Use of an Artificial Satellite to test the Clock ‘Paradox’ and General Relativity

Abstract

AN interesting and promising test for the effects of gravitation and motion on the relative rates of a satellite clock and an earthbound clock was proposed four years ago by S. F. Singer¹. For this purpose Singer used the Schwarzschild metric for the Earth's field and considered a circular satellite orbit. The neglect of the ellipticity of the Earth has been justified by B. Hoffmann², provided that the mean radius is used. Neglecting also the rotatory motion of the Earth clock Singer found for the red shift of the satellite clock relative to the Earth clock the expression : where R is the radius of the Earth, M its mass, h the height of the satellite above the surface of the Earth, and γ and c have their usual meanings.