a linear simulation for the rotating disc situation. The accepted formula for centrifugal acceleration in general relativity is then analysed with the use of one of these transformations. It is shown that for this general relativity formula to be valid throughout all space-time there has to be everywhere a local standard of absolutely zero rotation. It is then concluded that the field off all possible space-time null geodesics or photon paths unify the absolute local non-rotation standard throughout space-time. Thus it is suggested that Mach's principle holds in the restricted sense that there is a universal standard of absolute local rotation rate related to the apparent rotation of the celestial sphere. However this apparent rotation is actually the earth's rotation relative to a local mapping of null geodesic endpoints from that time and space distant sphere to the local time in the local zero-rotation environment. A connection of local inertia with the celestial sphere is not found.